COMPIT 2005 in Hamburg - TUHH

!!"
#$% &'()
*
!!!" #$ %
&'&%()$*!
&#+#$&+%&$(
*%+,!!!-,

.
%
-./01$* 2
!"#
3(*&# ,
$% & %'" %
*+#$/$%$ 42
( )
/5+067#0)&8 9
%)
:0; 0:?6$$08 4
-,./.0*' $
@%+0+7AB.0-(& ,4
)1
= (7 4<
'$ $!2 )
*((@0)%$#0''30'& "
-(
@$@0& 9
%) . )$
&#@08#/$0##8#

-0'%/%+0)%$#0--## ,
*! !
-('0'#: ,,
"*, !$$
$-0/+*& ,4
$! !
'$A0&# ,42
& %*,) ( 1"
+@#& , 4
$!*
#0*#:+ ,
2 # #6)/)0(
!= 0@3.= $ ,"
"*('
)0'%@05B ,2,
78989*:7; $ ) ($ ) (
(<
6E$E&@0F7+0-!$&0'+ ,"4
( 5 " 3
/(@#&@+0((= 06(0-:( ,9
)$! 6)( ($
B:%0$#B*B+&B 42
$ * ! -$
G%+B0-0-#B+3 4
) -
:%#0)%$#0-$= + 4,
!/ 0$!')
#&#$ 44<
% ) %%(
&#@ 4 9
2 !$
-3#$0&507##0#(5 4<
( !
;%$@A0&*&# 422
6.$5'5' 1
'
'%@0&G 4"
& %( $"'=
4

*# 49
) ) #
@(5 499
' # % $
F7+0#$@0F06E$E&@0-!$&0'+ 9
6 2)
+ ,<
) & %*,
$% 3
:$0&#00'(*0@'(8
.) )% 3
/+'30@$
$ 2 )
/!AAB0-@H#0);0= # #!$2*!=
( " 3
G%+B0-#B)B
( ))
7B53
63 %+1 %"6 )
/#+# ,,
*'$ ' %'3( 4!
:#53$+0#*0+ 44
807@ "
),1' ' )
$?# "

Impacts of Next Generation Ship Navigation and Communication Systems
Abstract
Martha Grabowski, Le Moyne College, Rensselaer Polytechnic Institute, Syracuse/USA,
grabowsk@lemoyne.edu
Over the past two decades, there have been enormous advances in computing, communications,
network, display and control systems. These advances have resulted in increasingly capable, complex,
and intelligent shipboard and shoreside communications, control and navigation systems. The
interface between intelligent ships and AIS-equipped shore stations is an interesting example of the
challenges faced by ship and technology designers and developers interested in enhancing ship and
human performance as well as the safety of navigation. As increasingly capable ship and shoreside
systems have proliferated, questions have surfaced about the effectiveness, usefulness and usability of
such systems. This paper discusses the promises and pitfalls of current ship and shore-based
advanced technology systems, describes recent empirical work to evaluate the impact of these
technologies on the St. Lawrence Seaway, and provides a vision of future systems with interesting
implications for future mariners.
1. Introduction
Over the past two decades, there have been enormous advances in computing, communications,
network, display and control systems. These advances have resulted in increasingly capable, complex,
and intelligent shipboard and shoreside communications, control and navigation systems. The
interface between increasingly capable ships and AIS-equipped shore stations is an interesting
example of the challenges faced by ship and technology designers and developers interested in
enhancing ship and human performance as well as the safety of navigation.
As increasingly capable ship and shoreside systems have proliferated, questions have surfaced about
the effectiveness, usefulness and usability of such systems. This paper discusses the promises and
pitfalls of current ship and shore-based advanced technology systems, describes one recent study to
evaluate the impact of a new technology on the St. Lawrence Seaway.
2. The Pitfalls of Technology and Automation
New technology is often introduced in systems as a way of improving the system, and human
performance in the system. In marine transportation, a particular accident or incident can be the
catalyst, as the accident may identify circumstances in which human error was seen to be a major
contributing factor. Technology can be designed in an attempt to remove the source of error and
improve system performance, often by automating functions carried out by a human operator. Often
the assumption is made that technology will simplify the operator’s job and reduce errors and costs,
Wickens et al. (1997), p.265.
The available evidence suggests that this assumption is often supported: technology shrinks costs and
reduces or even eliminates certain types of human error. However, technology can also introduce new
human error forms, Wiener (1988), and “automation surprises” can puzzle the operator, Sarter and
Woods (1995). These effects can reduce system efficiency or compromise safety, negating the other
benefits that technology provides. These costs and benefits have been noted especially in the case of
cockpit automation, Wiener (1988), but they also occur in marine transportation as well.
One of the ironies of technology is that automation designed to reduce operator workload sometimes
increases it, Bainbridge (1983, Rochlin (1997). In addition, the introduction of technology can lead to
manual skill deterioration, alteration of workload patterns, poor monitoring, inappropriate responses
to alarms, and reductions in job satisfaction, Wiener and Curry (1980). Problems can arise not only
5

ecause of the technology per se but also because of the way the technology is implemented in
practice. Problems of false alarms from automated alerting systems, automated systems that provide
inadequate feedback to the human operator, Norman (1990), and automation that fails “silently”
without salient indications, fall into this category. Sometimes these problems can be alleviated by
more effective operator training, but not always.
Problems can also arise from unanticipated interactions between technology, human operators, and
other systems in the environment. These can be problems inherent to the technology, as well as to the
technology’s behavior in a larger, more complex system, Tenner (1996). This can be seen in
integrated ship’s bridge systems, where system performance can be determined by the interaction of
multiple sensors, systems, people, and technologies, Grabowski and Roberts (1996), Grabowski and
Sanborn (2001).
The benefits of new technology in marine transportation can include cost savings, more precise
navigation and vessel control, fuel efficiency, all-weather operations, elimination of some error types,
and reduced operator workload during certain phases of the voyage. For instance, some of the benefits
of today’s bridge and navigation systems include improved awareness of hazardous conditions, the
ability to detect risk of collision, elimination of some routine actions that allow the operator to
concentrate on other tasks, and, on some waterways, a reduction in unnecessary verbal
communications on congested voice traffic frequencies.
However, the benefits of new automation and technology in marine transportation are not guaranteed.
In some cases, the economic arguments that initially stimulate investment are clearly reinforced by the
financial return on that investment. On the other hand, technology benefits can also be overcome by
disadvantages or cost. For instance, bridge automation can reduce operator workload during some
voyage phases, but can increase workload in other phases of the voyage, perhaps during arrival or
departure, particularly if the operator is unfamiliar with the technology, Grabowski and Sanborn
(2001). As a result, the anticipated workload reduction benefit of the technology may not be realized.
Thus, there are promises and pitfalls to the introduction of new technology. We can expect that some
of these phenomena will be evident in new technology systems, and we can expect that new promises
and pitfalls will arise as new systems are introduced. We now explore the impact of the introduction
of one such technology, automated identification systems (AIS).
New Technology Introduction: Automated Identification Systems
Automated Identification Systems (AIS), a communications protocol being developed under the aegis
of the International Maritime Organization (IMO), was initially implemented aboard vessels around
the world in 2003. This technology is designed to automatically provide vessel position and other data
to other vessels and shore stations and to facilitate the communication of vessel traffic management
and navigational safety data from designated shore stations to vessels. The onboard "AIS unit"
(which consists of a VHF-FM transceiver, an assembly unit, and a communications transceiver) continuously
and automatically broadcasts identification, location, and other vessel voyage data, and receives
messages from other ships and shore stations, National Research Council (2003).
Many benefits of AIS have been projected. For ship owners, AIS is projected to reduce transit times,
with accompanying lower fuel consumption, improving fleet management. Since arrival times will be
accurately known, better scheduling of passages through locks, minimizing delays, is possible, as pilots,
inspectors, and other shore-based personnel can be dispatched when needed. AIS is also projected
to enhance safety by transmitting precise environmental information to vessels and by transmitting
real-time ship-to-ship communications of course and location of each equipped vessel. AIS is
also projected to enhance traffic management by continuously monitoring vessel location and speed in
all weather conditions, permitting timely pilot dispatching, timely ship inspections, better speed control,
better scheduling of lockages and vessel tie-ups, and faster response times to accidents and/or incidents,
particularly when hazardous cargoes are involved.
6

However, there is much discussion in the maritime community about the costs and benefits of AIS,
Creech and Ryan (2003), and the effectiveness of AIS displays, National Research Council (2003),
particularly in the wake of collisions that might have been avoided with use of AIS, Darce (2004). As
a result, investigating the impact of AIS is a topic of current research interest. This paper reports on
the impacts of the introduction of AIS in a maritime system that was among the first in the world to
require AIS carriage for commercial vessels transiting its waterways – the St. Lawrence Seaway. The
following sections discuss the hypotheses under investigation, the motivation for the hypotheses, and
the measures, variables and data collection methods used. Results and conclusions from the study are
contained in the final section of this paper.
3. Hypotheses and Measures
Determining the impacts of AIS technology introduction on operator performance and perceptions
was the focus of this study. The hypotheses and measures utilized thus assess how operators perceived
that the AIS system supported them, how adequate the system’s decision support facilities were, how
the technology impacted operator performance, and how operators perceived the utility and/or benefits
of the AIS technology.
Both input-output and process measures are used in this study to assess the impacts of AIS technology
on operator performance. Operators are defined as individuals using the AIS technology on vessels
and in the St. Lawrence Seaway traffic management system; thus, subjects are vessel masters, mates
on watch, and Seaway Traffic Management System (TMS) operators. Hypotheses 1-2 in Table I
consider input-output measures: the performance of the AIS users, and whether users consider more
alternatives in their decision-making. Hypotheses 3-7 consider process measures of and human
reactions to the technology: whether users report lower workloads and stress, greater confidence and
satisfaction, increased effort using the system, greater vigilance and lower fatigue when utilizing the
technology. The operationalizations, dependent variables and data collection methods for each
hypothesis are summarized in Table II.
Table I: Hypotheses
1 AIS-supported operators will show better decision performance than operators not using AIS.
2 AIS-supported operators will consider more alternatives than operators not using AIS.
3a. AIS-supported operators will report lower workload than operators not using AIS.
3b. AIS-supported operators will report lower stress than operators not using AIS.
4a. AIS-supported operators will report greater confidence in the system than operators not using AIS.
4b. AIS-supported operators will report greater satisfaction in the system than operators not using
AIS.
5 AIS-supported operators will show decreased effort in using the system, compared to operators
not using AIS.
6a. AIS-supported operators will report greater monitoring vigilance than operators not using AIS.
6b. AIS-supported operators will report less fatigue than operators not using AIS.
7a. AIS-supported operators will perceive greater decision support capabilities provided by the technology
than operators not using AIS.
7b. AIS-supported operators will perceive greater system benefits than operators not using AIS.
7c. AIS-supported operators will report lower degrees of distraction provided by technology than
operators not using AIS.
7

Table II: Operationalizations and Measurement of Dependent Variables by Hypothesis
Operator Performance Input-Output Assessment Measures
Hypothesis
Dependent
Variable
Variable Operationalization
Hypothesis 1 Operator decision performance
Operator Decision Performance
in:
• Situation Awareness
• Threat Avoidance
• Situation Monitoring
• Voyage Plan Monitoring
Data Collection Method
• Post-transit questionnaire
Hypothesis 2
Hypothesis 3a
Hypothesis 3b
Number of decision alternatives
considered by operators
Operator workload
Operator stress
• Ability to evaluate alternative
avoidance maneuvers
• Vessel and TMS operators’
perceived workload
• Self reported operator stress
• Post-transit questionnaire
• NASA Task Load
Index (TLX) assessment
of subjective
workload
• Post-transit questionnaire
Hypothesis 4a
Operator decision confidence
• Self reported operator confidence
• Post-transit
questionnaire
Hypothesis 4b
Operator satisfaction
• Self reported operator satisfaction
Hypothesis 5 Operator effort • Self reported physical effort
• Self reported mental effort
Hypothesis 6a
Operator vigilance
• Self reported operator vigilance
• Post-transit questionnaire
• Post-transit questionnaire
• NASA TLX
• Post-transit questionnaire
Hypothesis 6b
Operator fatigue
• Self reported operator fatigue
• Post-transit questionnaire
Hypothesis 7a
Hypothesis 7b
Hypothesis 7c
Operator perception of
decision support capabilities
Operator perception of
system benefit
Operator perception of
degree of distraction
• Operator perception of support
provided by technology
for situation awareness
• Operator perception of system
benefit
• Operator perception of degree
of distraction provided
by technology
• Post-transit questionnaire
• Post-transit questionnaire
• Post-transit questionnaire
4. Procedure
Data for the AIS pre-implementation and post-implementation phases were gathered. Baseline data
for the pre-AIS condition were gathered prior to AIS carriage requirement initiation, from May 2002
to December 2002. Data were collected in the form of a survey that was administered to the subjects.
The survey consisted of a questionnaire and a workload index survey. The questionnaire solicited operator
opinions about the effects of the technology on the operators’ decision performance, satisfaction,
and confidence. For each question, the answers had a range along a seven-point scale, from
“Strongly Agree” to “Strongly Disagree.” In the analysis, “Strongly Disagree” was interpreted to cor-
8

espond to a score greater than or equal to 6 on the 7-point scale. “Strongly Agree” was interpreted to
correspond to a score of less than 3 on the 7-point scale, and “Partially Agree” was interpreted to correspond
to a score of 3 or greater, but less than 6, on the 7-point scale.
The workload index referred to as the NASA (U.S. National Aeronautics and Space Administration)
Task Load Index (TLX) solicited opinions about six factors that contribute to workload when using a
technology, Hart and Staveland (1988). In the NASA TLX, operators were asked to compare which
of two workload factors was dominant when an operator was using either the pre-AIS (existing bridge
technology) or AIS technology. The operator was asked to circle one factor in each pair that was
dominant when the operator was using the technology. Operators were also asked to rate on a scale
from zero to 100 the six factors that contribute to workload in their daily tasks — mental demand,
physical demand, temporal demand, effort, performance, or frustration. These terms were defined for
the operator within the body of the survey.
Data for the post-AIS condition were gathered immediately following AIS carriage requirement initiation,
from May 2003 to August 2003. Thus, subjects were exposed to two technology treatments – one
pre-AIS, and one post-AIS technology – and were queried about their perceptions of the technology.
Data for both conditions were collected aboard participating vessels making vessel transits along the
St. Lawrence Seaway between Montreal and Duluth, Minnesota and from St. Lawrence Seaway Traffic
Management System (TMS) controllers operating the St. Lawrence Seaway Traffic Management
System center in Massena, New York.
4.1. Subjects
Human subjects were bridge watch team members – captains and mates on watch aboard vessels making
transits of the St. Lawrence Seaway during the data collection periods – as well as Seaway Traffic
Management System (TMS) operators at Eisenhower Lock in Massena, New York. Thus, there were
three types of subjects in this study: vessel captains, mates on watch, and TMS operators. Demographic
information such as position, educational qualifications, experience at sea or at the Traffic
Management Center, and familiarity with the technology under study was sought from the subjects. A
total of 48 subjects participated in the study: 21 subjects for the pre-AIS condition, and 27 for the
post-AIS condition. Table III provides the breakdown in types of subjects; Table IV provides information
on the educational background of the respondents. Table V provides other demographic information
such as age and familiarity with the system.
Subject Type
Number of
subjects
Table III: Participation by Subject type
% Participation in
Pre-AIS survey
Number of
subjects
% Participation in
Post-AIS survey
Masters 6 33.32% 18 66.67%
Mates 11 47.63% 5 18.52%
TMS Operators 4 19.05% 4 14.81%
Total 21 27
In the pre-AIS condition, respondents were mostly mates, with 48% of the respondents in the pre-AIS
condition mates, 33% ship captains (masters) and the remaining 19% TMS operators. In the post-AIS
condition, most (67%) of the respondents were ship’s captains; with 19% mates on watch and the remaining
respondents TMS operators.
Table IV: Subjects’ Educational backgrounds
9

Highest degree
received
Number of
subjects
% Participation in
Pre-AIS survey
Number of
subjects
% Participation in
Post-AIS survey
Undergraduate 5 23.81% 7 25.92%
Graduate 4 19.04% 0 0%
Professional
Training
7 33.34% 16 59.26%
Other 5 23.81% 4 14.82%
Total 21 27
In terms of educational background, in the pre-AIS condition, respondents were fairly evenly split,
with 33% of the respondents reporting having received professional training, 23% of respondents reporting
having received an undergraduate degree, and 19% of respondents reporting having received a
graduate degree. This educational background breakdown was echoed in the post-AIS condition, despite
the overwhelming number of ship’s captains in the post-AIS condition response pool. In the
post-AIS condition, almost 60% of the respondents reported receiving professional training, such as a
maritime school or union training course; about 25% reported receiving an undergraduate degree. All
subjects in both treatments were highly experienced, with an average of 23 years of sailing experience
in the pre-AIS condition, and an average of 26 years of sailing experience in the post-AIS condition.
The average age of participating subjects in the pre-AIS condition was about 45 years while that of
those participating in post-AIS was 47 years. Note that the mates were a younger group of subjects,
particularly in the post-AIS group. All the subjects reported a familiarity level of 2.3 to 2.5 out of 7
with the system in use. The familiarity level was measured on a scale of 1 to 7 with 1 being ‘Very
Familiar’ and 7 being ‘Very Unfamiliar’. Table V shows that the TMS operators indicated the highest
level of familiarity with the AIS technology.
4.2. Experimental Design
The experiment was a 3 x 2 design: three types of subjects – Masters (captains), Mates and Traffic
Management System Operators – were exposed to two technology treatments: the pre-AIS condition,
and the post-AIS. AIS transits varied according to the participating vessels’ schedules throughout the
data collection period. Data were captured in form of the questionnaires and workload index surveys
for both technology treatments. Not all transits involved data collection from subjects, and because
the number of respondents was small, the replications in Table VI are also small.
Table V: Participating Subjects’ Demographic Information
Subject Type Pre-AIS Post-AIS
Average Age Familiarity to system Average Age Familiarity to system
Overall 45.71 2.3 47 2.52
Masters 50.33 2.33 50.13 2.88
Mates 41.63 2.36 32 2
TMS
Operators
50 2 49.25 1.33
Table VI: Subjects Exposed to Technology Treatments
10

Type of Subjects Pre- AIS Post-AIS Total
Masters 6 18 24
Mates 11 5 16
TMS Operators 4 4 8
Total 21 27 48
4.3. Method
The hypotheses in Table I consider the performance of AIS users, and whether users considered more
alternatives, reported lower workloads, reported greater confidence and satisfaction, reported requiring
greater effort when using the system, and reported lower fatigue and greater vigilance when using
the AIS. All hypotheses used a post-transit questionnaire, and H3a and H5 utilized the NASA Task
Load Index (TLX) in addition to the post-transit questionnaire.
Hypothesis 1 focuses on operators’ perception of decision performance pre-AIS and post-AIS. Hypothesis
2 focuses on the number of alternatives considered by operators pre- and post-AIS, while
Hypothesis 3 focuses on subject workload and stress associated with the use of the technology. Hypothesis
4 focuses on operators’ decision confidence and satisfaction, and hypothesis 5 assesses operator
effort when using the technology. Hypothesis 6 focuses on operator fatigue and vigilance, and
hypothesis 7 focuses on operator perceptions of the technology, particularly any perceived system
benefits, perceptions of decision support capabilities provided by the technology, and operator perceptions
of the degree of distraction introduced by the technology.
Operator decision performance is an important variable to consider when using technology in a safety
critical system. This dependent variable includes factors such as operator and decision performance
with respect to situation awareness and monitoring, threat avoidance, and voyage plan monitoring.
Each of these factors has been identified as an input towards the operators’ decision performance,
Grabowski and Sanborn (2001). Hence, the post-transit questionnaire set included questions that individually
addressed each of the factors identified above. Operators were asked their opinion about
whether the technology improved their decision performance using the above-identified dependent
variables.
The data were analyzed using Chi-Square tests, which provide the basis for judging whether two
population proportions can be considered equal, and whether the hypothesis of independence between
variables is tenable. In this study, the hypothesis of independence between pre-AIS and post-AIS was
tested, which contradicts H o , and the results of the data analysis will be phrased in terms of accepting
or rejecting the hypothesis of independence; further analysis is then made in terms of supporting or
rejecting H o . Data for overall subjects, and then subjects under each category individually, have been
presented for each variable.
For the Chi-Square test, the p-value is compared to the level of significance to check whether the hypothesis
is accepted or rejected. P-values lower than or closer to the significance level indicate strong
or partial support to the hypothesis. The p-values reported in Table VII are compared with the level of
significance to check the acceptance or rejection of the hypothesis for each of the variables measured
such as situation awareness, threat avoidance, situation monitoring, and voyage plan monitoring.
Operator workload was measured through the NASA TLX metrics scores, Hart and Staveland (1988),
for the pre-AIS and post-AIS periods. The NASA TLX is a subjective workload assessment tool used
to perform subjective workload assessments on operator(s) working with various human-machine systems.
It is a multi dimensional rating procedure that derives an overall workload score based on a
weighted average of ratings on six subscales: Mental Demand, Physical Demand, Temporal Demand,
Performance, Effort and Frustration.
11

The NASA comparison cards and rating scale were performed by each subject and cumulative workload
scores for each were obtained by adding up the results for each of the NASA TLX metrics. The
mean for workload scores was then calculated for the three different types of subjects, as well for subjects
overall.
The Kruskal-Wallis test was used to analyze the workload index. The Kruskal-Wallis test provides a
statistical procedure for testing whether the two populations are identical. In this research, the hypothesis
of identical populations between pre-AIS and post-AIS was tested, which contradicts H?.
The results of the data analysis are thus phrased in terms of accepting or rejecting the hypothesis of
identical population. Further analysis is then be made in terms of supporting or rejecting H o . Data for
overall subjects, and then subjects under each category individually, have been presented for each
variable.
Operator stress was measured by self-reported stress levels provided by the operator in their responses
to the post-transit questionnaire. The question asked the operators whether using a particular technology
was stressful. Operator effort was measured by operators’ self-reported effort in the post-transit
questionnaire, and the effort score in NASA TLX. The first question asked the operator whether the
technology helps reduce physical effort and the second question asked whether the technology help
reduce mental effort in completing their tasks in the questionnaire. The metrics of ‘Effort’ in the
NASA TLX reflect the operators’ perception of the mental and physical effort required to use the system,
Hart and Staveland (1988).
5. Results
Table VII summarizes the findings of the data analysis. The results show a mixed reaction of subjects
toward AIS. On the plus side, subjects reported overall improved voyage plan monitoring (p= 0.038),
greater monitoring vigilance (p=0.049), and greater decision support capabilities when using AIS (p=
0.038). At the same time, overall, more physical effort was required by subjects using AIS (p=0.014).
Thus, overall, subjects found the contribution of AIS to be in voyage plan monitoring, vigilance
monitoring and decision support capabilities, rather than in threat avoidance or situation monitoring.
However, these overall benefits arrive with the cost of increased physical effort. These are important
results for operators, fleets and technology managers deploying AIS.
Interestingly, different subject types reported significantly different results. For instance, Masters
reported that greater physical effort was required when using the AIS (survey p= 0.023, TLX
p=0.208), as well as greater fatigue when using AIS (p= 0.058). Mates, in contrast, did not report the
same results. They reported significantly improved voyage plan monitoring (p=0.039), significantly
reduced workload (p=0.180), and significantly less mental effort required (survey p=0.052, TLX p=
0.371). Finally, TMS Operators reported significantly improved threat avoidance (p=0.028),
significantly reduced workload when using AIS (p=0.564), and significantly improved monitoring
vigilance (p= 0.047).
6. Discussion
This research provides interesting results with respect to early adoption impacts of new AIS
technology introduction. The research analyzes operator feedback of two technology treatments: pre-
AIS and post-AIS. Seven hypotheses were defined to test various dependent variables about operator
technology impacts. Data were collected in the form of a post-transit questionnaire and the NASA
Task Load Index, a workload measurement instrument.
The purpose of the study was to understand and identify the impact of AIS on operator performance in
the early stages of technology adoption—during the first year of AIS introduction. The results show
that overall, operators perceived that AIS contributed by significantly improving voyage plan
monitoring, a critical facet of master, mate and TMS operators’ decision performance.
12

Table VII: Results Summary
H# Hypothesis Findings Supported? P-value
1 AIS-supported operators
will show better decision
performance than
operators not using AIS
Results indicate a partial
support to H1.
Partially
Situation Awareness
Threat Avoidance
Situation Monitoring
Overall, subjects report
that AIS does not improve
situation awareness
Overall, subjects report
that AIS does not improve
threat avoidance; however,
TMS operators indicate
that AIS improves threat
avoidance
AIS does not improve
situation monitoring
No
Partially
No
Overall
p= 0.784
Overall p=0.940
TMS Operator
p= 0.028
Overall p=0.414
Voyage Plan Monitoring
2 AIS-supported operators
will consider more
alternatives than operators
not using AIS
3a
3b
4a
4b
AIS-supported operators
will report lower workload
than operators not using
AIS
AIS-supported operators
will report lower stress
than operators not using
AIS.
AIS-supported operators
will report greater
confidence in the system
than operators not using
AIS
AIS-supported operators
will report greater
satisfaction in the system
than operators not using
AIS
Overall results indicate
that AIS improves Voyage
Plan Monitoring; Mates
report significant
improvement in voyage
plan monitoring
Overall, the subjects’
believe that use of AIS
does not encourage
considering more
alternatives.
Overall, subjects report no
significant change in the
workload. However, Mates
and TMS operators report
a significant reduction in
workload by using AIS.
Overall, the results
indicate that AIS does not
lower stress levels
Overall, results indicate
that using AIS does not
induce greater confidence
in system.
Overall, results indicate
that using AIS does not
enhance operator
satisfaction in the system
Yes
No
Partially
No
No
No
Overall p=0.038
Mates
p= 0.039
Overall
p=0.324
Overall
p= 0.04
Mates
p= 0.180
TMS Operators
p= 0.564
Overall
p=0.375
Overall
p=0.446
Overall
p=0.824
13

H# Hypothesis Findings Supported? P-value
5 AIS-supported operators
Partially
will show decreased effort
in using the system,
compared to operators not
using AIS
6a
6b
7a
7b
7c
AIS-supported operators
will report greater
monitoring vigilance than
operators not using AIS
AIS-supported operators
will report less fatigue
than operators not using
AIS
AIS-supported operators
will perceive greater
decision support
capabilities provided by
the technology than
operators not using AIS
AIS-supported operators
will perceive greater
system benefits than
operators not using AIS
AIS-supported operators
will report lower degrees
of distraction provided by
the technology than
operators not using AIS
Survey analysis shows that
AIS significantly increases
physical effort in all
subjects.
- Masters report
greater
physical effort
required.
- Mates report
lower mental
effort
required.
TLX workload analysis
shows significantly
reduced workload for each
subject type.
- Overall results indicate
that using AIS improves
monitoring vigilance.
- TMS Operators report
significantly improved
monitoring vigilance.
- Overall
results
indicate that
using AIS
does not
reduce fatigue
level.
- Masters report
greater fatigue
using AIS.
Overall results
significantly indicate that
subjects perceive AIS to
provide greater decision
support capabilities.
Overall results indicate
that subjects do not
perceive any significant
system benefit by using
the AIS.
Overall results indicate
that AIS does not provide
lower degree of distraction
than the traditional bridge
equipment.
Yes
No
Yes
No
No
Survey
Overall p=0.014
Masters
p= 0.023
Mates
p= 0.052
TLX
Masters
p= 0.208
Mates
p= 0.371
TMS Operators
p= 0.773
Overall
p=0.049
TMS Operators
p= 0.047
Overall
p= 0.340
Masters
p=0.058
Overall
p=0.038
Overall
p=0.712
Overall
p=0.169
14

AIS was also found to significantly improve monitoring vigilance for all operators, and for traffic
management system (TMS) operators in particular. Finally, AIS was perceived by operators to offer
significant decision support capabilities, particularly in terms of better and more efficient decision
making, in planning the voyage, in situation monitoring, and in reduced mental workload. Each of
these benefits can contribute to improved operator performance.
AIS impacts varied significantly by subject type, suggesting that AIS technology impacted operators
in different ways. Understanding these differences is important for regulators, managers, operators,
and those interested in understanding technology impacts in safety-critical systems. For instance,
TMS operators found that AIS significantly improved their threat avoidance ability, significantly
reduced their workload, and significantly improved their monitoring vigilance. TMS operators are
responsible for monitoring traffic in the channel as well as monitoring the status of each vessel in the
vicinity. Improvement in TMS threat avoidance, monitoring and workload capabilities are thus
important technology impacts.
Mates also reported significantly improved voyage plan monitoring, and significantly reduced
workload and mental effort when using the AIS. Thus, for operators with similar cognitive tasks,
Grabowski and Sanborn (2001), AIS users reported similar benefits.
The same could not be said for operators with more strategic cognitive task responsibilities; i.e.,
vessel masters. Masters using AIS reported significantly more physical effort required, as well as
greater fatigue. Thus, the overall AIS benefits of improved voyage plan monitoring, improved
monitoring vigilance, and improved decision support came at the expense of increased workload and
effort for masters, but decreased workload for mates and TMS operators. These findings are
consistent with earlier findings that identified differential technology impact on vessel operators with
different cognitive task requirements, Grabowski and Sanborn (2001). The findings provide important
insights with respect to technology impacts in safety-critical systems.
However, caution is advised with the use of these findings. First, the overall number of subjects (48)
is low, which limits the statistical strength of these findings. Follow-on work is required to increase
the number of subjects in the study in order to strengthen the statistical validity of the results. In
addition, the number of masters, mates and TMS operators is low, suggesting that more of these types
of subjects are required in follow-on work in order to strengthen the validity of the by-subject
analyses. Finally, no ship’s pilots were involved in this first phase of AIS impact research. Follow-on
studies to study pilot impressions of AIS technology impacts are an important next step.
It is worth noting that this evaluation is an early post-implementation study, conducted immediately
after the introduction of the AIS technology on the Seaway. It is anticipated that results from a later
implementation study of the AIS technology might differ significantly from these early postimplementation
results. This research provides findings from first movers in technology adoption in a
large-scale system. It remains for future work to investigate the generalizability of first mover
findings over the long term. Follow-on surveys for later post-AIS technology impact evaluation are
required in order to develop steady state, mature technology insertion findings.
Finally, these results reflect a relatively homogenous subject pool of well-educated, highly
experienced, middle-aged English-speaking males who were very familiar with the technology under
study. Results with a less homogenous subject pool—with less well educated, less experienced, more
international, less technology-familiar and of varying ages—may provide interesting results and
comparisons. The generalizability of the current findings across demographic, social, cultural and
technology attributes can be established with such cross-comparisons, the topic of future work.
The results of this preliminary assessment suggest that technology contributions and costs can differ
widely among operators in the same safety-critical system. Managers, researchers, regulators and
operators should therefore consider overall costs and benefits, as well as technology impacts on
different types of operators, when deploying new technology in a safety-critical system.
15

References
BAINBRIDGE, L. (1983), Ironies of Automation, Automatica 19, pp.775-779
CREECH, J.A.; RYAN, J.F. (2003), AIS: The Cornerstone of National Security?, J. Navigation (U.K.),
56, pp.31-44.
DARCE, K. (2004), Tracking River Traffic, The New Orleans Times-Picayune, 13 March 2004
GRABOWSKI, M.; ROBERTS, K.H. (1996), Human and organizational error in large-scale
systems, IEEE Transactions on Systems, Man, and Cybernetics 26, pp.2-16
GRABOWSKI, M.; SANBORN, S.D. (2001), Evaluation of Embedded Intelligent Real-Time
Systems, Decision Sciences, 32:1, pp.95-123.
HART, S.; STAVELAND, L. (1998), Development of NASA-TLX (Task Load Index): Results of
Empirical and Theoretical Research, in Hancock, P., Meshkati, N., Human Mental Workload. Elsevier
Science Publishers B.V.
NATIONAL RESEARCH COUNCIL (2003), Shipboard Automatic Identification System Displays:
Meeting the Needs of Mariners, National Academy Press
http://books.nap.edu/html/SR273/SR273.pdf
NORMAN, D.A. (1990), The “Problem” with Automation: Inappropriate Feedback and Interaction,
not “Over-Automation”, Proc. Royal Society B237
ROCHLIN, G. (1997), Trapped in the Net: The Unanticipated Consequences of Computerization,
Princeton University Press
SARTER, N.; WOODS, D.D. (1995), How in the World Did We Ever Get Into That Mode?, Human
Factors 36
TENNER, E. (1996), Why Things Bite Back: Technology and the Revenge of Unintended
Consequences, New York: Alfred A. Knopf
WICKENS, C.D.; MAVOR, A.S.; McGEE, J.P. (editors) (1997), Flight to the Future: Human
Factors in Air Traffic Control. Washington, D.C.: National Academy Press
WIENER, E. L. (1988), Cockpit Automation, In Human Factors in Aviation, E.L. Wiener & D.C.
Nagel (editors). San Diego: Academic Press
WIENER, E.L.; CURRY, R.E. (1980), Flight Deck Automation: Promises and Problems, Ergonomics
23, pp.995-1011
16

Robust Pareto – Optimal Routing of Ships
utilizing Ensemble Weather Forecasts
Jörn Hinnenthal, Technical University Berlin, Berlin/Germany, hinnenthal@ism.tu-berlin.de
Øyvind Saetra, The Norwegian Meteorological Institute, Blindern/Norway, oyvinds@met.no
Abstract
Sophisticated routing of ships establishes a multi-objective, non-linear and constrained optimization
problem. The paper proposes an optimization approach to ship routing on the basis of hydrodynamic
simulation and advanced weather forecast. Response amplitude operators are employed to describe a
ship in waves. The probabilistic ensemble forecast is applied to account for the stochastic behavior of
weather. An elaborated example is given for a container service between Europe (Le Havre) and
North America (New York). A severe weather situation for the North Atlantic is taken into account.
The robustness of the optimization result against weather changes is assessed. A perturbation
approach with respect to a parent route and a B-spline technique to describe the route increase
computational efficiency. The implementations uses a multi-objective genetic algorithm within the
commercial software modeFRONTIER.
1. Introduction
Ship monitoring, routing assistance and decision support became important topics for save and
reliable sea transport. Types of Route optimization regarding weather and sea state can become an
important tool to improve (i) the reliability of sea transport within a transport chain, (ii) comfort and
safety of crew and passengers. In order to provide a meaningful database for a route decision support,
a route optimization tool has to take different opposing objectives into account (e.g. estimated time of
arrival and fuel consumption). Probable weather changes can affect optimized routes, abolish their
advantages or even make them infeasible to sail. The approach presented here applies a stochastic,
multi-objective optimization strategy on ship routing with regard to a deterministic wave forecast.
This serves to provide a database of advantageous Pareto optimum routes. Subsequently the
robustness of the optimization result regarding assumable weather changes is assessed. Therefore, an
ensemble wave forecast generated by the ensemble prediction system of the European Centre for
Medium-Range Weather Forecasts (ECMWF) is utilized. The optimization presented here belongs to
a westbound Atlantic crossing of the Hapag Lloyd panmax container ship ‘CMS Hannover Express’.
2. Deterministic and ensemble wave forecast
Deterministic and ensemble forecast were provided by the ECMWF. They are wave forecasts of a
severe sea condition in the North Atlantic from 20 th to 30 th of January 2002. Data for the significant
wave height H 1/3 , the peak period T P and the wave angle β are given in time steps of 12 hours on a
grid with 1.5° mesh size. While estimated time of arrival (ETA) and fuel consumption (FUEL)
depend on all environmental conditions, accelerations and slamming are primarily influenced by
swell. Swell - i.e., long-crested waves - being the crucial factor, it was decided to focus on this
influence, leaving out wind-sea, current, wind, drift-ice, shallow-water etc. for later and more refined
work.
The deterministic forecast represents one likely development of the sea state but no information about
the probability of its occurrence. In contrast, the operational ensemble prediction system (EPS)
generates a set of 50 forecasts. These ensemble members have an almost equal probability of
occurrence. They are generated by superposing small perturbations to the operational analysis before
launching the forecast calculation. The ensemble spread measures the “differences” between the
ensemble members. It is related to the forecast uncertainty. Small spread indicates low forecast
uncertainty, and vice versa. Generally the uncertainty increases while going further into the forecast,
ECMWF (2002). This characteristic of the ensemble forecast is used to assess the robustness of ship
17

outes against weather changes.
For the seakeeping calculation a continuous wave energy spectrum as a function of the wave
frequency is needed. Therefore the data were associated with the description of a Bretschneider wave
spectrum, Lewis (1998):
2
172.8 ⋅ H 1
⎪⎧
⎪⎫
−5
− 691.2
3
−4
S
ζ
( ω)
=
⋅ω ⋅ exp ⎨ ⋅ ω
4
4 ⎬
(1)
T1
⎪⎩ T1
⎪⎭
T1 = 0. 772 ⋅T p
, transformation of peak to mean period, Journée (2001).
3. Ship responses in waves
Response amplitude operators (RAOs) and response functions for the added resistance due to waves
(RFs) are employed to evaluate the ship performance in waves. Both have been calculated prior to the
optimization by means of the strip theory code SEAWAY, Journée (2001), based on potential theory.
Besides RAOs for the center of gravity motions for all six degrees of freedom and RAOs for the
motions of selected points also relative to the free surface, two different methods are available to
determine the added resistance due to waves: The radiated energy method of Gerritsma and
Beukelman and the integrated pressure method of Boese. Fig.1 shows RAOs of the motion on the
bridge, RAOs of the relative motion at the bow and RFs of the added resistance due to waves as
computed with SEAWAY. The plots serve to illustrate the input to the response simulations within
the route optimization.
The ship responses and numerical results considered within the optimization are:
• RAOs of the translatory motion on the bridge to calculate the loading on the crew by means of
accelerations.
• RAOs of the motion relative to the free surface (for a point on the keel line 10% behind the forward
perpendicular) to assess the slamming probability.
• RFs for the added resistance due to waves (preferably according to the integrated pressure method
which displays a smoother distribution over the wave frequency ω than its radiated energy
counterpart).
Fig.1: RAOs of motion on the bridge, RAOs of the relative motion at the bow and RFs of the added
resistance due to waves
The determination of the calm water resistance is based on a regression analysis of model tests and
full-scale data, following Holtrop and Mennen (1984). The operating point of the propeller is
calculated according to the ITTC (1978) power prediction method, using the characteristic of a
propeller with the same diameter, number of blades, similar pitch and blade area ratio as given in
18

Yasaki (1962). In a final step the fuel consumption and the compliance with the permitted operating
condition is determined in agreement with the project guide available from the producer of the ship's
main engine, MAN B&W (2000).
4. Setting up of the optimization task
Automated optimization is the formal process of finding a good (the best) solution from a set of
feasible alternatives. It requires a complete mathematical problem formulation in terms of objective
functions (what is to be improved), free variables (what shall be consciously changed) and constraints
(what restricts the feasibility). The computation of the ship behavior for a given route and wave
forecast is accomplished in MATLAB modules. For the optimization, these modules are embedded
into the generic optimization environment modeFRONTIER, www.esteco.it. A multi-objective genetic
algorithm (MOGA) was applied to search optimum routes within the sea condition described by the
deterministic forecast.
4.1. Free Variables
To provide free variables for both the spatial and the temporal description of the route, the course and
the velocity profile are expressed as B-splines. An initial course and velocity profile are given (parent
route). Perturbations of the parent route in time and space are realized by superposing Greville-spaced
shift splines to the parent splines. The vertices of the shift splines are controlled by shift parameters
that are taken as the free variables of the optimization task. The velocity perturbation is performed as
a reduction of the design speed of 23 kn. The spatial perturbation provides a shift of maximum 10% of
the arc length of the original parent route to either starboard or portside. Fig.2 presents example routes
as realized with five parameters for the spatial shift. The optimization focuses on the open water part
of the journey. Pilot time and estuary traveling are deliberately left out of the investigation. The
geographical feasibility is checked during the optimization process. A restriction of shift parameters
to avoid land collision, e.g. at Newfoundland, is possible, but not applied here. Investigations showed
that at least 9 free variables to describe the velocity profile and 7 variables to describe the course are
necessary for a sufficient temporal and spatial resolution of the route that correlates to the wave
pattern as well as to the geographical conditions in the North Atlantic.
4.2. Constraints
Fig.2: Parent route, perturbation and investigated area
Constraints are imposed by defining limiting values to the slamming probability (3%) and to lateral
and vertical accelerations (0.2g). Furthermore, the operation point of the main engine has to comply
with the engine characteristics.
19

4.3. Objectives
Two major objectives, the estimated time of arrival (ETA) and the fuel consumption (FUEL), are
taken into account, both of which have to be minimized. Especially in rough weather conditions the
velocity of initial route variants has to be quiet low to avoid infeasibility due to active constraints. The
following objective functions are suited to accelerate the propagation of the initial routes towards
faster route variants within the applied multi-objective optimization method:
Objective
ETA
( ETA − set value ETA) 2
= , (2)
⎛
ETA ⎞
Objective FUEL = weight ⋅ ⎜ FUEL − FUEL ⋅
⎟ . (3)
⎝
set value ETA ⎠
The set value ETA is derived from optimum results at calm water conditions (ETA = 118 hours after
departure, the value matches the estimated duration of a journey as stated in the sailing lists of the
ship operator) The weight assigned to the FUEL objective is 0.05, so as to produce objectives of an
equal magnitude at the biggest deviants of the set value.
4.4. Optimization with modeFRONTIER
For the setup of the optimization task the generic optimization software modeFRONTIER uses a
process flow chart, Fig.3. Initially free variables, used as input parameter of the optimization loop, are
collected in an input file (parameter.txt). Afterwards, an application is started to build the new route
by means of a perturbation of the parent route according to the actual input parameter (makeroute).
Next, the route is evaluated (virtualShip) and results are given back to modeFRONTIER. Finally, the
optimization routine observes the constraints, calculates the objectives and, if necessary, launches a
new investigation.
2
5. Optimization results
Fig.3: modeFRONTIER, process flow chart
Fig.4 shows a result of the MOGA. Each dot represents a feasible route that can be taken into account
for a route decision considering ETA and FUEL.
20

Fig.4: Optimization results
The optimization results build a database that yields information about weather conditions and ship
behavior for many route variants. These can be filtered according individual preferences.
Consequently a more conscious decision can be made about which route to take. Sometimes this will
yield fuel savings for arriving at the desired time. Sometimes this will show which route is still the
best (or least worse) for severe conditions. Typically, two lines (1 + 2) border a solution space. Line
(1) is a Pareto frontier – the set of all solutions for which a single objective cannot be further
improved without deteriorating any other objective. All routes lie above and to the right of the Pareto
frontier. Those variants that are closest to the frontier display low passage time for reasonably low
fuel consumption. Apparently, it is impossible to decrease ETA below certain limits without
impairing FUEL. Line (2) is caused by the fact that longer routes require more fuel. This line cuts off
the Pareto frontier. The ability to push this line to the left, towards faster route variants, strongly
depends on the setup of the optimization and the applied optimization strategy (if not restricted by the
capability of the ship). Area (3) marks the set of initial routes, the start population of the genetic
algorithm. They were randomly generated and have to be at a quiet low speed level to decrease the
number of infeasible routes due to active constraints. Point (4) marks the arrival at calm sea
conditions. Obviously, an arrival on schedule seems impossible within this severe weather situation.
In this case, the optimization result provides useful information about feasible routes and their
properties. The probability of weather changes is neglected so far.
6. Robust assessment
After the optimization, the robustness of routes to weather changes was assessed considering 2000
routes from the optimization result, with ETA between 130h and 150h, near the Pareto frontier. The
characteristics of these routes were evaluated when launching them to the ensemble forecast
members. The different sea conditions cause a spread in fuel consumption or make routes infeasible
due to active constraints. Thus different approaches to assess the robustness of a route are thinkable:
• Relate robustness to the number of ensembles where a route remains feasible
• Relate robustness to a minimum spread in the fuel consumption
• Definitions that take both aspects into account
• Include aspects that account for the gravity of constraint violations….
So far, the first aspect is taken into account. Therefore we do not claim to establish parameters for the
decision support, but to evaluate if the ensemble forecast can be used for a robust assessment within
this optimization approach.
21

Fig.5: Robust assessment (global view (left) and stretched zoom (right))
Fig.5 shows results of the evaluation. The evaluation was conducted in steps of 1 day. For the 5 th day
(120h) the evaluation of the whole routes were taken into account, even if they take longer. The
figures start at the end of day 1. Till then, all routes remain feasible within more than 90% of the
ensemble members. During the second day the feasible route variants decrease drastically. E.g., only
about 20 routes remain feasible in more than 50% of the ensemble forecast members. The next days
show a successive decrease so that finally only 10 routes are left that remain feasible in 50 to 60% of
the forecast members.
Fig.6, optimized route, ETA = 143,5h, fuel consumption 608t
Fig.6 shows the fastest variant of these routes (ETA 143.5h, FUEL 608t). Furthermore, the wave data
of the deterministic forecast are depicted. All wave fields in the figure propagate from west to east.
24 hours after the departure, the ship reaches a strong wave field (upper left picture). Approaching to
this wave field during the second day, this route became infeasible at about 32% of the ensemble
members. Faster route variants, that took course closer to this wave field, mostly went infeasible. A
second wave field, passed northerly, has only minor affects to the route (upper right picture). Here,
the reduced velocity is not necessary within the deterministic forecast, but enables the route to stay
22

feasible within other ensemble members. Shortly before reaching Newfoundland, the velocity has to
be reduced to pass a third wave field (lower left picture). From day 3 to day 5 additional 9% of the
ensemble forecasts rank this route as infeasible. Finally, the route has been assessed as feasible by
59% of the forecast members. Still, the uncertainty of the weather forecast, expressed by the ensemble
spread, is not explicitly considered. In other words, it is not specified if the ensemble caused
infeasibility due to probable weather changes or if the uncertainty of the forecast was the reason for
that. Nevertheless, the characteristics of the graphs in Fig.5 appear plausible. Therefore, the inclusion
of the ensemble prediction weather forecast is a promising approach to assess the robustness of ship
routes against weather changes within a route optimization.
7. Summary and conclusions
Initially the paper provides a brief introduction to the applied wave forecast and the mathematical
model of a ship in waves used within the presented route optimization. A method for the spatial and
temporal generation of route variants based on B-splines was presented. The major advantage of
parametrically modeled route- and velocity profiles lies in the reduced number of free variables. This
enables the application of a multi objective, stochastic algorithm with a reasonable time exposure.
Here, a multi objective genetic algorithm was applied to optimize a ship route with regard to a
deterministic wave forecast (Other strategies, e.g. evolution strategies, might also be considered but
were beyond the scope of this study). The decision making of the navigating officer is supported by
building up a significant amount of information from which the best compromise (Pareto optimum)
can be found in accordance with individual preferences. Subsequent to the optimization, an ensemble
forecast was used to assess the robustness of selected routes against weather changes. For the time
being, the number of ensemble forecasts at which a route remained feasible measured robustness. For
the future, robustness of a route should be included as a further objective to the optimization, to
increase the percentage of feasible route variants. Strategies have to be employed how to handle the
uncertainties of a weather forecast, e.g. by optimizing once a day regarding the course from the
current waypoint to the port of destination. A ratable relation between robustness and benefit is to be
established to provide meaningful results for a decision support.
References
ECMWF (2002), User guide to ECMWF products, http://www.ecmwf.int/products/forecasts
HOFFSCHILDT, M.; BIDLOT, J-R.; HANSEN, B.; JANSSEN, P.A.E.M. (1999), Potential benefit of
ensemble forecast for ship routing, ECMWF Techn. Memo. 287, Internal Report, ECMWF,
Reading/UK
HOLTROP, J.; MENNEN, G.G.J. (1984), An approximate power prediction method, International
Shipbuilding Progress, Vol. 31
ITTC (1978), Performance prediction method for single screw ships, 15 th Int. Towing Tank Conf.,
The Hague
JOURNEÉ, J.M.J. (2001), User and Theoretical Manual of SEAWAY, Rel. 4.19, TU Delft
MAN B&W (2000), K90MC MK6 Project Guide Two-stroke Engines, 5 th Edition, www.manbw.dk
LEWIS, E.V. (Ed.) (1998), Principles of Naval Architecture - Motions in Waves and Controllability,
SNAME, Jersey City
YASAKI, A. (1962), Design diagrams for modern four, five, six and seven-bladed propellers
developed in Japan, 4 th Naval Hydrodynamics Symp.
23

! "
#
!
!! !! "
# $ #% &! #
$ #%%& ' !! $ ! !
! $$ $& $ $$
$& $
$$ ! $!!$!! #!
! $! $ $ !
()*+ ! $ $ !
$, &! ! - - $
! # $ - ! $ ! $
!! $ $ ! $
! ($ +
# .-# & $ )* $ ## ## $
#! ##
' ( #%%) $ / $
) * # 0 # ()*0 + ' $
# ' $ !
! 1 ! $ 2 3 $
# ! $!
4 !! $
5 ( #
$$ +
, $!#- -
# $#-$ !! !!!
$! $# $ !$
$!! !-
# $#-
$!! 67+ ! $ !
( # ! -# ##+ + !! $
!3+ $ !! !

# ! ! $ # $
!!
$!! $#8 # #
! ! &!# 0
! 8 3 $ ! $ !!
8 # ! ! $ $ !
8 1! $!! !
, 8 9 ! $#-
"#$
8 $#-67+$ !!
+! !3+
" %
!! !! "
# $ #% &! #
$ #%%&8! $
# !) $
! # $$ !!
# # ! !!: ! (6+
!! !! $ # # !!
!! # ! !!
# $$ !! !!
$ $ !!
*#++)6 $ ' $
!(6' + !2 # !!
!! #!
$! !!6! $ #%%&
0 ! !!!!
# !! ! # #
!!! ! ! $# !
- & $ & ! , ! -
! ; !!$!!!
$ !! !
$ # $! $. $$
! !! $ ! 8 ! !
$$ ! ' !
!!
0 $ ! 6
! $ #%%& ! $ $ ! $
! (! + # / 0
$ $ #
! # ! $ ! !!
# !! ! $ $

!5! ! !! !<
$ ! ,
$$ #$& $!5 ! $ 6!
- ;#- !!
! $ ! -
""
0 $ ! !!
$$ # # !! ( ! < !
+ ! ' 8 $ $
$ $$! (! + $$
" # #! !
! 0 # !!( +$ !(+
, $ ! !!# !!!! $
#%%& !! $ ! !#
7+ $ # - +# ! -
!! - ! !
# - ! ! $ # - !$
!#! ## & $ )*0
( &! #+# # ##$! ##=!
## ! ! $ ! , &! /. # - 1
##! ! $= ., !
! !! $ ! %- % $
# - ! ! ! - > !
!
$$!!! ! $ $
? ! $ $ ) ,
#%%- ! $ !< $
(?.=*+# !! ( !!!
*8+$ !< $$$
$$
, $ !!# ! ! #
!$) ( +.#%%&.#%%)
# # ! !$ $
( +$ ! )
!!& 1 $ # /1 $
! (!!& /1+#(/1+
$ !# " ! !
$ !! !
# ! # ! $
! !$ ! $
$ ! ! $! ! #
! $$ $ # . !
! ! ! $ ! !
$ $$ ! #
! - ! ! $ &
! $!! ! .
* ##!! - !
9

6 ! #- # !!
$ # ! ! #- # ! #
(& ' ! ! + ! $
! ! $ # $#-#
$!! !$ $
! 6
$( +$ $ ! 2
$ # ! ' ! 2 $
! ! - ! $&
! 2$ #- !
"&
!. # $ $
# - ' ( #%%) $
$$ # #
= !! !
$ *.> *.?! $ ! !& '
(#%%)= !! !!
$#!. &!
, ! !!
' ( #%%) # $ $ )
* # 0 # ()*0 + /
&! # ! ! $ )*0
$$ 6 7+ +
3+ # #
$6+! @- !-$# &!+
! &! @ $
&! 4 ! ! $
$ $ #- !! $
$
$ (6! $+$ !! $ -
$!#$
! ! $
! !8 $
# $ ! , ' $
# ' $ !
># ' ! !&
! 8 1! $ 23$#
! $! 5
#
( +, ! $# $& (
+ ! $ ! ( !+
! $$ &! $ !
! ! ! ' ( ! ! +# $
&
8 7+ !$ !(! ++
$$! $ !()*+
/

& '(
; !# &!$!
? !! 1 ( ! +
!$$'
- ! !! !$
' ' 7 # '
3 '
0 #$ !!
! ' #
' ! 7 !!
'
&! !$ $ $ # ! - ! ! " $ #
$ ! $# -
B 8 $ ! ! $
!! 8 1
B 0 ! ! $ !
$! $ !
! ># # $ $ ! !!
# !# ## &!
B # ! $ $ !2
' ! 7 0 $! ! !$
B
!! 5$ #$ &!!$ ' !#
, $ $
? ' # !$!( #
$!+ ! ! #
. $
&")
0 $ !!! &!$
! $ 8 ! $ #-
)*()*+ & ! !
)*#! -# ##()**C0 +
&" *+
, )**C0 $ ! ! /
$ ( 6!+ ( 6' +0 $ /
( ! + # $ #
! # ( ! + ! &
&"",-
; (D(0+ !$ 0$E7 $#
! $ $# 1 FE7!
!4 !$ !! $
7 ,## ' !# ! - !> ! !
$ ' ! ' ! $ ' *
$
A

!-!$ !0 $& $
6;$)*(*C+0
Variable Type Denotes
1. 0 set set of nodes (customers)
2. set set of arcs (roads)
3. 2 set set of vehicles
4. $ integer total available capacity
5. integer service time at node
6. 1 integer travel time from node to node 1
7. 1 integer cost of using #1
8. integer demand of node
9. time arrival time of vehicle
10. time departure time of vehicle
11. " trinary availability function of node
12. time starttime servicing of node by vehicle
13. 1 binary #1is used by vehicle
### )*! ! 7@
A7@73 $ $$ )*!6
1
1
(7+
∈ 2 (
1+∈
&"&
)* & # ##5!-## ! $
## ! $ (! ! +
! $ (! $ +!
# $ $$ ##$
! -## ##$ $-##
! )*0 !
0 ##$ ! $ "
6
→ I−7F7
H
# ( "
( + = 7+ ( "
( + = −7+ $ -#
# "
( + = F 0 $-#$$
∀ ∈ 6 "
(
+ ≠ F 0 $ $ $ ##
#! !!
; ## $ ! # ## $
$ )* # ## ()*0 + $ #%% , - #
## # F E7 J F F K - DJ E7 E7 K - DJ4 - ; - K # 4 - ; -
! !$ !( !+ !
! !( !+!
&&)
; 340 L IF E7H " ! $ $ )*0 $
#%%# $ !$# 3 0 . #-
># # $ ## $ $ ##
$$$# ##$ ( $#%%+
3 4'(+@(9+(G+@(77+ - $$#%%0 $$
G

$# #! -# ##! $ $
1 #! $(7+
?(+ $ & 2(3+
!2(+
2(1+ - !2(9+
$ ' - 2
(/+ # (
( "
( + = 7+ -#( "
( + = F ++2 '(A+
$ ( # ! $ !+2
' (G+ ! 2 $ (7F+ (77+
&.
& $ #- $# ! $
$ ! $ ! !!& 8
! ! (!
! + & ! ! !! (
& +
5 !! $ # ! !
! 5#%% &! # $#!$$
# $ $!!! $
$ !
$ 2# #
5 #%% # ! $
!

$! $ ! ! !
- $
5!?5* # -$! $$
# $ !$ # $ $!
$# !!( +!$
. '+
, ! $ !! ($ )**C0 +# !!
5 . #%%) 8
! $ # $ ! $ ! 0 ! #
! $ ! 8 $ $
! !$ ! $
. '+
! 8 79$##-
$)*0 !0 &! $
'#%%%! $)*0 #.!
!!6 7+ (M+ .
$2+ ! !!9$$
$ ! !
# # $
! - $ #
! ( ' $ + #
!# $ $ )*0 !
7#%% $ #)*
(M+ M $
M & $M $ !
! $ $ 2$ &! $#
J3/_A91__G7F_K# ! ( +- .
M#- #!! # $ $
# #
# $ $$ !! $ ,
# & #-. (-D7+7 #++8
M!2$
! !
9 ( #+++ ! # (48+ $ )*0 "
$ $$
# # ! $ ! "
! $ ! )*0 # ! < $
$ $
$ ! &!
48! $ ' # $)*0 ># # 48
$ ($$$ ! - +
# $
$!
37

."
!$$& ' $ #
!$& ! $ ( ! # -+$ $$ ! .
#++- ! - $#-
. #++- ! # $
' 0 $ (# # #
' # ! $+
,!# & $!!
& 1 & . !
# $N=;$ $$
# ! >=;
$ !
.&!
0 ! &! !
.&
!$7/ $/!! #3! (7+
/ $ ! $? $#$ -$
!$) 7A@ !!& 7F!
!! / ! !#-
.&"
5 ! ' 0 ! $
! ( + $ $
!
-4! $ $ # ! !
! $
' 7+!:+' :3+ $
$&
/0 ! # ! 6 0 .
! # #!$# #!( OD7+=
( PDFF+ (PDFF7+
! !!$1FF#
#!! $ 71FFF
)0# ! 8 3 $ $
$ $ ! ( + #
! 8 33
% # !! # !! $
1 !6 -Q-$7339&
3

$$& $ #! #
# $ $ # .
#!!
.&&'(
0 # &! &! # / ! (# 3
+/ (! + &! 7# GA
2 &! # 7/ " &! #
=:FF*?#7M"$)=: M;&, &!
?* $G1R $FR
.&.-
,764&! !5 =;.$ +
&!$ !# $N=;$
! # # ' $ ! (
+ &! $(!+
&! ! !$ &!
- # ! $,$ #
! $$4&! 7 !
$ 3 2 &! $ $ G 0 !
33

! &! ! !
$# $8 #
# 0
, !#
# ($! +
! $.# ># !(
&+ ! $$
1
!!! ! .
#%%& . #%%) ? , # &! $
! 0 ! ! # ! 6 (+
$! (+- ' !& !( $ +
! &!6 !+# #! 2 !3+
(1+#$ # !' ! 2 !+#
#! 8 !7+ !! #!
2 !9+ ! !
,6: #$ !
$#! 6!! (85+'
! (S5+!! (8+
0 !$ &! $ # !
!,, !! ( !+ ! # !
$ ! ! &! 8
!$ &!, ' ! ( !+ ' !
' #! !
$$ ! , # ' ! ! $
!# $
!!! !! !( !719,+
! ! ! ( + # N=; $
! ! $ !
! ! >=; ( ,7+ ' $
$$ !
3

2
!! 67+ !( #! -#
##++!! $!3+
!! ! !#$!
! ! # 7+ ## $ !
! -# + ! ! $ !
!! # ## !! !!
!
## !.!! ! $ #
& - ! # # $#-,$
# .! (! ! # & + . ! ( !.
! ! # & + , $ #- # ! $
$$ $!!
# !# !!# $ !
&( $! +
$
#- -M)884=2,M4)>5;C2)54:(FF+..
!8 3A(7+!!7.7A
?5):4T,2:48;4)8M2:48)584)8T285;5=5=285=8,(FF7+
0*: *:( + !8
!! = !!71/.7G3
4"4 (FFF+ 5 6
;C ") ( + !
$4?!8! !!73.1A
4"428=>T(FF3+; 5$8!
,M4)>5;C(FF1+*.
!6 ### - $)
>5="4)M4) T2 M4>)M > (7GGG+
,5)3/!!G/.37A
=?>:5*2)48T2,*4)4),2?584(FF+06
0 ; ( + M 4 ?! ?$
(M4??5.FF+=C$!!9GF.9G9
31

=?>4;;=(7GGA+; ( =*
)54:(7GG3+. 4! T5! ) /7(3+!!31.
333
8?>4), (7GG1+ ) ! ?8.)G19/ ?
0 - $
8?> =2 C4)5* =2 ;44)8 =2 =4;8 =2 =;;4) (FF+
6 ); =;8( +79
4! ?$$ (4?FF+58*!!/11./1G
8?>U;4")M =2 =;;4) 2 =4;8 =2 :4 )C "2 C4)5* =2
;44)8 =2 )4) T2 8?> = (FF3+ 5 !
? -: $
39

!"#$
% %
& '
" '
(
% "# %
( !
" # !
& )* * + "
'"
' % & %
% "
! "# $" % # #
&' ##&()
* # # +
+ *, ! #
#+ ! -# + &'
&( . ! #
/0,&! #&'&( )
##&'&(
! !1
+ # !
+ &'&(##*
+&'&(#+
# . "# +)#+
#!

*+
# ## # ##
# ) 3(4 * 4'5
! ! 6 #
7 # ( $7(% # !
1 # #
!&'&( "#
! ! #!#64'5
! +
) ## #
# ! +
! ) #&'
&( # # ! ' #
&'&() #
! #* #
#
/8,&'&(
# #
• #+ #
&'&(
• +
# ! &'&( !
&&'&( ! #!#
# 7 + 9&# #
## + #
) # #
#+) !
$ % +)
# !
2

,&( !#+9&
#
! # ! 6
# .
!#' # !
/ # ! !+ # +
# #
#
&. # ! #
) ##! &'&(
! #
#" * #
! +,
• !
• ! ##+.!
#+)
• ! !
• # ) $ + %
!
" #
#&'&( # #
7 # ( $7(% 7( # #
! # !
"! #6
# ! # * # + !
75&'&(
; *####
• "-0

@,() ##!
+ )/!+###
.! !++ * *
7 # ( $7(% #+ !
!+)##!#&'&(
7( #"-0

&'C&( * D#
D ! #!1
/>,& #&'&(
6 4'5 "# ! ! &' &(
! ! ##" +
# # * 6
#
"# # ! # * # ##
###) # !
! ## !
## . # &'E&(,
• ##&'
• ! #&'&(#
• #9&# ##
• ## * #+
• #
F # * # #. #
&'E&(,
•
##1$ ++
#+# ! % )#1
!# . $
#. + #%
• "$
! # #1 !
#.+!
• % &'
= #+## GH
G+)#+H+)#+ # +
# *
+ # *
" # + # #
##+++ # !
@0

* , #+
## +# # F
#+ #
! # C #!+C+!
&' &( # +
7 #( #1
!!
&' &( GH /A
& G H +
# # + +
)##
"# &' 5 F
# +) +# #
5"I#
'
5
'
5
9
& "
'
5
&
A
D
P
T
7
&'
'
5
'
5
75
3
/A,& &'&(
"# &(
* ## 7(
# ###
&' #
"#&'# &'
&' # &
6 + # !
# &' # +)
6#&'& " ?&
G9! = "4 H/6 ! #5"I#
&'
@8

,&'C"#5 &
&( # #
5 # !
! ! ##
&( #! &(##
&(#6#&(
) *
#, #+ ) ## #
F) ! &'
#, ! # 6
#, ) #
+ 9&/
# +)#+ +
5
-'F
54'F
D
J' )
D
"#
!
'F
…
….
(
D
5
5
.0
/2,9 &
9
8
@

#, ! +&' #
#+,
•
• I# + $*
# ! % $ 6 +
! % # # #+
• +)
•
• )
•
• # #+
• !# #
6 7(#!#
# ! # &' &(
#&'&(
+
) +
+ # #
5 * . # #
,
•
•
• # !#
• )#
# # # ## * # #
# ' +
)# *
#
#"*##
) * , -
5# + # )
# # -# )!
! )
G H ###
56 + #+ ,
• )
• .
• 6
• ###
• #
•
• $ %
• )
•
@@

) .
#&(#
+ # !
!
+ ) #
#
) # # GH # # )
+
3(4## ## #)
# "#
## +5
# 3(4 # 7
# )
9&# ) 6
# ##
/ !&
& # &'#&(
# ) "!
#*+ &'&(#+ #
. " #+ ! +
"# # # & + #
+ I ## + +
##
! ),
• 5 ) + # #
• " # + 1 #
• ' # + .
• "! # # + . + )
• &! #
• ) # #
• +)#+ !+
• "#"
/ + 0 ( &
#,## + #1
+) #+) -' ##
+) ! #+).
# + ! # J
= )5' #)
+ ##.
5# # 6 +)#+##,
@>

• &#
• =
• F
• #
6#! # ! +
5 ! # ! # # )
= ! ! * #) !
! !+ )
/ !& .1 ! 2&
5 . * ! # )
# # # ,
• = . $! %
• &#
• .
) ! + * ) ;
4 # + #
) #
*
/ # 5+
) # ) ; 4
• #
•
•
• #
) + #)
+ #, %
! " ! # $
)%+
3 + 0
#, ! *#,"
# "# ! #
• & #+
• 5 #
• 5 #
• 7 #
3 " '&
/ # !
+)# + #
## #+ +
#+ # # #,
"# ! ' ! # #
6 # ! # !
* + + !
@A

# # 6 ## #*
# )++
(
-'F
+ 0
( &
+ 0
%
# 5
6
54'F
57'F 5
5
/
'B
+ 0
$
+ 0
K.
6
4
9
.
0
.nc2
/:, D5
3
' ! ## # (# 51
( '## +)#+! !
! # &
#! # #,
# # *!
. # !#
+)#+ # * # * #
!
3 #
##,## *
#! 3(45"$&;% #*
## + ####
# # #
7
! # #
! 6 #
! # !
! # ,
• 9 +? *+
# #
&'&( ++
#*
@

• + #+ # ##
+ # !
#
• &' &' #
#! ! #
# &( +
! &(+ ! #
• + + ##
++ #+
• + ! 1 ##
• "# &(
! #!+#
#
#
F477B("447FB7L-= 5BL-& $8

¨!#"$&%(')*¥*+£¦¨,¥!#%-.§¨¤/"
¢¡¤£¦¥§¥§¨¤¥©¨¤¥©¨¨
02143657198;:77@#ACBED7FC5HGID7JK17@MLN=6BO3QPOR)S93T=T=6DVUXWZY¦[]\&^`_a7bVc¤dOef\&^OcagbVcdVW
U B‚D7P`U }~K€
Ĥ‰v‘ŽT’“†ŒŽ”ˆ •–‰—ˆ,‡X‡gŠ˜’$ˆXo„›šo’OŠœŽ6„4‰ †ŒŽ”’Oˆ$•r‰N‡gžŸÔZZ…6–• ’š›¤’`7Ž”Ô…6+‰vŠ¡†,„?…|‡g†v¢
ƒC„?…Q†‡4ˆ,‡V‰oŠ‹‡gŠ‰Œ†o‰o7Ž6†
Î
h$ì j d`k$lmkoǹ W+lm^`bZk`WVprqmlslm^OtvuEw*tbZxZxzy|{Vk
ŠŒ…6¤§ˆ`Š,…6ž¦¥E§…6)Ž6„4‰¨Š¤†vŽ©‡gžŸÔZ7…Q–• †vŽf‰ª‡«Ž6„4‰¡¬¤‰og­O…6–•—¤®’O¤¯‰v7Ž6†¡Ôg­›†¤„4‰¤ÔŠ°šo’OŠ˜,‰v†;šv’OŠ±ˆ9•X…Q²`‰v Ž”’`Ž”Ôž
£
‰­°†ŒŹ¬µo‰¤$ŽzŽ”’Œ‰vŠvŽ”Ô…Q·¤’`V†ŒŽTŠ˜Ô…67Ž6†v¢¯ƒC„–…s†©…Q†©­X’`+‰&M…6Ž6„§Ž6„4‰Ç¹ £ Ôžº•?’OŠŒ…6Ž6„–¤
¤’`7Ž”Ô…6+‰vŠ¦žŸ’$ˆX­§ˆ`Š˜‰¤…Q7…Q¤…m³
¸‰¼o´7‰o7ŽT…Tˆ`ž&¹½ŹˆX­OŠ˜ˆ`ŽT… £ Š’•XŠˆ`¤¾¤…6–•v¿œ’OŠŽ6„4‰¯À¾‰vžŸ­?‰vŠŒÁ”›‰ˆ?­ Ôž •–’OŠŒ…6Ž6„?¤¾§;Ä?…v„œŠ‰Œ†Œ´4žÄŽ6†…Qň±Æ‰o…Ç•`„–Ž
»
’O²`‰vŠŽ6„4‰†¤„?…ȇ¢É¸+‰¤¤’O+­4ž¦¥E§#…69Ž6„4‰†o‰¤¤’O+­É‡gžŸÔZ7…Q–•¯†vŽf‰ª‡œŽ6„4‰žŸ’$ˆX­`…Q–•·’˜šÉŽ6„V‰°,’O7Ž”Ô…6+‰vŠ,†…s†
­O…Q†ŒŽTŠŒ…¬o´VŽT…T’O
ÊE…Qr•®…67Ž”’¯ˆ?¤¤’`ŕgŽ#Ž6„4‰’,‡+ŽT…6¤§ˆ`žzƉv…Ÿ•O„–ŽÆ­O…s†vŽTŠ,…”¬v´VŽT…’O2Ä–…To„Ëʆ
Š‰ÔžÄ…Ÿ³‚‰­·¬v¥¾„4‰o´4Š,…Q†ŒŽT…†vŽ”’Oˆ$•r‰ŠŒ´4žŸ‰v†ÉŽ”
,’Og,‰oŠ,7…Q–•
¤ˆ`žÇ$ŕžŸˆ`Žf‰¤­2…6Ž6„4‰¨#Š¤†vŽÃ‡gžŸÔZ7…Q–•2†vŽf‰ª‡¢—ƒC„?…s†Ë‰oV†,´4Š‰Œ†®Ž6„rˆ`Ž*Ž6„4‰§†¤„?…ȇ“…s†®’,‡+ŽT…6¤®ÔžQžÄ¥±žÇ’$ˆ?­?‰­
¬’XŽ6„2Ž6„4‰°†¤„?…ȇ½Ì†;žÇ’`–•`…TŽTŹ­O…Q+Ôžz†vŽTŠ˜‰o–•XŽ6„‡4ˆ`ŠÔ¤¯‰$Žf‰vŠ,†§Ô+­ËŽ6„V‰žÇ’•X…s†vŽT…T¯Ê†”‡V‰¤$Ž6†o¢Í‰Œ†”‡+…6Žf‰¾Ž6„4‰žÄ…6¤¾…TŽ”ˆ`ŽT…’OV†
­?‰vž¦§Æ…6Z…TŽT…TÔžCŠ˜‰v†,´4žÄŽ6†ÔŠ˜‰¦‡+Š’O¤…Q†,…6–•?¢
’š°Ž6„V‰¤§’
Ï ¥É+% ;Ð®Ñ ¨&¥
jXÓ t^`q Ó koc¤ÔIxZ^ i k*t j ak&l j dXqmÔ˜tqmÕo^`lmlmn¾ÖIk$lml+Ô˜t j ÖIk${ jXÓ ^¾Õ jXÓ t^`q Ó koc©Ôx7qŸ×zWX×7^Oc¤tqmÕobZlm^Oc¤lmn¾t j ^ ì j qs{‹ck$Ô˜t j Ö&Ôoy
Ò
j ck`Ẁ txZkIl jXÓ dXqŸtbZ{Zq Ó ^`l`Ô˜t˜ck Ó d`tx¾×7^Oc¤^`_®kot˜koc¤ÔÃxZ^ i k©t j akÆt^Op`k Ó q Ó t j Õ jXÓ Ôqm{Vkoc¤^Otq jXÓ yÙck i q j bZÔ
ØZbVc¤txVkoc¤_
j ^`Õ¤xVk$ÔIt j Ô j l i ktx7qmÔ#×Zc j a7lŸk$_ÚÕ j _®×7lŸkot˜k$lŸnarn®Õ j _§×7bVt˜koc¤ÔI{Zqm{ ÓVj tÆÛTbZlŸÜglmlrtxVk Ó bZ_§koc j bZÔ#×Zc,^`ÕvtqmÕo^`l
^O×Z×Zc
Ò j _§×gbVt˜kocÔbV×7× j c¤t½^`lmck$^`{VnkvÝ4qmÔtÔ©Û j c&txVkd`c¤^O×7x7qmÕ{ZqmÔ˜×glm^$ǹ WVtxVk;Õ,xVk$Õp4bVס^ Ó {·txVkt˜c,^ Ó ÔqŸt j Û
qmÔÔ¤bVk$Ôoy
Ó7Ó q Ó d¦c¤k$ÔbZlŸtÔoyÞ&Õvtb7^`lmlŸǹ Ẁ txVk½Ô˜t j Ö½^Od`k¦×7ls^ Ó qmtÔ˜k$lŸÛZxZ^`Ôt j akd`k Ó koc,^Ot˜k${§a–n^&×koc¤Ô jXÓ‹ß ^ÉÔ˜t j ÖI^Od`k
txVk½×7lm^
Ó7Ó kocŒà,yMY¦xVkÉÔqŸáok j ÛKÕ jXÓ t^`q Ó koc¦Ôx7qŸ×7Ô#kvÝ4×Zck$Ô¤Ô˜k${‹q ÓËÓZj _®q Ó ^`l+Ôl j t½Õo^O×7^`ÕoqŸtªn ß Y¦âÆ[ÉàÆq Ó Õvck$^`Ô˜k${‹q Ó txVk
×7lm^
Ó { x7^`Ô;c¤qmÔk Ó {Vc¤^`_¯^OtqmÕo^`lmlŸn¡q Ó txZkËlm^`Ô˜t°ÛQkoÖ(ǹ k$^Oc¤Ôoy2Ùck$Ô˜k Ó tlŸǹ WÃ× j Ô˜te”×7^ Ó _®^EÝre
×7^`Ô˜ttxVckok{Vk$Õo^`{Vk$Ô¾^
i kÔl j t*Õo^O×7^`ÕoqŸtqŸk$Ô&bV×2t j‹ãOä`ä`ä Yâ[WgÔl j t&Õo^O×7^`ÕoqŸtqŸk$Ô*bV×Nt j¡å$æOä`ä`ä Yâ[ç^Ock°{7qmÔÕobZÔÔk${ yIØ j c
ÔxZqm×7Ô©xZ^
jXÓ Ô°txVk¯d`k Ó koc,^Otq jXÓœj Û©^NÔ˜t j ÖI^Od`k‹×7ls^ Ó a–n ^NxrbZ_®^ Ó ak$q Ó dNÔ˜kok$_®Ô;t j ak$Õ j _§k¯_ j ckË^ Ó {
txVk$Ô˜k¯ck$^`Ô
j ck{ZqŸè¯ÕobZlmtoy _
k°×7ck$Ô˜k Ó txVkock°^ Ó koÖê^O×Z×7c j ^`Õ¤x2t j _ j {Vk$l txVkÔ˜t j Ö½^Od`k×glm^ ÓZÓ q Ó d j ÛM^®Õ jXÓ t^`q Ó kocÉÔxZqm×NÕ j _§×7lŸkot˜k$lŸn
é
j _®×7bVt˜koct^Oprq Ó d›q Ó t j Õ jXÓ Ôqm{Zkoc¤^Otq jXÓ a j txÅtxVk2ÔxZqm×zë|Ô®l jXÓ dXqmtbZ{Zq Ó ^`l½Ô˜t˜c¤k Ó d`tx“×7^Oc,^`_§kot˜koc¤Ô^ Ó {
arnÕ
l j dXqmÔtqmÕo^`l ^`Ô˜×k$ÕvtÔoy
ì í ;Ч!¡,¨¤¥©
kËÕ jXÓ Ôqm{Vkoc jXÓ k¯Õ jXÓ t^`q Ó kocÔx7qŸ×œ^ Ó { jXÓ kËckodXq jXÓ WKk`yºdVyâÆbVc j ×k j c°Þ*Ôqm^ j ctxVk¯[î4Þ(ÖqŸtx Ô˜k i koc,^`l
é
j ctÔ¦Ö&xVkock°txZk¾Ôx7qŸ×2Õo^`lmlmÔ$y©ï,yºk`yq ÓNj bZc*_ j {Vk$lWgtxVkÔt j Ö½^Od`k®qmÔ¦×7ls^ ÓZÓ k${·Û j c*^Ô˜×k$ÕoqŸÜ7Õ°ÔxZqŸ×2^ Ó {2Û j c
×
kckodXq jXÓ ð Y¦xVk;Ôx7qŸ×·Õ j _§k$Ô©Û6c j _ñckodXq jXÓ2ò ^ Ó {·^Occ¤q i k$Ô©q Ó txVkÜZc¤ÔtI× j ct j ÛÃckodXq jXÓ·ó WZÕo^`lmlmÔ©^`lsltxVk
jXÓ
j ctÔ j Û+ckodXq jXÓ§ó ^ Ó {§txVk Ó lŸk$^ i k$Ô#txZqsÔÃckodXq jXÓ ^ Ó {§Ô^`qslmÔÃt j ckodXq jXÓ®ô y#õÉbVc#_ j {Vk$l4^`lml j ÖÔÃt j d`k Ó koc,^Ot˜k
×
j ÖI^Od`k×7lm^ Ó k`yºdVyZÛ j c^`lml+txVk× j ctÔ j ÛCc¤kodXq jXÓNó t^Op4q Ó d®q Ó t j ^`ÕoÕ j b Ó t¦txVk;Õo^Ocd j ^`lŸck$^`{Vn jXÓ e”a j ^Oc¤{
^§Ô˜t
Ó Õo^`lmlsq Ó d^OtIÜ7c¤Ô˜t½× j ct j ÛckodXq jXÓ‹ó yY¦xVkÉÔ˜t j ÖI^Od`kÛ j c©ckodXq jXÓó qmÔI×7lm^ Ó7Ó k${Ëq Ó tªÖ j Ôt˜ko×7Ô ð ÞöÜ7c¤Ô˜t
ÖxVk
j ×Ztqs_®qŸáok$ÔItxVk;l jXÓ dXqmtbZ{Zq Ó ^`lgÔ˜t˜ck Ó d`tx‹×g^Oc¤^`_§kot˜koc¤Ô j ÛKtxVk;ÔxZqŸ×CyÞêÔ˜k$Õ jXÓ {·Ô˜t˜ko×N^`ÔÔ¤qŸd Ó Ô½d`c j bV× j Û
Ô˜t˜ko×
jXÓ t^`q Ó koc¤ÔÆt j Õo^Oc¤d j x j lm{ZÔoW?Õ jXÓ Ôqm{Vkoc¤q Ó d;× j ctÔ j ÛK{Vk$Ô˜tq Ó ^Otq jXÓ ^ Ó {ËÔ˜t˜ck Ó d`txlmqm_®qmtÔoyÞ÷_¾bZlŸtqm×7lmqmÕoqŸtªn j Û
Õ
i ^ Ó Õvk ß k`yºdVy;txZktxZqmc¤{2{Zqs_§k Ó Ôq jXÓ2j Û#txVk§ÔxZqm× ß xVk$qŸdXx–t,à,W txVkÕvc¤^ Ó kvefÔ˜×glmqŸtoW
^`Ô˜×k$ÕvtÔÉÖqŸtx2×Zc¤^`ÕvtqmÕo^`lck$lmk
Ó {{Z^ Ó d`koc j bZÔÆd jrj {ZÔ$Wrø ä`ù efÕ jXÓ t^`q Ó koc,ÔoWZÔ˜×k$Õoqm^`l7Õ jXÓ t^`q Ó koc,ÔoWVxZ^OtÕ¤x·Õ j‚i koc¤ÔoWVtxVk i qsÔqŸa7qmlsqŸtfn¾lmq Ó k‚à
ckokoÛ6koc¤Ô½^
xZ^ i k ÓVj t©ǹ kot&a+kok Ó t^Op`k Ó q Ó t j ^`ÕoÕ j b Ó toy½î j ÛT^Oc$W jXÓ lmnÔ˜t^ Ó {Z^Oc¤{ æOä`ù efÕ jXÓ t^`q Ó koc¤Ô*^Ock°Õ jXÓ Ô¤qm{Vkock${ y
ø ã

¡ ¨¤% "Z ¢¡¤£¦¥§¥§¨¤¥© !/
t Ó k$Õvk$ÔÔ^Oc¤qmlmn°krbZqm{ZqmÔt^ Ó t,àÔ˜k$Õvtq jXÓ Ô:¤ ¦ ÖqŸtx/¨ å;¢ ^`ÕoÕ j c¤{7q Ó dt j txVk&l jXÓ dXqŸtbZ{7q Ó ^`l–× j Ô¤qŸtq jXÓ Ô
ßTÓVj
¦ÆÖqŸtx?¨ ä@;¢ W

M
j Ö*à,WZÖIk°xZ^ i k ô N£¦¥¨§© ä y
a
j ck`W7txVkÛ j lsl j Öq Ó d§Õ jXÓ Ô˜t^ Ó tÔ^Ock°{ZkoÜ Ó k${‹Û j c¦k$^`Õ¤x±Ô˜×k$ÕoqŸÜ7Õ j ×Ztqm_¯qŸá$^Otq jXÓ ×Zc j a7lŸk$_·y
ØZbVc¤txVkoc¤_
D N¤©£:¦ Åæ Y x j ls{ZÔoy
ä
YxVk;_®^EÝVqm_b7_ñl j ^`{Zq Ó d§ÖIk$qŸdXx–t j ÛÃk$^`Õ¤x±Ôl j tN ¤©£:¦ q Ó t jXÓ ÔEY¦â[WZÖxVkoc¤k
M
Y¦xVk;Ô¤xZqŸ×zë|Ô½l jXÓ dXqmtbZ{Zq Ó ^`l+Õvk Ó t˜koc j Ûd`c¤^ i qŸtªn

N ¦J 4
N
y"!¾RK1±=6:7D$#)3 € PX:&%('Ã=61?U‚1r=Q>)#Ã3 € U BE3 ~ JzU‚1*#¢:gF¢U‚RK1 € R3+' ð
å
4
¦
y769: € 1rP`U‚36:+F(3 € :98+1–BO=6:7D,#1*#;:¡Y¦xVk‹ak Ó {Zq Ó d±_ j _§k Ó t§^ Ó {HÔxVk$^Oc§Û j c¤ÕvkNq Ó k$^`Õ¤xÅÔ˜k$Õvtq jXÓ ¤¦ W
5
å;¢ _¾bZÔ˜t ÓZj t¦kvÝ4Õvkok${2×koc¤_®qmÔÔ¤qŸa7lŸk*lmqm_®qŸtÔ ð
¨
€ R3+')3 € 3TF¢1*=zJ3T=T3 ~ BO36J4%>:½YxVk;ÔxZqŸ×Cë|Ô½ÖÆk$qŸdXx–t^ Ó {·qmtÔ©a7b j nX^ Ó Õvn·xZ^ i kt j _®^OtÕ¤x ð
øVy"!¾RK1
S ß TÉà N
qŸtx·tx7qmÔ©Õ jXÓ {ZqŸtq jXÓ ^ Ó {£¨ ¢Åß ÔxZqŸ×zë|ÔIa j ÖÉàIÛ j lsl j ÖÔ½Û j c¦txVkÔxVk$^Oc¦Û j c¤Õvk°q Óœßå à 𠤢¡ ä y
é
y"!¾RK1 € RK3+' € D73T= € :gF)1?8+1rF 5g1–14=@:&Y¦xZk°ÔxZqŸ×Cë|Ô©l jXÓ dXqŸtbZ{7q Ó ^`l Õvk Ó t˜koc j ÛMd`c¤^ i qmtfn2^ Ó {2qŸtÔl jXÓ dXqŸtb4e
Y
å;¢ ^OckÉ_®q Ó qm_®qŸáok${ÔbVaKJk$ÕvtÆt j ^`lmlZtxVk&Õ jXÓ Ôt˜c¤^`q Ó tÔdXq i k Ó ^Oa j i k`yØ j cItx7qmÔ#_®q Ó qm_®qŸá$^Otq jXÓ Ẁ txVk
¨
j c¤qŸtxZ_ ß îrk–bZk Ó tqm^`l ÉbZ^`{Vc¤^OtqsÕ*Ùc j d`c¤^`_®_¯q Ó d–à j c¦txVk k$lm{Zkoc˜eNk$^`{2^`lŸd j c¤qŸtxZ_ ÖÆkockbZÔ˜k${ y
î©ÉÙÅ^`lŸd
Y æ
X ¦ j Û
B # .%$'&)(¦$ .51$¡ )*¢ ¤£¦¥¨§(+.0© )0&@( .3*¦* (+* *:$"* I2 (>*)5
j i qm{Vk${ËtxVk*Ô¤xZqŸ×‹Ô^`qmlmÔ jXÓ k i k Ó p`kok$l ß Ö&qŸtx j bVtÆt˜c¤qm_Ëà#txVkÉÔxVk$^Oc½Û j c,Õvk ¤¡ ¦ ^Ot½txVk*× j q Ó t < = ¦ qmÔdXq i k Ó
Ù#c
arn
¤¢¡I¦) 4
N K 4
S ±h?å ¨˜u
ßå à
Ó {‹txVkak Ó {7q Ó d_ j _§k Ó t ô NP¦Ã^Ot¦txVk× j q Ó t

j c,qŸtxZ_ñ^`lŸÖ½^$n4Ô¦Û j b Ó {·^®Ô j lmbVtq jXÓ y
&k$lm{Vkoc˜e2k$^`{2^`lŸd
j ×Ztqm_¯qŸá$^Otq jXÓ ×Zc j a7lmk$_®ÔÛ j ca j tx±txVktfÖ j ^`lŸd j c¤qŸtxZ_¯Ô*^Oc¤k¾Û j c¤_¾bZlm^Ot˜k${±ak$l j Ö°y¥£ j b Ó {Z^Ocn9Õ jXÓ e
Y¦xVk
jXÓ å k Ó Ô¤bVck$Ô*txZ^OttxVk®^`lŸd j c,qŸtxZ_ { j k$Ô ÓVj tÉ×Zc j {ZbZÕvk Ó kodX^Otq i k®ÖIk$qŸdXx–tÔoy¦£ j b Ó {Z^Ocn2Õ jXÓ {7qŸtq jXÓ¨§
{ZqŸtq
Ó ÔbZck$Ô*txZ^OtÉtxVk j ×7tqm_®qŸáok${±ÖIk$qŸdXx?tÉÛ j cÉtxVk§Ô˜k$Õvtq jXÓ ¤¦ W§Ü å¢ qsÔ ÓVj t_ j c¤k¾tx7^ Ó¡æOä© ^Oa j‚i k
k
N X ¦ W+¨ å¢ Û j c&txZk°ÖIk$qŸdXx?t j ÛMtxZqmÔ¦Ôk$Õvtq jXÓ y¦Y¦xZqsÔ¦Õ jXÓ {ZqŸtq jXÓ qmÔck$lŸkve
^ Ó {" *) G
^Ock^Oca7qŸt˜c¤^Oc,qmlŸn®Õ¤x j Ô˜k Ó ×7^Oc,^`_§kot˜koc¤ÔoW
ÖxVkoc¤k¥
J ~,+ 1rP`U®U : : €
æ y
6
X ¦3 ä
0$
4 2#"
jXÓ Û j ctxVkËb7Ô^Od`k j Û©txZk$Ô˜kËtªÖ j {Zq¡ kock Ó t°^`lŸd j c¤qmtxZ_®Ô°qsÔ;kvÝ4×7lm^`q Ó k${›q Ó txVkËÛ j lsl j Öq Ó dVy·Y¦xVk
Y¦xVk¯ck$^`Ô
j c¤qŸtxZ_ Ó kok${7Ô^{7q¡ +koc¤k Ó tqm^OaglŸk j aKJk$Õvtq i k§ÛTb Ó Õvtq jXÓ ^ Ó { {Zq¡ kock Ó tqs^Oa7lŸk¾a j b Ó {Z^OcnNÕ jXÓ {7qŸtq jXÓ
î©ÉÙ÷^`lmd
Ó Õvtq jXÓ Ô$yY¦xVk°^OagÔ j lmbVt˜k i ^`lmbVk°Û6b Ó Õvtq jXÓ qmÔ ÓVj t*{Zq¡ kock Ó tqm^Oa7lŸk`yYxVk;a j b Ó {Z^Oc¤nËÕ jXÓ {Zqmtq jXÓ ë|Y¦xVk;Ô¤xZqŸ×
ÛTb
jXÓ k i k Ó p`kok$l”ëZxZ^`{t j a+kq Ó t˜kod`c¤^Ot˜k${·q Ó txVk j a J˜k$Õvtq i kÛTb Ó Õvtq jXÓ q Ó txVk &k$lm{Vkoc˜e2k$^`{·^`lŸd j c¤qmtxZ_·W
Ô^`qmlsÔ
j b Ó {§txZ^OtÆqmt#ÖI^`ÔIqm_§× j ÔÔ¤qŸa7lŸk½t j p`koko׋qŸtI^`Ô#a j b Ó {Z^Oc¤n¾Õ jXÓ {7qŸtq jXÓ yÃØ j cItxVk$Ô˜k*ck$^`Ô jXÓ ÔtxVk
ak$Õo^`bZÔ˜k&ÖÆk&Û
×Ztqm_¯qŸá$^Otq jXÓ ×7c j a7lŸk$_®ÔCl j–j p{Zq¢ +kock Ó toyÃY¦xVk^`{ i ^ Ó t^Od`k j Û4txVk©î©ÉÙ±^`lŸd j c¤qŸtx7_ j i kocÃtxVk k$ls{Vkoc˜e2k$^`{
j
j c¤qmtxZ_ qmÔ¦txVk°× j ÔÔqma7qmlmqŸtªn j ÛMÛ j c¤_b7lm^Otq Ó d§a j b Ó {7^OcnÕ jXÓ {ZqŸtq jXÓ Ô$yÆï Ó txVkEk$ls{Vkoc˜e2k$^`{2^`lŸd j c¤qmtxZ_
^`lŸd
ÓVj t©× j ÔÔqŸa7lmk`yY¦xZka j b Ó {Z^Ocn¯Õ jXÓ {ZqŸtq jXÓ Ô½xZ^ i k°t j akÛ j c¤_b7lm^Ot˜k${·q Ó {Zqmck$ÕvtlŸǹ W4txZ^Ot¦_§k$^ Ó Ô¦n j b
txZqmÔ©qsÔ
i kt j Ö¦c¤qŸt˜kÉ^ ÓVj txVkoc¦×7c j d`c¤^`_-dXq i q Ó dÕvkoct^`q Ó ×7^Oc,^`_§kot˜koc¤Ô½t j txVk &k$lm{Vkoc˜e2k$^`{·^`lŸd j c¤qŸtx7_ñÔ j txZ^Ot
xZ^
j _§k j Û©txVka j b Ó {Z^Ocn Õ jXÓ {7qŸtq jXÓ Ô;^Oc¤k_§kotoyœî j _§k j txVkoc¤ÔÕo^ ÓZÓVj t¾ak¯t^Op`k Ó q Ó t j ^`ÕoÕ j b Ó t§q Ó txZqmÔ
Ô
yY¦xZkockoÛ j c¤k¦ÖÆkÜZc¤Ô˜tlmk$^ i ktxZk$Ô˜k&Õ jXÓ {7qŸtq jXÓ Ô j bVtoW4Ô˜t^OctÆtxVk&k$lm{Vkoc˜e2k$^`{¯^`lmd j c¤qŸtxZ_ ^ Ó {§ÖqŸtx¯qŸtÔ
Ö½^$ǹ
ÓVj txVkoc;×7c j d`c¤^`_ Öx7qmÕ¤x _ j {ZqŸÜ7k$Ô&txZk®Ô j lmbVtq jXÓ t j _§kokot°^`lmlÃa j b Ó {7^Ocn2Õ jXÓ {Zqmtq jXÓ Ôoy
ck$Ôb7lŸtÉÖÆk®Ô˜t^Oc¤t°^
i ^ Ó t^Od`k j Û¦txVk2î©Ùç^`lŸd j c¤qŸtxZ_qmÔ¾txZ^Ot§qŸt{ j k$Ô ÓVj t§^`lŸÖ½^$n4Ô§Õ jXÓ?i kocd`k`y¤£Ik$Õo^`bZÔ˜k j Û&txVk
Y¦xVk‹{ZqmÔ¤^`{
j i k_§k Ó tq jXÓ k${2^`{ i ^ Ó t^Od`k j ÛtxZkî©ÉÙ)^`lŸd j c¤qmtxZ_ j i kocÉtxVkEk$ls{Vkoc˜e2k$^`{9^`lŸd j c,qŸtxZ_ ÖIk°Ü7c¤Ô˜t¦t˜cn
^Oa
j Ü Ó {œ^NÔ j lsbVtq jXÓ Öqmtx txVk‹î+ÉÙ«^`lŸd j c,qŸtxZ_·yËïªÛ½txVkockqmÔ ÓVj Õ jXÓ?i kocd`k${Ô j lsbVtq jXÓ ^OÛ6t˜koc¾^2Ô˜×k$ÕoqŸÜZk${
t
j ×Ztqm_®qmá$^Otq jXÓ ÖqŸtx±txVkk$ls{Vkoc˜e2k$^`{œ^`lŸd j c¤qŸtx7_·yØ j c j bVc;ÔÕvk Ó ^Oc¤q j W txVk
tqm_§k§lmqs_®qŸtÖIk§ck$Ô˜t^Oc¤ttxVk
txVkck$Õ j _®_§k Ó {Zk${ i ^`lmbVk .
^ Ó t&Û j c*txVk°Ô˜k$Õ jXÓ {2×7ls^ ÓZÓ q Ó d§Ô˜t˜ko× ð é qŸtx j bVt&txZqmÔ¦Õ jXÓ {ZqŸtq jXÓ txZk j ×Ztqm_¯qŸá$^Otq jXÓ _¯qŸdXx?tdXq i k°ÖIk$qŸdXx–tÔ
i
Ó Ô j _§kÔ˜k$Õvtq jXÓ ÔÉÕol j Ôk¾t j txVk_®^EÝVqm_¾bZ_ ×koc¤_¯qmÔÔqŸaglŸkÉÖÆk$qŸdXx–tÔÉÛ j c&txVk$ÔkÔk$Õvtq jXÓ ÔoyÉï ÛMtxVkock§^Ock ÓVj t
q
ÓVj bVdXx xZk$^ i n±Õ jXÓ t^`q Ó koc¤Ô;t j Ô˜t j Ö;WKqŸtqmÔqm_§× j ÔÔqma7lŸk;t j ck$^`lsqŸáoktxVk j ×Ztqm_®qmáok${9ÖIk$qŸdXx–t;{ZqmÔ˜t˜c,qŸa7bVtq jXÓ y
k
j b Ó {Z^Ocn§Õ jXÓ {7qŸtq jXÓ k Ó Ô¤bVck$ÔÆtxZ^OtI^ Ó kvÝVÕvkok${Z^ Ó Õvk j Û æOä© j ÛztxZk&ck$Õ j _¯_§k Ó {Vk${ i ^`lsbVk&Û j cItxVk
Y¦xVk&a
j ÛM^§Ô˜k$Õvtq jXÓ ¤¦ W6¨ å¢ { j k$Ô ÓZj t¦lŸk$^`{·t j ^ Ó kvÝVÕvkok${Z^ Ó Õvk j ÛKtxVk_®^EÝ4qs_bZ_(×koc¤_®qsÔÔqŸa7lmk
ÖIk$qŸdXx?t
j ÛKtxZqsÔ¦Ô˜k$Õvtq jXÓ y
ÖIk$qŸdXx?t
j ×7tqm_®qŸá$^Otq jXÓ Õ jXÓ Ôqm{Vkoc,ÔtxVk¯lm^`Ôt× j c¤t j Û½^2ckodXq jXÓ WKak$Õo^`bZÔ˜k§txZqmÔ°qmÔtxVk¯_ j Ô˜t°qm_§× j ct^ Ó t× j ct
Y¦xVk
Ó Õvk*txZk Ó txZk;ÔxZqŸ×‹lŸk$^ i k$Ô¦txZqmÔIckodXq jXÓ ^ Ó {·qmtÔIl jXÓ dXqŸtbZ{Zq Ó ^`l7Ô˜t˜c¤k Ó d`tx‹×7^Oc¤^`_§kot˜koc,Ô¦xZ^ i kt j _®kokot©txVk
Ôq
Ó dtxVkÉl jXÓ d7J j bVc Ó kon jXÓ txVk j Õvk$^ Ó yMï Ó qmtqm^`lmlŸǹ Wr^{Zq¢ +kock Ó tÆ^`lmt˜koc Ó ^Otq i kÉÖ½^`ÔÆt˜k$Ôt˜k${ ð ï Ó k$^`Õ¤x
lmqm_¯qŸtÔ{ZbZc¤q
ÛCtxZk&× j ctÔ ó ¦ W ¨ å;¢ txVk j ×Ztqm_¾bZ_(ÖÆk$qmdXx?t©{ZqmÔt˜c¤qŸa7bVtq jXÓ§j ÛztxVkÕ jXÓ t^`q Ó koc¤Ô½txZ^Ot½ÖIkockÉt j l j ^`{
j
Ó txVkÔ˜k$Õvtq jXÓ Ô j ÛtxZk°ÔxZqŸ×‹Ö½^`Ô&Õo^`lsÕobZlm^Ot˜k${ yYxVkt j t^`lCÖIk$qŸdXx–t j ÛÃtxVk°Õ jXÓ t^`q Ó koc¤Ô&^`lŸck$^`{Vn‹Ô˜t j ÖÆk${±q Ó
q
jXÓ ¤¦ W©¨ å¢ ÖxVk Ó Õo^`lslmq Ó dtxZqmÔ½× j ct©Ö½^`Ô¦t^Op`k Ó q Ó t j ^`ÕoÕ j b Ó toy£½bVt©ÖIk;ck$^`lmqŸáok${NtxZ^Ot
txVk°Ôk$Õvtq
j ×Ztqm_¾bZ_ ÖÆk$qmdXx?tÉ{ZqmÔ˜t˜c,qŸa7bVtq jXÓ Ô¦Õo^`lmÕobZlm^Ot˜k${¡q Ó txZqmÔ&Ö½^$n2ÖIkockq Ó Û6k$^`ÔqŸa7lmk;ÖqŸtx9txVkÕ jXÓ t^`q Ó koc¤ÔÉt j
txVk
j ^`{Vk${ y ak;l
D7=6

æ y
6
X ¦3 ä
© °!M&¥Ð ¢¡¤£¦¥§¥§¨¤¥© !/
Y ø
0
4 2"
2§¦ 0 <

j ct j ÛztxVkÕ jXÓ Ôqs{Vkock${ËckodXq jXÓ ð¡ ;ÓZj Öq Ó d°txVk Ó bZ_°akoc½^ Ó {txVkÉÖÆk$qmdXx?t j ÛztxVk$ÔkÉÕ jXÓ t^`q Ó koc,Ô©^ Ó {
ÜZc¤ÔtÆ×
jXÓ q Ó ÖxZqmÕ,x¡txVkon9^Ock®Ôt j ÖIk${ WCÖIk§p ÓZj ÖçtxVk§ck$_¯^`q Ó q Ó d‹Ôl j tÕo^O×7^`Õoqmtfn ^ Ó {¡txVkck$_®^`q Ó q Ó d
txVk®Ô˜k$Õvtq
j l j ^`{ j ÛMk$^`Õ¤x±Ô˜k$Õvtq jXÓ y¦Y¦xVk°Ô˜t j ÖI^Od`kc¤b7lŸk$Ô¦^OckÕ jXÓ Ô˜t˜c¤b7Õvt˜k${2q Ó txZ^OtÖ½^$nNtx7^Otck$Ô˜t j ÖÔ*^Ock
ÖIk$qŸdXx?t&t
ì j qs{Vk${ yÉõbVc¦×Zc j d`c,^`_ ×Zc j {Zb7Õvk$Ô^Ô˜kot j Û^`{7_®qmÔÔqma7lŸkÔ˜t j Ö½^Od`k§×7lm^ Ó ÔoWZÖxZqsÕ¤x2^Oc¤k°c¤^ Ó p`k${±^`ÕoÕ j c¤{Zq Ó d
^
j txVk¯Û j lml j Öq Ó dNÕvc¤qmt˜koc¤q jXÓ ð Y¦xVk$Ô˜kËck$ÔbZlmtÔ°^OckÕ¤x j Ô˜k Ó ÖxZkock®a j txœtxVkak Ó {Zq Ó d‹_ j _§k Ó t^ Ó {›txVk
t
j c,ÕvkËq Ó k$^`Õ,x Ôk$Õvtq jXÓ›j Û½txVkÔxZqŸ×œq Ó ^`lmlMtxVk¯× j c¤tÔ ó C ó¡j Û½txVkÕobVcck Ó t;ckodXq jXÓ ó ^Ock
ÔxVk$^OcÛ
ÖqŸtx7q Ó txVk×koc¤_®qmÔÔ¤qŸa7lŸk*lmqm_®qŸtÔ ß ^`{ZxZkock Ó Õvk j Ûa j tx ô N£¥§© ¦Ã^ Ó { ¤¢¡¤£¦¥¨§© ¦”à,y
"! ¥I5 £¢ . J(¥¤( $"(+8
k¦akodXq Ó ÖqmtxtxVk©ÜZc¤Ô˜tÃ× j ct ó C j Û j bVcÆÕobVcck Ó tMckodXq jXÓ§ó yMÙ#c¤qm_¯^Oc¤qmlŸn°^`lslrÕ jXÓ t^`q Ó koc,Ô#txZ^Ot#xZ^ i k ó C#^`Ô
é
j ct j ÛÃ{Vk$Ô˜tq Ó ^Otq jXÓ¡ß Ù½õ§¦;àI^Ock;b Ó l j ^`{Vk${ yMÞÛ6t˜kocÖ½^Oc¤{ZÔ©^`lml Õ jXÓ t^`q Ó koc,Ô jXÓ txVkÉnX^Oc¤{·ÖqmtxÔ¤^`_§k
txVk$qŸc©×
j _a7q Ó k${2q Ó·jXÓ k;d`c j bV×zyÆYxVk$Ô˜k;d`c j bZ×7Ô j ÛMÕ jXÓ t^`q Ó koc¤Ô&^OckÔ˜t j ÖÆk${±q Ó txZk;×7^Oct˜a7^ nrÔ j ÛÃtxVk
ÙIõ¨¦ç^OckÕ
ÓZÓ q Ó d¾Ö&qŸtxNtx j ÔkxZ^ i q Ó d¯txVkÛ6^OctxZk$Ô˜t&Ù½õ§¦ ß Õ j b Ó t˜k${±ÛQc j _ × j ct ó C,à,yY¦xVk;×7c j Õvk${7bVck j Û
ÔxZqm×NakodXq
j–j Ôq Ó d§txVk×7^Oct˜ag^$n·qmÔ½kvÝ4×7lm^`q Ó k${ak$l j Ö;y#Y j ^`Õ¤xZqŸk i k°txVk j ×Ztqm_®^`lÖIk$qŸdXx–t{ZqmÔt˜c¤qŸa7bVtq jXÓ q Ó txVklm^`Ô˜t
Õ¤x
j ct ó Õo^`lmÕobZls^Ot˜k${œq Ó txVk§ÜZc,Ô˜tÉ×7lm^ ÓZÓ q Ó dÔt˜ko×zWztxVk¯Õ jXÓ t^`q Ó koc,Ô;^Ock®t˜ck$^Ot˜k${ {Zq¡ kock Ó tlŸǹ y ß Þ&ÔtxZkock
×
^Ock*txVckok&×7^Oct˜a7^ nrÔ½q Ó k$^`Õ¤x‹Ô˜k$Õvtq jXÓ W4txVk j ×Ztqm_®^`l7ÖÆk$qmdXx?tIÛ j c jXÓ k*×7^Oct˜a7^ n®q Ó Ôk$Õvtq jXÓ ¤ ¦ WR¨
å ¢
qmÔ§Ô˜kot§t j
C
©
j Û*txVk j ×Ztqs_®^`lIÖÆk$qŸdXx–t j Û*txVkNÔ˜k$Õvtq jXÓ ¤§¦ªW:¨/ å¢ y¦à Ò j ^`Ô˜t^`l¦Õ jXÓ t^`q Ó koc¤ÔoWIÖxZqsÕ¤x
jXÓ t^`q Ó koc¤Ô¾txZ^Ot^Ockl j ^`{Vk${ ^ Ó { b Ó l j ^`{Vk${›q Ó ckodXq jXÓ ó W#^Ock‹l j ^`{Vk${—q Ó t j txVk‹Õ¤x j Ô˜k Ó ×7^Oc¤t˜a7^$n
^Ock‹Õ
j qŸtÔ_®^EÝ4qs_bZ_×koc¤_®qmÔ¤ÔqŸa7lŸkÖIk$qŸdXx–toyœY¦xVk‹ÔxZqŸ×zë|ÔÕ j ^`Ô˜t^`l4J j bVc Ó konœq Ó ckodXq jXÓ—ó qmÔ¾txVkÕo^`lslmq Ó d
bV×—t
ÛÉ^`lmlItxVk·× j ctÔ ó C ;ó ^ Ó {txVkN_®^EÝVqm_¾bZ_×koc¤_®qmÔÔ¤qŸa7lŸk®ÖIk$qŸdXx–t§Û j c jXÓ k·×7^Oct˜a7^ n—q Ó Ô˜k$Õvtq jXÓ
j
W)¨¥ å¢ qmÔ;Ô˜kot°t j
C
¤¦ j Û½txVk¯_®^EÝVqm_¾bZ_ ×koc¤_®qsÔÔqŸa7lmk;ÖÆk$qmdXx?t j ÛÆtxVkËÔ˜k$Õvtq jXÓ ¤§¦ªW^`Ô;txVkockË^Ock
©
Ó k$^`Õ¤x¡Ô˜k$Õvtq jXÓ y*â#Ýr× j ct&Õ jXÓ t^`q Ó koc¤ÔoWÖxZqmÕ,x2^OckÕ jXÓ t^`q Ó koc¤Ô*ÖqŸtx9ÙIõ§¦Úq Ó txZk Ó kvÝ4t
txVckok¾×7^Oct˜ag^$n4Ô&q
jXÓ WZ^Ock°l j ^`{Vk${·q Ó t j txVkÕ¤x j Ô˜k Ó ×7^Oct˜a7^ n‹bZ×·t j ^§Õvkoct^`q Ó t j lmkoc¤^ Ó Õvk i ^`lmbVk ß Ô˜kok°a+k$l j Ö*àI^Oa j i kqŸtÔ
ckodXq
Õo^`lmÕobZls^Ot˜k${ j ×Ztqm_®^`lzÖÆk$qŸdXx–toyY¦xZk×Zc j Õvk${ZbVck j ÛÃÕ¤x jrj Ôq Ó dË^×7^Oct˜a7^ n‹qsÔ ð
y¦é kÔ˜k$^Oc¤Õ,xœÛ j c;tx j Ô˜k®×g^Oct˜a7^$n4Ô;xZ^ i q Ó dN^`lŸck$^`{Vn¡Õ jXÓ t^`q Ó koc¤Ô°Û j c;txZk¯Ô^`_§k®Ù½õ§¦ñ^`ÔtxVk®d`c j bV×
å
ÛÉÕ jXÓ t^`q Ó koc¤Ô§t j l j ^`{ ÓVj Ö°yHïªÛ*_ j ck·txZ^ ÓHjXÓ kNÔbZÕ¤x×g^Oct˜a7^$nHqmÔ¾Û j b Ó {txVk·×g^Oct˜a7^$n j Û*txVk
j
jXÓ Õol j Ô˜k$Ôt©t j txVka j ÖöqmÔ©Õ,x j Ô˜k Ó WZ^`Ô¦ÖÆkÛ j b Ó {‹txZqsÔÆak Ó koÜgÕoqm^`l+Û j c¦txZk*ak Ó {7q Ó d_ j _§k Ó tÔoy
Ôk$Õvtq
ÛCtxZkd`c j bV× j ÛÕ jXÓ t^`q Ó koc,Ô½t j l j ^`{ ÓVj Ö«kvÝ4Õvkok${ZÔ¦ÖÆk$qŸdXx–t j c¦Ôl j t©Õo^O×7^`Õoqmtfn·lmqm_®qmtÔ j ÛKtxVk;Õ¤x j Ôk Ó
ï
× j ÔÔ¤qŸa7lŸk Ó bZ_akoc j ÛÕ jXÓ t^`q Ó koc¤Ô©qmÔ½Ô˜t j ÖÆk${Nq Ó t j txZqmÔÆ×7^Oct˜ag^$n‹^ Ó {txVk Ó
×g^Oct˜a7^$nËtxVk_®^EÝVqm_b7_
j lŸkÉ×Zc j Õvk${ZbZck;^`Ô¦q Ó å à½Ôt^OctÔ^OdX^`q Ó Û j ctxVkck$_®^`q Ó q Ó d§Õ jXÓ t^`q Ó koc¤Ôoy
txZk;Öx
y¦ï Û ÓZj ×7^Oct˜a7^ n—{Vk$Ô¤Õvc¤qŸak${ q Ó÷å à¾qmÔÛ j b Ó {^ Ó { txVk·d`c j bV× j ÛÉÕ jXÓ t^`q Ó koc¤Ô§tx7^Ot®qmÔ¾t j l j ^`{ JbZÔ˜t
æ
Ö jXÓ lŸn®Õ jXÓ Ô¤qmÔ˜tÔ j ÛzkvÝr× j ct½Õ jXÓ t^`q Ó koc¤ÔoW4k$_§×7tfn®×7^Oc¤t˜a7^$n4Ô½^Ock*Ôk$^Oc¤Õ¤xVk${‹Û j c$yÃï ÛC_ j ck*txZ^ ÓËjXÓ k
ÓZj
n°qmÔ^ i ^`qmlm^Oa7lŸk jXÓ k j ÛZtxVkIÛ j lml j Öq Ó dtxVckok½^`lŸt˜koc Ó ^Otq i k$ÔÃqmÔCc,^ Ó { j _®lŸnÕ,x j Ô˜k Ó yÃé qŸtx
k$_®×Ztfn×7^Oct˜a7^
kock Ó t°^`lŸt˜koc Ó ^Otq i k$Ô i ^Ocn4q Ó d2Ôt j Ö½^Od`k×glm^ Ó Ô;^OckËd`k Ó koc¤^Ot˜k${—ÖxVk Ó c¤b ÓZÓ q Ó d‹txVk
txZk$Ô˜k¯txVc¤kokË{Zq¡
j Ö½^Od`k×7ls^ ÓZÓ q Ó dÔ˜k i koc¤^`lCtqm_§k$Ô©Ö&qŸtx‹txVk°Ô^`_®k;q Ó ×7bVt©{Z^Ot^4yÆÞ&_ jXÓ d®tx j Ô˜k°{7q¡ +koc¤k Ó t¦Ô˜t j ÖI^Od`k
Ôt
Ó Ô½txVk;×7ckoÛQkoc¤ck${ jXÓ k°Õo^ Ó ak;Õ,x j Ô˜k Ó _¯^Oprq Ó d®bZÔ˜k j ÛÃ^®{Vk$ÕoqmÔq jXÓ Õvc¤qŸt˜koc¤q jXÓ {Zk$ÔÕvc¤qŸak${ak$l j Ö;y
×glm^
^?à‹YxVkd`c j bV× j ÛÆÕ jXÓ t^`q Ó koc¤Ô*t j l j ^`{ ÓVj ÖqsÔ*Ôt j ÖIk${ q Ó t j ^×7^Oct˜ag^$nNÖqmtx9k ÓZj bVdXx¡Ôl j tÉ^ Ó {
ß
j ctxZqmÔ©d`c j bZ× j ÛMÕ jXÓ t^`q Ó koc¤Ôoy#ï Û_ j ck;txZ^ Ó·jXÓ k°ÔbZÕ,x·×7^Oct˜a7^ n·qmÔ©Û j b Ó {
ÖIk$qŸdXx–tÕo^O×7^`ÕoqŸtªn·Û
jXÓ k*ÖqŸtxËlŸk$^`Ô˜t½Ôl j t½Õo^O×7^`ÕoqŸtªnËqmÔÆÕ¤x j Ô˜k Ó t j p`koko׋×7^Oct˜a7^ nrÔIÖqmtx¯xZqŸdXxZkocIÔl j tÆÕo^O×7^`ÕoqŸtqmk$Ô
txZk
j cÛTbVtbVckd`c j bV×7Ô j ÛÆÕ jXÓ t^`q Ó koc,ÔoyïªÛ ÓVj Ô¤bZÕ¤x±×7^Oct˜ag^$n9qsÔ&Û j b Ó {9txVkd`c j bV× j ÛÕ jXÓ t^`q Ó koc,Ô
Û
i q Ó d‹txVk®xZqmdXxVk$Ô˜tÔl j tÕo^O×7^`ÕoqŸtªn qmÔÕ j _§×7lŸkot˜k$lmn9l j ^`{Vk${ ^ Ó {¡txVk
qsÔÔ˜×7lmqŸtoy¾Y¦xVk×7^Oct˜ag^$n¡xZ^
Ó q Ó d¯Õ jXÓ t^`q Ó koc¤Ô*^Ock¾Ôt j ÖIk${ {ZbVk;t j·æ àÖxVkock°^OdX^`q Ó9jXÓ k j Û#txVk¾txVckok¾^`lŸt˜koc Ó ^Otq i k$Ô
c¤k$_®^`q
^?àfe ß Õ àqmÔ©c,^ Ó { j _®lŸnËÕ¤x j Ô˜k Ó y
ß
a+àYxVkËÖIk$qŸdXx–t j Û&^`lmlÆtxVk·Õ jXÓ t^`q Ó koc¤Ô j ÛtxZkËd`c j bZ×qsÔ¾{7q i qs{Vk${œarnœtxVk‹d`c j bV×Cë|Ô Ó bZ_akoc j Û
ß
jXÓ t^`q Ó koc,ÔoyMØ j c#k$^`Õ¤x®×7^Oct˜a7^ n°txVk rb j tqŸk Ó t j ÛgqŸtÔ j ×Ztqm_¯qŸáok${¾ÖÆk$qŸdXx–t#^ Ó {qŸtÔÃÔl j tMÕo^O×7^`Õoqmtfn
Õ
j ÖÚtxVk®d`c j bV× j Û©Õ jXÓ t^`q Ó koc¤Ô;qmÔ;l j ^`{Vk${ q Ó t j txZ^Ot;×7^Oc¤t˜a7^$n±ÖxVkock§txZk$Ô˜k
qsÔ;Õo^`lmÕobZlm^Ot˜k${zy
tªÖ j2i ^`lmbZk$Ô*^O×7×Zc j ÝVqm_®^Ot˜k$lmn2_®^OtÕ¤xzy°ï ÛtxVkd`c j bV× j ÛIÕ jXÓ t^`q Ó koc¤Ô{ j k$Ô ÓVj tÕ j _§×7lŸkot˜k$lŸn9ÜZt
Y7Y

Ó ^Otq i k$Ô ß ^?àfe ß Õ àqmÔ½c¤^ Ó { j _®lŸnÕ¤x j Ô˜k Ó y
txZk;txVckok;^`lŸt˜koc
Õ à‹YxVkÆd`c j bV× j Û+Õ jXÓ t^`q Ó koc¤ÔÃqmÔÔ˜t j ÖIk${§q Ó t j ^&×7^Oct˜a7^ n°Öqmtx°k ÓVj bZdXxÔl j t^ Ó {¾ÖIk$qŸdXx–tÕo^O×7^`Õoqmtfn
ß
yYxZqmÔc¤bZlŸk©qmÔÃ^O×Z×glmqŸk${qŸÛ ÓZj ×g^Oct˜a7^$nqmÔÃÛ j b Ó {¾arn¾bZÔ¤q Ó d*txVk©c¤bZlŸk$Ô å àÃ^ Ó { æ à,yÃÞ¢×7^Oct˜ag^$nqmÔMÕ¤x j Ôk Ó
5
j ^`{Vk${9arn2Õ jXÓ t^`q Ó koc¤Ô*ÖqŸtx±ÙIõ§¦ÚÛ6^Oc¤txVkoc^$Ö½^$n±txZ^ Ó txZkÙ½õ§¦ j ÛtxVkd`c j bV×
tx7^OtÉqsÔ&^`lŸc¤k$^`{Vn2l
Y¦xVk Ó txZk°Ô^`_§k j ×koc¤^Otq jXÓ Ô©^`Ôq Ó × j ct ó C ^Ock°{ jXÓ k;ÔbZÕoÕvk$ÔÔ¤q i k$lŸn‹q Ó × j ctÔ ó
×koc¤^Otq jXÓ Ô^OdX^`q Ó akodXq ÓZÓ q Ó dÖ&qŸtx‹txVkÜZc¤Ôt©× j c¤toy
j
j Û+txVk¦^`lŸt˜koc Ó ^Otq i k$ÔMq Ó®æ àKÖIk¦^Ock¦^Oa7lŸk½t j d`k Ó koc,^Ot˜kÔ˜k i koc¤^`lZ{7q¡ +koc¤k Ó tMÔ˜t j ÖI^Od`k&×7lm^ Ó ÔÛ j cMtxVk
Þ*Ô#^Éck$ÔbZlmt
Ó t j txZqmÔ×7^Oct˜ag^$n°{ZbZkÆt j txVk½×7^Oct˜a7^ ngë|ÔÃÔl j tÕo^O×7^`Õoqmtfǹ W?txZkÆd`c j bZ×qsÔKÔ˜×glmqŸtK^ Ó {°txZqsÔC×7^Oc¤t˜a7^$n
q
Ó tqŸck$lmn¯l j ^`{Vk${ yMY¦xZk&ck$_¯^`q Ó q Ó d¾Õ jXÓ t^`q Ó koc¤Ô©^OckÔ˜t j ÖÆk${·{ZbZk&t j®æ àÆÖxVkoc¤k*^OdX^`q ÓjXÓ k j Û
qsÔÆk
j c©txZqmÔId`c j bZ× j ÛKÕ jXÓ t^`q Ó koc¤ÔoyMï ÛK_ j ckÉtxZ^ Ó‹jXÓ k j ÛKÔb7Õ¤x‹×7^Oct˜ag^$n4Ô©qmÔIÛ j b Ó {ËtxZk jXÓ kÖqŸtx
Û
j tÆÕo^O×7^`ÕoqŸtfnqmÔÕ,x j Ô˜k Ó yMï Û ÓVj Ô¤bZÕ¤xË×7^Oct˜a7^ n®qmÔ#Û j b Ó {zW–^`lŸt˜koc Ó ^Otq i ka+à#qmÔ^O×7×7lmqŸk${
txZk&lŸk$^`Ô˜t½Ôl
t j Ü Ó {·^§×7^Oc¤t˜a7^$ǹ y
ÛKÕ jXÓ t^`q Ó koc¤ÔIt j l j ^`{ ÓVj Ö;yMï Ó txZqmÔÆÕo^`Ô˜kÉtxVkÉÕ jXÓ t^`q Ó koc¤Ô½^Ock&×koc¤x7^O×7ÔM×7bVt jXÓ t j × j ÛzÕ jXÓ t^`q Ó koc,Ô
j
ÓVj txVkoc°Ù½õ§¦¾yJk i koctxZk$lŸk$ÔÔoWzc¤k$Ô˜t j ÖÔ°^Ock®^ ì j qm{Zk${ ak$Õo^`bZÔ˜k§txVk§Õ jXÓ t^`q Ó koc¤Ô×gbVt jXÓ t j ×
Ö&qŸtx¡^
ÛKtxVk j txVkoc¤Ô©^OckÉk$^Oc¤lsqŸkocIb Ó l j ^`{Vk${ yMY¦xZk*Õ,x j qmÕvk j ÛCtxVkÉ×7^Oc¤t˜a7^$nqmÔ½_®^`{VkÉ^`Ô½Û j lml j ÖÔoyMÙÃ^Oct˜a7^ nrÔ
j
ÖqŸtx Õ jXÓ t^`q Ó koc,Ô;xZ^ i q Ó d·^·Ù½õ§¦ jXÓ k§× j ctÉÛ6^OctxZkoc°^$Ö½^$n txZ^ Ó txZk®ÙIõ§¦ j ÛItxVk
^Oc¤k¯Ô˜k$^Oc¤Õ,xVk${
j bV× j ÛÆÕ jXÓ t^`q Ó koc¤Ô*t j l j ^`{ ÓVj Ö;y*ïªÛ ÓVj ÔbZÕ,x2×g^Oct˜a7^$n4ÔÉ^Ock¾Û j b Ó {2×7^Oc¤t˜a7^$n4Ô*ÖqŸtx2Õ jXÓ t^`q Ó koc,Ô
d`c
j × j c¤tÔ½Û6^OctxZkoc^$Ö½^$nN^Ock;Ôk$^Oc¤Õ¤xVk${zWZkotÕOyÆÙc j Õvkok${7q Ó d§q Ó txZqmÔ½Ö½^$ǹ WgtxVk×7^Oct˜ag^$n4Ô
Ö&qŸtx·ÙIõ§¦]tªÖ
j ^`{Vk${a–nÕ jXÓ t^`q Ó koc¤Ô©xZ^ i q Ó d jXÓ k j ÛKtxVklm^`Ô˜t½× j ctÔ j ÛCtxZkÉÕobZcck Ó tIc¤kodXq jXÓ ^`Ô
tx7^Ot¦^Ock^`lŸck$^`{Vnl
Ó akÉb7Ô˜k${Û j c¦l j ^`{7q Ó d^`lslgtxZk$Ô˜k;Õ j ^`Ô˜t^`lzÕ jXÓ t^`q Ó koc¤Ô©x7^ i q Ó d¾× j c¤tÔ j ÛK{Vk$Ô˜tq Ó ^Otq jXÓ
txZk$qŸc©ÙIõ§¦]Õo^
yMïªÛgtxVk¦d`c j bZ× j Û+Õ jXÓ t^`q Ó koc,Ô{ j k$Ô ÓVj tÕ j _®×7lŸkot˜k$lŸn¾ÜZt#q Ó t j txVkÕ,x j Ô˜k Ó ×g^Oct˜a7^$n{ZbVk©t j qŸtÔ
^`xZk$^`{
j tÕo^O×7^`ÕoqŸtªǹ WgtxZk;d`c j bV×2qsÔ¦Ô˜×7lmqmtoyY¦xVk;Õ,x j Ô˜k Ó ×g^Oct˜a7^$nNqsÔ©k Ó tqmck$lŸn‹l j ^`{Vk${N^ Ó {NtxVk;ck$_®^`q Ó q Ó d
Ô¤l
Õ jXÓ t^`q Ó koc,Ô^Ock°Ôt j ÖIk${2{ZbVkt j 5 à,y
Û ÓVj ×g^Oct˜a7^$nœqsÔÛ j b Ó {œbZÔq Ó d·c¤bZlŸk$Ô å àÉt j 5 àqŸt¾qmÔ Ó k$Õvk$ÔÔ¤^Ocn t j Ô˜t j Öñq Ó t j ×7^Oct˜a7^ nrÔ¾^`lŸck$^`{Vn
øVy¦ï
j ^`{Vk${¯arn®Õ jXÓ t^`q Ó koc¤Ô½xZ^ i q Ó d^¾ÙIõ§¦ö^`xZk$^`{ j Û txZk&d`c j bZ×zë|Ô j ÛzÕ jXÓ t^`q Ó koc,ÔÆ× j ct j Ûz{Vk$Ô˜tq Ó ^Otq jXÓ y
l
j ^`{Zq Ó d®q Ó t j txVk$Ôk;×7^Oct˜a7^ nrÔ&Õo^ Ó Õo^`bZÔ˜k°ck$Ô˜t j Ö&Ô¦ÖxZqsÕ¤x·lŸk$^`{·t j xZqŸdXxVkoc¦Õ j Ô˜tÔ$y
ó y
qŸtxZq Ó txVkË×g^`Õp4q Ó d±c¤bZlŸk$ÔÖÆkt^Op`k·Õo^Ock j Û¦txVk‹_®^EÝVqm_b7_ ×koc¤_®qsÔÔqŸa7lmk¾ak Ó {7q Ó d2_ j _®k Ó t j Û¦k$^`Õ¤x
é
jXÓ ¤¦ªW ¨ å;¢ Ô¤q Ó Õvk‹txZqmÔ§xZ^`{Å^`lŸÖI^ nrÔ®a+kok Ó txZk2Õvc¤qŸtqmÕo^`l rbZ^ Ó tqŸtfnq Ój bVc®Ô¤Õvk Ó ^Oc¤q j y“Y j
Ô˜k$Õvtq
j bVc°×Zc j d`c¤^`_ ×Zc j {Zb7Õvk$Ô^Ot°lŸk$^`Ô˜t jXÓ kËÔ˜t j Ö½^Od`k¯×7ls^ Ó Û j c;k$^`Õ,x›qm_¯^OdXq Ó ^Oa7lŸkÔÕvk Ó ^Oc,q j W
_®^Op`k¯Ô¤bVcktxZ^Ot
j Ö txVk9ak Ó {7q Ó d›_ j _®k Ó tÔ‹q Ó Ô j _§k¡Ô˜k$Õvtq jXÓ Ôt j ak9xZqmdXxVkocËtx7^ Ó txVk _®^EÝVqm_¾bZ_
ÖIk9×Zc,qm_®^Oc¤qmlmn—^`lml
Ó {7q Ó d_ j _§k Ó tÔ j ÛCtxVk$Ô˜k;Ôk$Õvtq jXÓ Ôoy#Y¦xZkockoÛ j c¤k`W4^ Ó ^Oc¤a7qŸt˜c¤^Oc¤qslŸn®Õ¤x j Ôk Ó ×7^Oc¤^`_§kot˜kocÔkotÔ
×koc¤_®qmÔ¤ÔqŸa7lŸk©ak
jXÓ ¤¦ W)¨ å;¢ bZ× t j ÖxZqsÕ¤x¡txVk§ak Ó {Zq Ó d_ j _§k Ó tÔxZ^ i kËt j ak§lŸk$ÔÔ j c;krbZ^`lMt j txVk
txVk¯Ôk$Õvtq
Ó {Zq Ó d*_ j _§k Ó tÔ#Û j cMk$^`Õ,x¯Ô˜k$Õvtq jXÓ yÃÞ)Ô˜k$Õ jXÓ {¯^Oca7qŸt˜c¤^Oc,qmlŸn;Õ¤x j Ô˜k Ó ×7^Oc¤^`_®kot˜koc
_®^EÝVqm_¾bZ_×koc¤_®qmÔÔ¤qŸa7lŸkMak
Ó t^Od`k§txZ^Ot^`lml j Ö&Ô&txZkak Ó {Zq Ó d¯_ j _§k Ó tÔq Ó txVk§Ô˜k$Õvtq jXÓ Ô ¤¦HGIC ; ¤ ›ß qyºk`y Õol j Ô˜kt j
Ô˜kotÔÉtxVk¾×koc¤Õvk
j Ö*à;t j akËxZqmdXxVkoc°txZ^ Ó txVk_®^EÝ4qs_bZ_ ×koc¤_®qmÔÔ¤qŸa7lŸkak Ó {Zq Ó d‹_ j _§k Ó tÔq Ó txVk$Ô˜k‹Ô˜k$Õvtq jXÓ Ô$yNïªÛ
txVkËa
Ó d;txVk*×7^`Õ¤prq Ó d j ×koc¤^Otq jXÓ q Ó txVkÉÔ˜k$Õ jXÓ {‹Ô˜t˜ko×·q Ó ^ Ó nË× j cttxVkÉak Ó {Zq Ó d;_ j _§k Ó t©q Ó ^ Ó n¯Ô˜k$Õvtq jXÓ
{ZbVc,q
Ó txVk i ^`lsbVk°ck$Ô¤bZlŸtq Ó d§Û6c j _ txVkÔ˜k$Õ jXÓ {2×7^Oc,^`_§kot˜koc*{ZkoÜ Ó k${2^Oa j‚i k`W j cÉ^ Ó nNÕ jXÓ t^`q Ó koc,Ô
qmÔd`ck$^Ot˜kocÉtxZ^
ÓZÓVj tak2l j ^`{Vk${ j bVc×Zc j d`c¤^`_ Ô˜t j ×7ÔËqm_®_§k${Zqs^Ot˜k$lŸnHq Ó txZqmÔ¯× j ct¯^ Ó {)Ô˜t^OctÔËtxVk2Ö&x j lŸkN×7^`Õ¤prq Ó d
Õo^
Ó ^Oc¤q j ^`_ jXÓ dtx j Ô˜k^;×7lm^ ÓZÓ kocMÕo^ Ó Õ¤x jrj Ô˜k¦txVk jXÓ kxVk©×ZckoÛ6koc¤ÔoyÃY j _®^Op`ktxZqsÔM{Vk$ÕoqmÔq jXÓ k$^`Ô¤qŸkoc
Ô^`_§k&ÔÕvk
j c;xZqm_ ÖÆk§Ö½^ Ó tt jNj +koc;x7qm_ Ô j _§k®Õvc¤qŸt˜koc,qm^t j ×7qmÕp jXÓ k j ÛtxZk§×7lm^ Ó ÔoyÞ½t;txVk®_ j _§k Ó t jXÓ lŸn jXÓ k
Û
jXÓ WXtxVk©ak Ó {7q Ó dÉ_ j _§k Ó tÕvc¤qŸt˜koc¤q jXÓ WXtxZ^Ot#×gqmÕp4ÔMtxVkÔt j Ö½^Od`k&×7ls^ Ó ÖxVkock©txVka+k Ó {Zq Ó dÉ_ j _§k Ó t
Õvc¤qŸt˜koc,q
Ó k$^`Õ¤x§Ô˜k$Õvtq jXÓ q Ó ^`lsl?txVkI× j ctÔ ó C ;ó qsÔKlŸk$Ô¤ÔKtx7^ Ó txZkI_®^EÝVqm_¾bZ_]×koc¤_®qmÔÔ¤qŸa7lŸkÃak Ó {Zq Ó d_ j _§k Ó t
q
Ó txVkÉ×7^OctqsÕobZlm^Oc½Ô˜k$Õvtq jXÓ WZqmÔ½qm_®×7lŸk$_§k Ó t˜k${ yÃï Ój bVc¦bZ×Ve”t j e ÓVj ÖêÔÕvk Ó ^Oc¤q j ^Ô˜t j ÖI^Od`k×7lm^ Ó _®^Oprq Ó d§bZÔ˜k
q
Û©txVkËa+k Ó {Zq Ó d·_ j _§k Ó tÕvc,qŸt˜koc¤q jXÓ ÖI^`Ô¾^`lŸÖ½^$n4Ô°Û j b Ó { y·Y¦xZk¯{Vk i k$l j ×7_®k Ó t¾^ Ó {›qm_®×7lŸk$_§k Ó t^Otq jXÓ j Û
j
i ^ Ó Õvk·lmqŸp`ktxVkÕvc,^ Ó kvefÔ˜×7lmqmtqmÔ¾×7lm^ Ó7Ó k${ y±ïªÛ ÓZj Ô˜t j ÖI^Od`k2×7lm^ Ó qmÔ
ÛTbVctxVkocÕvc¤qŸt˜koc¤qs^2Öqmtx›×Zc,^`ÕvtqmÕo^`lIck$lŸk
i k Ó ^`Ô&^¯ck$ÔbZlmt©ÖxVk Ó b7Ôq Ó d§txVkak Ó {Zq Ó d§_ j _®k Ó tÉÕvc¤qŸt˜koc¤q jXÓ W j bVc*{Vk i k$l j ×k${Na7^`lslm^`Ô˜te”Ö½^Ot˜koc˜ef_ j {Vk$l
dXq
{Vk$ÔÕvc,qŸak${q Ó txVk Ó kvÝ4t¦Ô˜k$Õvtq jXÓ qmÔ©^O×Z×7lmqmk${ y
Y

t^ Ó p4ÔxZ^ i k®{7q¡ +koc¤k Ó tÉ_®^EÝVqm_b7_‘Üglmlmq Ó d –bZ^ Ó tqŸtqŸk$Ô$W3N§¦ ¥©¨¨¥ W © ¦ W3Ü
å¢ y°Y¦xVkl jXÓ dXqmtbZ{Zq Ó ^`l
Ó t˜koc j ÛId`c¤^ i qŸtfn j ÛItxVk§a7^`lmlm^`Ôte”ÖI^Ot˜koc$W < W ¦ ¥©¨¨¥© © ¦ WKq Ó txVk§t^ Ó p j ÛÆtxVk®Ôk$Õvtq jXÓ ¤¦ WJ¨F å¢ qmÔ
Õvk
j Ôk${¯t j ak*p ÓVj Ö Ó yMï ÛztxVkÉak Ó {Zq Ó d_ j _§k Ó t©q Ó ^Ot¦lŸk$^`Ô˜t jXÓ kÔ˜k$Õvtq jXÓ‹j ÛKtxVkÔ˜t j Ö½^Od`k°×glm^ Ó dXq i k Ó
ÔbV×7×
kok${Vk${zWVÖxVkock;Ô j _®k j ÛKtxZk°Õo^`lmÕobZlm^Ot˜k${N×7^Oc¤^`_§kot˜koc¤Ô&Õ¤xZ^ Ó d`k ð
Ó
j t^`lÖIk$qŸdXx–t/NP¦ j Û¦^±Ô˜k$Õvtq jXÓ ¤¦qmÔ;dXq i k Ó arnœ^ Ó ^`{7{ZqŸtq jXÓ j Û¦qmtÔlmqmdXx?tÔx7qŸ× ÖÆk$qmdXx?t/NPO@Q7¦ WÃtxVk
Y¦xVkËt
X ¦ txZ^Ot¯^Ock2Ôt j ÖIk${¢q Ó txZk2Ô˜k$Õvtq jXÓ ¤ ¦ W½^ Ó {HtxZkNt j t^`l¦ÖIk$qŸdXx–t j Û*txVk
a7^`lmls^`Ô˜te”ÖI^Ot˜koc N¦ ¥¨¨¥© © ¦ ×7bZ_§×k${‹q Ó txVk;t^ Ó p j ÛÃtxZqmÔ©Ôk$Õvtq jXÓ ð
N%¦) N O@Q7¦32 N X ¦32 N§¦ ¥¨¨¥ © ¦
N O@Q7¦ 0 < O@Q7¦”à 2 ß N X ¦ 0

å ¥©¨¨¥ © ¦ 3 ä
æ
yN§¦
¥©¨¨¥ © ¦ N¦ ¥©¨¨¥© W © ¦
yN§¦
¡ !"+ѧ¡˜+"
N
X ¦ Û j c
ÖxVkoc¤k¥ "—^ Ó {¨¦ ) G
^Ock°^Oca7qmt˜c¤^Oc¤qmlŸnËÕ¤x j Ô˜k Ó ×7^Oc¤^`_§kot˜koc,ÔoW
€ J ~,+ 1rP`U®U : :
5 y < ¤¢¡)¦ < ¤¢¡£¥§© ¦

Y ã
Ôx j ÖÔ½txVk;{ZqsÔ˜t˜c¤qŸa7bZtq jXÓ§j ÛtxVkÕ jXÓ t^`q Ó koc¤Ô j i koctxVktxVckokÉ×7^Oct˜ag^$n4Ô j ÛCtxVk;Ô¤xZqŸ×Û j c©txVk;{Zko×7^Oc˜e
ØÃqŸdVy
Ó × j ct*Ô˜k i k Ó W+ÖxVkock;txZkÕ jXÓ t^`q Ó koc¤ÔÉ^Ock¾Ô j ct˜k${±^`ÕoÕ j c¤{Zq Ó dËt j txZk$qŸc× j ctÔ j Û#{Vk$Ô˜tq Ó ^Otq jXÓ y½é k
tbVck¾q
×7qmÕ¤p j bVtÉ× j ct Y
Û j ctxVk× j c¤tÔ å t j WK^`ÔkvÝ4^`_®×7lŸk`yÞ*Ô_§k Ó tq jXÓ k${ q Ó txVk§Ü7c¤Ô˜t*×7lm^ ÓZÓ q Ó dËÔ˜t˜ko×CW txVk
jXÓNj‚i koc;txVk§Ô˜k$Õvtq jXÓ Ô j ÛÆtxVk§ÔxZqŸ×¡qmÔ jXÓ lŸn j ×Ztqm_®qŸáok${¡q Ó txVk§lm^`Ôt*× j ct j ÛÆ^‹c¤kodXq jXÓ y
ÖIk$qŸdXx?t{ZqsÔ˜t˜c¤qŸa7bZtq
§ e åoä cko×Zc¤k$Ô˜k Ó t&txVk^`Õvtb7^`lKÔ˜t^Ot˜k j Û#txVk¾ÔxZqŸ×9^OttxVk¾{Vko×7^OctbVc¤kq Ó × j ct Y ß Ù½õ Y à,yï Ó × j c¤t Y
ØÃqŸdXÔoy
ÓVj Õ jXÓ t^`q Ó koc¤Ô&^Ock°b Ó l j ^`{Vk${‹^ Ó {·ø 5 Õ jXÓ t^`q Ó koc¤Ô¦Öqmtx·^t j t^`lCÖIk$qŸdXx–t j Û 555 å y 5 t jXÓ Ô¦^Oc¤k°l j ^`{Vk${ y
Assigned Patterns of POD
¢¡¢
¢¡¢
¢¡¢
¢¡¢
¢¡¢
¢¡¢
¢¡¢
¢¡¢
£¡£
¤¡¤
¥¡¥¡¥¡¥
¦¡¦¡¦¡¦ §¡§¡§ ¨¡¨¡¨ ©¡©¡© ¡¡
§¡§¡§ ¨¡¨¡¨ ©¡©¡© ¡¡
¦¡¦¡¦¡¦ ¥¡¥¡¥¡¥ ¤¡¤ £¡£
£¡£
¤¡¤
¥¡¥¡¥¡¥
£¡£
¦¡¦¡¦¡¦ §¡§¡§ ¨¡¨¡¨ ©¡©¡© ¡¡
§¡§¡§ ¨¡¨¡¨ ¥¡¥¡¥¡¥ ©¡©¡© ¡¡
¨¡¨¡¨ ©¡©¡© ¡¡ §¡§¡§ ¦¡¦¡¦¡¦
¤¡¤ ¥¡¥¡¥¡¥
£¡£
£¡£
¤¡¤
£¡£
¥¡¥¡¥¡¥
¦¡¦¡¦¡¦ §¡§¡§ ¨¡¨¡¨ ©¡©¡© ¡¡
§¡§¡§ ¨¡¨¡¨ ©¡©¡© ¡¡ ¥¡¥¡¥¡¥ ¤¡¤
£¡£
£¡£
¤¡¤
¥¡¥¡¥¡¥
£¡£
¦¡¦¡¦¡¦ §¡§¡§ ¨¡¨¡¨ ©¡©¡© ¡¡
§¡§¡§ ¨¡¨¡¨ ¥¡¥¡¥¡¥ ©¡©¡© ¡¡
¨¡¨¡¨ ©¡©¡© ¡¡ §¡§¡§ ¦¡¦¡¦¡¦
¤¡¤ ¥¡¥¡¥¡¥
£¡£
¡¡¡ ¡¡ ¡¡ ¡¡
¡¡ ¡¡ ¡¡¡ ¡¡
¡¡
¡
¡ ¡
¡ ¡
¡ ¡ ¡¡ ¡¡ ¡¡ ¡¡ ¡¡¡
¡ ¡¡
¡¡¡ ¡¡ ¡¡ ¡¡
¡¡ ¡¡ ¡¡¡ ¡¡
¡¡
¡
¡ ¡
¡ ¡
¡ ¡ ¡¡ ¡¡ ¡¡ ¡¡ ¡¡¡
¡ ¡¡
¡¡¡ ¡¡ ¡¡ ¡¡
¡¡ ¡¡ ¡¡¡ ¡¡
¡¡
¡
¡ ¡
¡ ¡
¡ ¡ ¡¡ ¡¡ ¡¡ ¡¡ ¡¡¡
¡¡ ¡¡ ¡¡
¡¡
¡
¡ ¡ ¡¡¡
¡¡ ¡¡
¡¡ ¡¡
¡¡ ¡¡
¡¡ ¡¡
¡¡ ¡¡
¡¡ ¡¡
¡¡ ¡¡
¡¡ ¡¡
¡¡ ¡¡
¡¡ ¡¡
1 2 3 4 5 6 7 8 9 10 11 12
POD
¢¡¢
¤¡¤ ¥¡¥¡¥¡¥ ¦¡¦¡¦¡¦ §¡§¡§ ¨¡¨¡¨ ©¡©¡© ¡¡
£¡£
¡¡ ¡¡ ¡¡ ¡¡ ¡
¡ ¡ ¡¡¡
¡¡ ¡¡
¢¡¢
¤¡¤ ¥¡¥¡¥¡¥ ¦¡¦¡¦¡¦ £¡£
¡ ¡¡
ØÃqŸdVy ærð Ckod`k Ó {
10
MC ges
=41264.7
9
8
7
MC(i) [1000 t]
6
5
4
3
2
1
0
0 2 4 6 8 10 12 14 16 18 20
Section i
ØÃqŸdVy 5 ð é k$qmdXx?t*{ZqmÔ˜t˜c¤qma7bVtq jXÓ¯j i koc*txVk°ÔxZqm×zë|Ô½Ô˜k$Õvtq jXÓ Ô&q Ó × j ct §
x V
(T)=137.1523, x M
=136.1293
3.5 x 105 Section i
1 x 104 Section i
BM(i)
3
2.5
2
1.5
1
0.5
0
0 2 4 6 8 10 12 14 16 18 20
SF(i)
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0 2 4 6 8 10 12 14 16 18 20
ØÃqŸdVyºø ð £Ik Ó {Zq Ó d®_ j _§k Ó tÔq Ó × j ct §
ØÃqŸdVy Y ð î4xVk$^Oc¦Û j c¤Õvk$Ôq Ó × j c¤t §

BM(i)
Weight in t
Weight in t
Weight in t
1000
800
600
400
200
1000
800
600
400
200
1000
800
600
400
200
¡ ¢¡¢
£¡£¡£
¤¡¤
¡ ¢¡¢
£¡£¡£
¤¡¤
¥¡¥¡¥
¦¡¦
¡
=¡=
>¡>
?¡?
@¡@
=¡=
ö o ö ö o
p¨p
u¡u
v¡v ö
ö o ö ö o ö ö o ö ö o ö ö o
p¨p
s¡s
t¡t
u¡u
v¡v
ö
q¡q
r¡rs¡s
t¡t
£¡£¡£
¤¡¤¡¤
£¡£¡£
§¨§¨§¨§
©¨©¨©
¡
¡
¡
¡
¡¡
¡¡
¡
¡
¡
¡
¡¡
¡
¡
¡
Ÿ¨Ÿ¨Ÿ¨Ÿ¨ ¨ ¢¡¢¡¢¡¡
£¡£¡£
¤¡¤¡¤
§¨§¨§¨§
§¨§¨§¨§
©¨©¨©
§¨§¨§¨§
¡
¡
¡¡
¡¡
¡
¡
¡¡
¡¡
¡¡
¡¡
¡
¡
¡¡
¡
¡
¡
¡¡
¡
"!"
"!"
#
$#
$
%!%& '¨'¨'
(¨(
+¨+¨+
,¨,
/¡/¡/
0¡0
43
7¡7
8¡8
9¡9¡9
:¡:¡:
;!;
;!;
;!;

Weight in t
Weight in t
Weight in t
1400
1200
1000
800
600
400
200
1000
800
600
400
200
1400
1200
1000
800
600
400
200
¡¡
¡
¡¡
¡
¡
¡¡
¡
¡¡
¡
¡¡
¡
¡
s¡s
x¡x¡x
y¡y¡y r¡r
3¡3¡3
9¡9 8¡8 2¡2¡2
D¡D
GFE¡E
¨¨
¨
0 0 5 10 15 20
0
0
¡
¢¡¢¡¢ £¡£¡£
¥¡¥¡¥ ¤¡¤¡¤
§¨§¨§
§¨§¨§
©¨©
©¨©
§¨§¨§ ©¨©
¡¡ ¡
¡¡
¡ ¡¡ ¡¡
¡
!¡!¡! "¡" #¡#
$¡$
%¡%
©¨©
&¡&¡&
¦¡¦
'¡'¡'
,¡,¡, -¡-¡- .¡.¡. /¡/ 0¡0¡0 1¡1¡1 2¡2¡2 3¡3¡3
(¡(¡(
)¡)
*¡*¡*
+¡+
6¡6
D¡D
7¡7
:¡:
E¡E
;¡;
4¡4
5¡5
>>
@¡@
A¡A
CCCCBBBBA¡A
H¡H
I¡I
J¨J¨J
K¨K
L¡L
M¡M
N¡N
O¡O
P
QP
Q
SR T
T
T
U
U
VU
WV
W
Ẍ Ẍ Ẍ X Ẍ Ẍ Ẍ X Ẍ Ẍ Ẍ X Ẍ Ẍ Ẍ X Ẍ Ẍ Ẍ X
Ÿ Y Ÿ Y Ÿ Y Ÿ Y Ÿ Y
Z¡Z¡Z
[¡[¡[
\¡\
]¡]
^¡^
_¡_
`¡`¡`
a¡a b¡b¡b c¡c d¡d¡d e¡e f¡f¡f g¡g
h¡h¡h
i¡i
j¡j
k¡k
l
ml
m
'¡'¡' &¡&¡& ¡
¡
§¨§¨§ ©¨©
¦¡¦ ¤¡¤¡¤ ¥¡¥¡¥
£¡£¡£
¤¡¤¡¤
£¡£¡£ ¢¡¢¡¢ ¡ ¡
¡
¡
p¡p q¡q r¡r
s¡s
¡
v¡v¡v ¨
w¡w¡w
x¡x¡x
y¡y¡y
x¡x¡x
¨¨¨
€¡€
‚¡‚
„¨„¨„
…¨…
ƒ¡ƒ
†¡†¡†
‡¡‡¡‡
ˆ¨ˆ¨ˆ¨ˆ
‰¨‰¨‰
Š¨Š¨Š¨Š
‹¨‹¨‹
Œ
Œ
Œ
ŒŽ¡Ž
¡
‘¡‘
’¡’
“¡“ ”¡” •¡•
–¨–¨–¨–
—¨—¨—
¡
˜¡˜
¡
œ¡œ¡œ¡ ž¡ž
Ÿ¡Ÿ
š¡š¡š
›¡›
¨ ¨
¡¨¡
¢¡¢¡¢
£¡£¡£
¤¡¤¡¤
¥¡¥¡¥¦¡¦ §¡§
¬¡¬¡¬ ­¡­ ®¡®
¯¡¯
°¡°
±¡±
²¡²
³¡³ ´¡´ µ¡µ
¨¨¨
·¨·
ª¡ª¡ª
«¡«
¸¡¸¡¸
¹¡¹
˜¡˜ †¡†¡† ˆ¨ˆ¨ˆ¨ˆ ~¡~ ¡ {¨{ w¡w¡wz¨z¨z
}¡}
|¡|
v¡v¡v ¨
¨¨¨
u¡u¡u ¡ t¡t¡t
¡
n¡n
o¡o
q¡q t¡t¡t u¡u¡u p¡p o¡o
n¡n
º¨º¨º
»¨» ¼¡¼
½¡½
¾¡¾¡¾
¿¡¿¡¿ º¨º¨º
¿¡¿¡¿ À¡À Á¡Á
¡Â
áà ¾¡¾¡¾
{¨{ †¡†¡† ‡¡‡¡‡ ˆ¨ˆ¨ˆ¨ˆ ‰¨‰¨‰ Œ z¨z¨z
Ä¡Ä
Å¡Å
Æ¡Æ
Ç¡Ç
”¡”
•¡•
”¡”
˜¡˜
¡
LEFT
CENTER
¢¡¢¡¢ £¡£¡£
–¨–¨–¨– —¨—¨— ˜¡˜ ¡ š¡š¡š ›¡› ¨ ¨ ¡¨¡ ¢¡¢¡¢ £¡£¡£ ¤¡¤¡¤ ¥¡¥¡¥ ‘¡‘
RIGHT
Ø¡Ø¡Ø Ù¡Ù
Ú¡Ú¡Ú
Û¡Û
Þ¡Þ¡Þ ß¡ß¡ßà¡à
á¡áâ¡â
ã¡ã
ä¡ä å¡å
ס×
Ö¡Ö¡Ö
¦¡¦
§¡§
5 10 15 20
ë¨ë
ì¡ì¡ì
í¡í¡íî¡î
ï¡ï ê¨ê¨ê
¨ ¨¡¨¡¨ ©¡© ¨¨¨
Ä¡Ä
Æ¡Æ Ç¡Ç Å¡Å
È¡È Å¡Å
É¡É
Ä¡Ä
Ê¡Ê
Ë¡Ë
Ì¡Ì
Í¡Í Î¡Î Ï¡Ï
СÐ
Ñ¡Ñ
Ò¡Ò
Ó¡Ó
Ö¡Ö¡Ö ×¡×
Ô¡Ô¡Ô
Õ¡Õ
Ü¡Ü¡Ü
Ý¡Ý¡Ý Þ¡Þ¡Þ ß¡ß¡ß
à¡à
á¡á
ä¡ä
å¡å
æ¡æ
ç¡ç
è¡è¡è
é¡é¡é
ê¨ê¨ê
ë¨ë
ì¡ì¡ì
í¡í¡í
î¡î
ï¡ï
ð¡ð
ñ¡ñ ò¡ò
ó¡ó ô¡ô õ¡õ ö¡ö ÷¡÷
ø¡ø¡ø
ù¡ù¡ù
Ê¡Ê É¡É
Å¡ÅÈ¡È
Ä¡Ä
0 0 5 10
15
È¡È É¡ÉÊ¡Ê
Ë¡ËÌ¡Ì
Í¡ÍСÐ
Ñ¡Ñ Ô¡Ô¡Ô Õ¡Õ Ü¡Ü¡Ü Ý¡Ý¡Ýà¡à
á¡áæ¡æ
ç¡ç
è¡è¡è
é¡é¡éê¨ê¨ê
ë¨ë
ì¡ì¡ì
í¡í¡í
î¡î
ï¡ïð¡ð
ñ¡ñ ø¡ø¡ø ù¡ù¡ùú¡ú
û¡û
Å¡Å
20
Section i
Section i
Section i
ØÃqŸdVy åoä4ð ¦ÉqmÔ˜t˜c¤qŸagbVtq jXÓËj ÛtxZk;Õ jXÓ t^`q Ó koc¤Ô j‚i koc&txVk×g^Oct˜a7^$n4Ôq Ó × j c¤t Y
' &¥#¡,Ñ"+¨¤&¥ £¦¥Ð ¡ ÑÑ% !þý % ÿ
ü
Ó koÖ Õ jXÓ Õvko×Zt·Û j c·txVkœÔ˜t j ÖI^Od`k ×7lm^ ÓZÓ q Ó d›Û j cNÕ jXÓ t^`q Ó koc2ÔxZqm×7Ô¯t^Op4q Ó dHq Ó t j Õ jXÓ Ôqs{Vkoc¤^Otq jXÓ a j tx
Þ
jXÓ dXqŸtb7{Zq Ó ^`lVÔ˜t˜c¤k Ó d`tx¯×g^Oc¤^`_§kot˜koc¤Ô½^ Ó {l j dXqmÔ˜tqsÕ¦^`Ô˜×k$ÕvtÔIÖI^`Ô½q Ó t˜c j {ZbZÕvk${ yÃØZbVctxZkoc¤_ j ck`W4^
txVkÉÔxZqŸ×Cë|Ô#l
j {Vk$l4Û j c#txVk j ×Ztqm_¯^`lV{ZqmÔ˜t˜c¤qma7bVtq jXÓ°j Ûga7^`lslm^`Ô˜te”Ö½^Ot˜kocÖ½^`ÔM×Zck$Ô˜k Ó t˜k${ yîrk i koc¤^`l7^`Ô˜×k$ÕvtÔMÖqŸtx×Zc,^`ÕvtqmÕo^`l
_
i ^ Ó Õvk ÓVj t¾ǹ kot¾t^Op`k Ó q Ó t j ^`ÕoÕ j b Ó t ß tx7qŸc¤{›{7qm_§k Ó Ôq jXÓœj Û¦txVk‹ÔxZqm× ß xVk$qŸdXx–t,à,W#Õvc¤^ Ó kvefÔ×7lmqŸtoWMxZ^OtÕ,x
ck$lŸk
j i koc,ÔoWZ^ Ó { i qmÔqma7qmlmqŸtªnlmq Ó k‚àÃÔxZ^`lslVakck$^`lmqmáok${¯lm^Ot˜kocIa–n®^ Ó kvÝ4t˜k Ó {Vk${‹_ j {Vk$lyï Ó ^`{Z{ZqŸtq jXÓ W j bVcÆ×Zck$Ô˜k Ó t
Õ
j {Vk$lÔ¤xZ^`lml©ak2kvÝ4t˜k Ó {Vk${¢t j q Ó ÕolmbZ{Zk·ckokoÛQkoc,ÔË^ Ó {¢{Z^ Ó d`koc j b7Ô¯d jrj {7ÔoW©ø ä`ù efÕ jXÓ t^`q Ó koc¤Ô·^ Ó {)Ô˜×k$Õoqm^`l
_
jXÓ t^`q Ó koc¤Ôoy Õ
j _§kœ_ j ck›Õvc¤qŸt˜koc,qm^Û j c2txVk›^`ÔÔ˜k$Ô¤Ô_§k Ó t j Û¾^ÅÔ˜t j Ö½^Od`k ×glm^ Ó xZ^ i k t j akœ{Vk i k$l j ×k${ y Y¦xZk Ó txVk
î
Ó7Ó kocMÕo^ Ó Õ¤x jrj Ô˜k^`_ jXÓ d;Ô˜k i koc¤^`lZÕvc,qŸt˜koc¤qm^ ß k`yºdVyMak Ó {Zq Ó d*_ j _®k Ó tÔoW–Õvc¤^ Ó kvefÔ˜×7lsqŸtoẀ kotÕOy¦à¾txVk¦Õvc¤qmt˜koc¤q jXÓ
×7lm^
Õvc¤qmt˜koc¤q jXÓ j bVc×7c j d`c¤^`_
xVk×ZckoÛ6koc¤Ôoy±é)qmtx›txZqsÔ°×Zc¤koÛQkocc¤k${
j {ZbZÕvk${‹arn j bVc_ j {Vk$ly
×Zc
ÖqmlmlÆÕ¤x jrj Ô˜k‹txVkak$Ô˜t×glm^ Ó ^`_ jXÓ d±tx j Ô˜k
å

A Multi-Swarm Algorithm for Multi-Objective
Ship Design Problems 1
Antonio Pinto, Emilio F. Campana, INSEAN - Italian Ship Model Basin, Rome/Italy
A.Pinto@insean.it, E.Campana@insean.it
Abstract
A Multi-Objective Deterministic Particle Swarm Optimization algorithm (MODPSO) is modified
to avoid premature collapse of the swarm toward the center of the feasible design space, and
to improve the search along the decision space bounds. MODPSO search is based on concept
of Pareto dominance. In order to build an accurate Pareto front, after an initial search, the
original swarm is decomposed in more small sub-swarms, selecting the particles on the basis
of their distance from the initial Pareto front. Each new sub-swarm has its own leader and
all the subs-warms cooperate to find out the final Pareto front of the multiobjective problem.
Effectiveness and efficiency of this approach are investigated by solving a set of test functions,
which summarize most of the difficulties that could be encountered in multiobjective optimization,
and by comparing the results with that of two well-known Evolutionary Algorithms, namely
the Nondominated Sorting Genetic Algorithm and the Strength Pareto Evolutionary Algorithm.
Finally, MODPSO is used to solve a ship design problem, reducing the heave and pitch motion
peaks of the Response Amplitude Operator of a containership advancing at fixed speed in head
seas.
1 Introduction
In many industrial design applications (naval, aeronautical, automotive) specific strategies have
to be used in looking for trade-off solution, ranging from aggregated approaches to those involving
the concept of Pareto optimal solution of the multiobjective (MO) problem. Among the
latter, the interest of optimization community has been shifting toward Evolutionary Algorithms
(EAs) due to their easiness in dealing simultaneously with a set of possible solutions, which in
turn allows to find several optimal solutions in a single run instead of running a series of separate
simulations. In comparison with other techniques, EAs are less influenced by the Pareto front
shape, easy to implement and to parallelize. A recent survey of the existing EAs variants is
provided by Coello (1999,2003).
The development of efficient and fast MO codes is fundamental, especially when the design optimization
requires the solution of partial differential equations (PDE), which are very expensive
from the standpoint of computational time. Also, the more the geometries are complex, the
more the cost of simulation process increases and if the optimizer is not efficient only a small
part of the design space can be explored.
Particle Swarm Optimization (PSO) is an EA technique introduced by Kennedy and Eberhart
(1995). Since it was proposed, it has received great attention from the optimization community,
Parsopoulos and Vrahatis (2002a). PSO has been also successfully used to solve engineering
problems, Shi and Eberhart (2001), Boeringer and Werner (2004), demonstrating its ability
in dealing with non-convex feasible spaces. Application may be found on naval hydrodynamics
(Pinto et al. (2004,2005)), structural (Fourie and Groenwold (2000),2001), Fukuyama and
Yoshida (2001), Schutte and Groenwold (2003)), aerodynamics (Ng et al. (2003)) and multidisciplinary
optimization problems (aerodynamic and structural, Venter and Sobiezczanski-Sobieski
1 This work has been supported by the Ministero delle Infrastrutture e dei Trasporti in the framework of the
research plan “Programma di Ricerca sulla Sicurezza”, Decreto 17/04/2003 G.U. n. 123 del 29/05/2003.
62

(2004)). Parallel implementations of the PSO algorithm, which allow to solve complex large-scale
engineering optimization problems, are described in Baker et al. (2000), Schutte et al. (2004).
Historically, the basic PSO algorithm was originally defined for single-objective unconstrained
optimization problems but soon modified versions able to deal both with constraints, Parsopoulos
and Vrahatis (2002b), and MO problems, Coello and Lechuga (2002), have appeared.
In the present work, a single objective PSO algorithm (the DPSO) is initially illustrated as well
as its MO counterpart, namely the MO Deterministic Particle Swarm Optimization algorithm
(MODPSO), Campana and Pinto (2005)). A new version of the MO algorithm is then presented,
modified to avoid the premature collapse of the swarm toward the center of the feasible space
and to improve the search along the decision space bounds. After an initial search the original
swarm of particles is decomposed in more small sub-swarms, depending on the distance of each
particle from the current Pareto solutions. In this way, each sub-swarm has its own guide and
all collaborate to build the Pareto front. The final aim is to reduce the number of objective
function evaluations needed to build the Pareto front improving the accuracy of the Pareto front
reconstruction at the same time.
A systematic analysis of the proposed MODPSO formulation on a set of algebraic test problems
is initially carried out. Tan et al. (2003) and Boeringer and Werner (2004) tested swarm
algorithms by comparing it with different EAs in specific applications. Here the validation
is performed by using algebraic test functions that summarize most of the difficulties which
could be encountered by EAs, Deb (1999). Then MODPSO is compared with other well-known
EAs, following a comparison test proposed by Zitzler et al. (2000). The Nondominated Sorting
Genetic Algorithm (NSGA), Srivinas and Deb (1995), and the Strength Pareto Evolutionary
Algorithm (SPEA), Zitzler et al. (1999), are used for the success demonstrated in their category
on the same set of test functions, Zitzler et al. (2000).
Finally, an optimum ship design application with functional and geometrical constraints is given,
namely the minimization of the heave and pitch motion peaks of the Response Amplitude Operator
(RAO) of a ship (containership S175) advancing at a fixed speed in head seas.
2 Set-up of a MO problem
Let us consider a system whose behavior is described by a set of equations, assume that its
status depends by a N-dimensional design vector ¯x = [x 1 , x 2 , ..., x N ] T and let’s introduce the
following bounds constraints:
b min
i
≤ x i ≤ b max
i , i = 1, ..., N (1)
The application of bounds in equation (1) defines a parallelepiped Π in the N-dimensional design
variables space. In a similar way, functional constraints are also imposed, assuming that
c min
j
≤ g j (¯x) ≤ c max
j , j = 1, ..., l (2)
where the g j (¯x) is a generic function of the design variables vector ¯x. The constraints in equation
(2), applied to Π, define the shape of the feasible solution set X in the N-dimensional design
space, i.e. X ⊂ Π is the set of design solutions that satisfy all the conditions. The vector function
¯f(¯x) = [f 1 (¯x), f 2 (¯x), ..., f M (¯x)] T includes all the objective functions of the problem, which we
want to optimize simultaneously. The MO problem may be finally formulated as follows 2 :
minimize
for
¯f(¯x)
¯x ∈ X
2 The case of the minimization of all the objective functions is here depicted, the maximization of the generic
¯f(¯x) being equivalent to the minimization of − ¯f(¯x).
(3)
63

eing f k : R N → R.
Consider now the above mentioned MO problem with M objectives, f k (¯x), and N decision
variables, x i . The solution of the MO problem is given by the vector ¯x ∗ = [x ∗ 1 , x∗ 2 , ..., x∗ N ]T , which
satisfy the constraints (1) and (2) and yields the optima values of all the objective functions.
Unfortunately, this result can not be achieved in typical MO problems, since usually does not
exist a single solution that is optimum with respect to every objective function, Miettinen (1999).
In fact, objective functions may be easily in conflict within each other. Let therefore introduce
two vectors ū = [u 1 , u 2 , ..., u L ] T and ¯v = [v 1 , v 2 , ..., v L ] T . We can say that a vector ū dominates
a vector ¯v (also written as ū ≽ ¯v) if and only if u i ≤ v i , i = 1, 2, ..., L and there exists at least an
index with u i < v i . Thus, a solution ¯x ∗ of the MO problem is said to be Pareto optimal if and
only if does not exist another solution ¯x ′ so that ¯f(¯x ∗ ) is dominated by ¯f(¯x ′ ). The decision vector
¯x ∗ , corresponding to a solution included in the Pareto optimal set P ∗ , is called non-dominated.
The Pareto front is defined as follow:
PF ∗ = {(f 1 (¯x), f 2 (¯x), ..., f M (¯x)) | ¯x ∈ P ∗ } (4)
3 Deterministic Particle Swarm Optimization - DPSO
Since the pioneering work of Kennedy and Eberhart (1995), PSO simulates the social behavior of
a group of individuals by sharing information among them while they are exploring the design
space. Each particle of the swarm has its own (individual) memory to remember the places
visited during the exploration, whereas the swarm has its own (collective) memory, to memorize
the best locations ever visited by any of the particles. The particles have an adaptable velocity
and investigate the design space analyzing their own flying experience, and the one of all the
particles of the swarm. Each particle is a potential solution of the optimization problem under
consideration. DPSO, Campana and Pinto (2005), is a deterministic version of the PSO for
constrained single objective problems, recalled here for sake of completeness.
Step 0. (Initialize) Distribute a limited number of particles on the decision variables space
bounds.
Step 1. (Compute velocity) For each particle i calculate a velocity vector v i using the particle’s
memory and the knowledge gained by the swarm.
– If constraints are satisfied then:
– else if constraints are violated:
vi n+1 = χ [w n vi n + c 1 (p n i − xn i ) + c 2 (p n b − xn i )] (5)
v n+1
i
= χ [ c ′ 2 (p n b − xn i ) ] (6)
where χ is a constriction factor on the particles speed, w is called inertia weight, c 1 , c 2
and c ′ 2 are positive constants, pn i is the best position ever found by the particle i and p n b is
the best position ever discovered by the swarm at step n.
Step 2. (Update position) Update the position of each particle x i using the velocity vector and
the previous position:
x n+1
i
= x n i + vn+1 i
(7)
64

Step 3. (Check convergence) Go to Step 1 and repeat until some convergence criterion is
matched.
The inertia parameter w regulates the trade-off between global (wide-ranging) and local (nearby)
exploration abilities of the swarm. A large inertia weight facilitates global exploration (searching
new areas), while a small one tends to facilitate local exploration, i.e. fine-tuning of the current
search area. In order to have good accuracy on both global an local search, an initial value for
w is initially set, and then it is decreased according to a given decrease rate (8). At the step n:
w n = w n−1 K w (8)
where w n−1 is the previous value for the inertia weight and K w is the decreasing rate (K w < 1).
Fine tuning of parameters in Eq.(5) is crucial for the optimization process, Shi and Eberhart
(1998), Parsopoulos and Vrahatis (2002a). Indeed, final solution and computing time are strictly
linked to these parameters setting. A fine calibration of these parameters was suggested by
Carlisle and Dozier (2001), Venter and Sobieszczanski-Sobieski (2003), in order to speed up the
overall process and to reduce the risks of being trapped by local minima. Clerc and Kennedy
(2002) describe the link between the dynamic of the swarm and its parameters.
3.1 Enhancement to the DPSO Algorithm
This section focuses on the development of an enhanced DPSO version. The proposed algorithm
incorporates a modification to avoid the premature collapse of the swarm toward the center of
the feasible space, and to improve the search along the decision space bounds, when an initial
face distribution is selected, Campana et al. (2005).
In the attempt of keeping low the number of objective function evaluations necessary to sample
the design space, the size of the swarm is reduced as much as possible. Hence, in the attempt of
not excluding a priori any region of the feasible design space, particles are initially distributed
on along the bounds, Fig.1. However, according to Eqs.(5) and (7) each particle is attracted by
the others. As a consequence, they can not escape from the dashed region indicated in Fig.1,
i.e. the corners of the design space cannot be reached by any particle of the swarm. A possible
strategy could have been to increase the inertia, allowing therefore the particles to move with
more freedom. This solution is however inefficient, leading to frequent violation of the constraints
and to a non exhaustive probing of the boundary regions.
In order to force the initial design exploration along the boundaries of the feasible space we then
introduce a dynamically changing speed limiter on that component of the particle’s velocity
directed toward the center of the feasible space, in the form:
|v n+1
i
| ≤ |bmax i
− b min
i |
(9)
g k
This threshold value is hence a function of the distance between the bounds of the whole design
space and of parameter g k . By changing g k , the inner speed limiter (9) may be relaxed after
a given number of iterations. Numerical tests have proved that by imposing condition (9) it is
possible to explore the corners of the design space avoiding the premature collapse of the swarm
toward the center of the feasible space, and find the correct global minimum, Fig.1. The path
of the four swarm particles for a n = 2 test function (Griewank) is depicted with and without
condition (9). The dashed (inner) region is obtained by joining together the initial position
of the particles. Without the speed limiter (a), particles are attracted each other and remain
65

confined inside the inner region, while using it the swarm finds the right optimum which lay
outside the dashed region.
Global
Minimum
a
b
Fig.1: The path of four swarm particles for a n = 2 test function (Griewank). Without the
speed limiter (a), particles are attracted each other and tend to be confined inside the dashed
region. The use of the normal speed limiter (b) allows the particles to explore the design space
outside the inner region and to find the global optimum.
4 A Sub-Swarm Strategy for Multiobjective Optimization
In Campana and Pinto (2005), the MODPSO formulation was presented and numerical tests
demonstrated its ability in solving MO problems, localizing the real Pareto front and producing
a large number of solutions on the frontier. For sake of completeness the MODPSO algorithm
is here briefly recalled.
The algorithm adopts a decomposition approach of the initial swarm S choosing different guides
(the Pareto solutions) for the particles of the small sub-swarms. Hence, for the i th particle of the
swarm the value of p b in the collective term (Step 1) is assumed now to be the nearest point on
the Pareto front. The initial swarm S is hence decomposed into smaller sub-swarms, each one
following a different guides. As a consequence, the i th particle moves toward an optimum point
which could be different from the j th particle’s optimum. The individual velocity term in Step
1 (p n i − xn i ) is obtained by choosing as p i the minimum of function g defined in Eq.(10) as in the
Conventional Weighted Aggregation approach (CWA), Parsopoulos and Vrahatis (2002a).
g =
Here W j is a given distribution of weights for the linear combination.
M∑
W j f j (¯x) (10)
j=1
For all the n sw particles of the initial swarm S (including those currently on the Pareto front),
the fundamental steps of the algorithm can be summarized as follows:
Step I. (Distance evaluation) the i th particle evaluates its distance, in the design space, from
all the K Pareto points (¯x ∈ P ∗ ) known at the current iteration;
Step II. (Guide selection) the i th particle selects the closest Pareto optimal solution as guide,
p k,b ;
66

By applying this procedure at each iteration the original swarm S is divided into k new smaller
sub-swarms S k , where k ≤ K, being K the current number of the Pareto optimal solutions.
Therefore, each sub-swarm S k has a guide which is different from all the other k − 1 sub-swarms
guides, Fig.2. Once selected all the guides p k,b , each sub-swarm follows its own guide by using
Eq.(5).
f 2
f 1
i=1
S 1
S
i=2
S 2
p 1,b
i=3
p 3,b
i=4
S 3
p 2,b
i=5
p b
Fig.2: S is the original swarm and S k are the new sub-swarms; black dots indicate the Pareto
optimal solutions and white dots are the current positions of the particles; p k,b is the best particle
of the sub-swarm S k ; in this case k = 3 and K = 4.
5 Multiobjective Test Functions
The key point in this paper is to compare MODPSO with existing, well assessed algorithms.
In particular numerical comparisons are presented among MODPSO and two well-known MO
evolutionary algorithms: the Nondominated Sorting Genetic Algorithm (NSGA), Srinivas and
Deb (1995), and the Strength Pareto Evolutionary Algorithm (SPEA), Zitzler et al. (1999). The
choice of these two algorithms among many available is mostly based on the results presented
in Zitzler et al. (2000), where a systematic comparison was carried out and NSGA resulted to
be the best Genetic Algorithm (GA), while SPEA demonstrated to be the best EA algorithm
among those tested. All the numerical data of this comparison are available on the web 3 . We
anticipate here that MODPSO compares surprisingly well against those two referred algorithms,
in particular giving a more interesting Pareto front with respect to NSGA and about the same
front of the one find out by SPEA but with about one order of magnitude less objective function
evaluations.
In order to evaluate effectiveness and efficiency of MODPSO, simulations are carried out on
a number of different algebraic problems commonly used to test multiobjective optimization
algorithms, e.g. Zitzler et al. (2000), Jin et al. (2001), Parsopoulos and Vrahatis (2002a), which
provide a wide spectrum of different MO tasks, Deb (1999).
A set of three MO test problems is initially defined, all having two objective functions, f 1 (¯x)
and f 2 (¯x). Each problem is then solved for two different set of design variables (N = 2 and
N = 30) to look for scale effects. Test functions T 1 , T 3 and T 5 are solved with N = 2 while
N = 30 is used for the test functions T 2 , T 4 and T 6 . The definition of the algebraic functions are
the following, Zitzler et al. (2000):
3 http://www.tik.ee.ethz.ch/∼zitzler/testdata.html
67

• Test functions T 1 and T 2 have a convex Pareto optimal front:
f 1 (¯x) = x 1 (11)
(
f 2 (¯x) = H 1 − √ )
f 1 (¯x)/H
(12)
• Test functions T 3 and T 4 have a nonconvex Pareto optimal front :
f 1 (¯x) = x 1 (13)
f 2 (¯x) = H ( 1 − (f 1 (¯x)/H) 2) (14)
• Test functions T 5 and T 6 have a Pareto optimal front consisting of several noncontiguous
convex parts:
f 1 (¯x) = x 1 (15)
(
f 2 (¯x) = H 1 − √ )
f 1 (¯x)/H − (f 1 (¯x)/H)sin(10πf 1 (¯x))
(16)
It is evident that test functions T 3 and T 4 represent the nonconvex counterpart to T 1 and T 2 ,
while T 5 and T 6 have discrete features. In all test problems, function H is defined as follow:
H = 1 + 9
N − 1
N∑
x i (17)
and all the exact Pareto optimal fronts are given by H = 1. Being focused on MO problems with
expensive objective functions, we decided to link the maximum number of functions evaluations
to the scale of the problem by imposing a limit of 100N. Bounds on the design variables are
(0 ≤ x i ≤ 1). Trying to keep low the number of particles in the swarm (and hence the number
of function evaluations) we selected an initial distribution composed by only 4N + 1 particles,
with just two particles per each hyper-face plus one particle in the middle of the design variables
space. Their initial velocity was set equal to zero. The set of MODPSO parameters needed in
(5) and (8) used to solve the six test functions are reported in Table I.
i=2
Table I: MODPSO parameters
Constriction coefficient (χ) : 1.0
Initial inertia weight value (w 0 ) : 1.4
Decreasing coefficient for the inertia weight (K w ) : 0.975
Cognitive parameter (c 1 ) : 1.0
Social parameter (c 2 ) : 0.8
Constrained social parameter (c ′ 2 ) : 0.75
Swarm size (n sw ) : 4N + 1
Max number of objective functions evaluations : 100N
The comparison is carried out for all N = 30 cases, i.e. T 2 , T 4 and T 6 .
In Zitzler et al. (2000), both NSGA and SPEA were executed 30 times on each test problem, and
each simulation was carried out using the parameters reported in Table II. Details concerning
the values of the parameters and implementations schemes are described in Zitzler et al. (2000).
Table II: NSGA and SPEA parameters, Zitzler et al. (2000)
Number of generations : 250
Population size : 100
Crossover rate : 0.8
Mutation rate : 0.01
Niching parameter σ share : 0.48862
Domination pressure t dom : 10
68

T 2
P * = 120
54
4
100N
P * = 167
5
4
T1 2
f 2
3
3
2
2
T 1
f 1
f 2
3
2
1
1
0
1
0.25 0.5 0.75 0 0.2 0.4 f 0.6 0.8 1
1
0
0 0.2 0.4 0.6 0.8 1
5
4
3
T 3
P * = 171
5
4
3
T 4
P * = 141
f 2
2
f 2
2
1
0
0 0.2 0.4 0.6 0.8 1
f 1
1
0
0 0.2 0.4 0.6 0.8 1
f 1
5
4
T 5
P * = 47
5
4
T 6
P * = 116
f 2
3
2
f 2
3
2
1
0
-1
0 0.2 0.4 0.6 0.8 1
f 1
1
0
-1
0 0.2 0.4 0.6 0.8 1
f 1
Fig.3: Test functions T 1 (N = 2) and T 2 (N = 30) have a convex Pareto front; T 3 (N = 2) and
T 4 (N = 30) have a non-convex Pareto front; T 5 (N = 2) and T 6 (N = 30) have a discrete Pareto
front; P ∗ is the number of Pareto optimal solutions found by MODPSO after 100N objective
functions evaluations.
69

5.1 Test Functions Results
Fig.3 shows numerical results for the solution of the six multi-objective tests. The solutions
belonging to the Pareto optimal set (empty circles) are compared with the real Pareto fronts
(black lines) formed with H = 1. For each test the number of Pareto optimal solutions P ∗ is
also reported.
MODPSO technique reproduces with good accuracy the real Pareto front for all the tests with
N = 2 design variables, i.e. T 1 , T 3 and T 5 . In particular, it is able to pick up all the branches
of the discontinuous Pareto front in test problem T 5 . The number of Pareto optimal solutions,
except in test function T 5 , is always greater than 100, giving a good resolution of the obtained
Pareto fronts. By increasing the complexity of the problem, i.e. for the higher number of design
variables ( N = 30) the results are still very satisfying. A reduction in the number of Pareto
points on the fronts is observable for the case T 2 and T 4 but the resolution of the calculated
Pareto front is still good. In test problem T 6 the solution is even better than that of the case of
two design variables (T 5 ).
1.54
1.54
T 4
13
T 2
T1 1
MODPSO = 120
100N
NSGA = 45
SPEA = 144
13
100N
T1 2
f 2
T1 2
f 2
0.52
01
0.25 0.5 0.75 0 0.2 0.4 0.6 0.8 1
T1 1
f 1
0.52
MODPSO = 141
NSGA = 30
SPEA = 76
01
0.25 0.5 0.75 0 0.2 0.4 f 0.6 0.8 1
1
T1 2
f 2
1.54
1
3
0.5
T 6
MODPSO = 116
NSGA 100N = 63
SPEA = 115
0
2
-0.5
1
0.25 0.5 0.75 1
0 0.4
T1f 0.6 0.8
1
Fig.4: Comparative results on test function T 2 , T 4 and T 6 (N = 30)
NSGA and SPEA were compared for the case N = 30. According to Zitzler et al. (2000) per
each test function the outcomes of the first five runs are stored together and then only the
non-dominated solutions are plotted and compared with the Pareto fronts found by MODPSO,
Fig.4. In test problems T 2 and T 4 , MODPSO was the only method capable to localize the
global minimum of functions f 2 . Comparing both the Pareto solutions as well as their number
MODPSO and SPEA solutions are better than those obtained with NSGA in all the cases
analyzed.
70

¿From the standpoint of the method’s efficiency however, it must be underlined that the number
of objective function evaluation used by MODPSO in finding the Pareto front was only 3000,
and this has to be compared to the 25000 function evaluations required by NSGA and SPEA
methods in each one of the three test problems. We can therefore conclude that the efficiency
of MODPSO in the solution of these MO tests is about 24 and 10 times higher than those of
NSGA and SPEA, respectively.
6 MODPSO test for seakeeping improvement
In order to show the capabilities of the MODPSO procedure in solving MO design problems,
containership S175 has been selected as test case. The goal is the minimization of the heave
and pitch motion peaks of the RAO, while the ship is advancing in head seas at the speed
of 16 knots (Fr = 0.198). The optima solutions are searched for non-dimensional frequencies
ω 0 / √ L pp /g > 0.4. For the evaluation of the RAO’s heave and pitch motion, a standard striptheory
approach has been applied. The method is widely accepted in preliminary design; 25
sections, each one with 10 segments, have been used to describe the hull, according to the
limitations of the adopted code, Meyers et al. (1981). However, in the attempt of increasing
the freedom of the optimizer, sections are not equally spaced along the hull, being instead
stretched in the control region R c of the optimization problem, Meyers and Baitis (1985). As a
consequence, during the optimization cycle, up to seven sections are used in the bow description
and are allowed to move from the original position.
To modify the control region R c , a perturbation approach, previously developed, Peri et al.
(2001), was adopted here: a surface patch – a Bezier polynomial surface – is superimposed to
the original hull shape. The ship’s geometry is modified only in the transversal direction by
using a Bezier patch B y applied to the hull. As a consequence, the keel line is left unchanged
during the optimization process.
The final design should satisfy some predefined constraints, geometrical and functional. In this
test case, three different constraints have been adopted. For the displacement ∆ and the beam
B, a range has been defined:
2400t ≤ ∆ ≤ 2460t (18)
25m ≤ B ≤ 26m (19)
These two constraints are nonlinear and in the present work they are treated as a black-box.
Also, bounds are applied directly on the design variables x i . With reference to the definition
(1), minimum and maximum values have been imposed:
b m i = −20.0, b M i = 20.0, i = 1, ..., 6 (20)
To deal with the constraints infeasible solutions were rejected by assigned a high-function value
and no further objective function evaluation are required until the particles come back into the
feasible design, see Campana and Peri (2005) for details. For this design problem the maximum
number of objective functions evaluations has been limited to 600 (100N). The initial particles
distribution has been selected performing a LPτ-net, Statnikov and Matusov (1995), distribution
of 65000 trial points, but only 25 (4N + 1) feasible points have been chosen from the above
mentioned distribution as starting points. As a consequence the swarm size is equal to 25. The
parameters utilized to solve the containership S175 design problem are summarized in Table I.
71

7 Numerical Results
MODPSO has been used to perform the seakeeping optimization of containership S175. The
detected Pareto front is shown in Fig.5. RAOs heave and pitch motion peaks are respectively
reported on x and y nondimensionalised by the values of the original S175 hull shape. The
number of Pareto optimal solutions, is 25. Three solutions from the Pareto front corresponding
to RAOs heave and pitch motion peaks lowest values, O #1 and O #2 respectively, and the point
with the best trade-off value between these two optimal points, O #3 are selected to compare
their seakeeping performances, Fig.6, and the optimized ship hull geometries, Fig.7.
PITCH *
1
0.95
0.9
O #1 MODPSO (P * = 25)
0.85 O #3
O #2
0.8
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
HEAVE *
Fig.5: Pareto optimal solutions achieved from the multi-objective optimization of S175
Fig.6 compares among the RAOs of the original hull shape and the three optimized ones. On the
horizontal axis the non-dimension frequency ω 0 / √ L pp /g is reported, while on the vertical axis
the amplitude of the RAOs heave and pitch motions is plotted. As to the RAO’s heave motion
curves, it is possible to see that in the optimized configurations O #1 the peak is absent. In case
of O #3 , the peak is quite dumped if compared with the original one, while it is still present in
the configuration O #2 . On the contrary, as to the RAO’s pitch motion curves, O #2 reduce most
the peak. Table III summarizes the seakeeping characteristics for the selected points, in term of
RAOs heave and pitch motion peak values, and improvement achieved by the three optimized
hulls.
A h
RAOs (heave motion)
0.7
RAOs (pitch motion)
A p
ω 0
/(L pp
/g) 0.5
1.2 Original
1
0.8
O #1
O #2
0.6
0.5
0.4
Original
O #1
O #2
O #3
O #3 (L pp
/g) 0.5
0.6
0.4
0.2
0.3
0.2
0.1
0
0.2 0.4 0.6 0.8 1
ω 0
/
0
0.2 0.4 0.6 0.8 1
Fig.6: RAOs for heave (left) and pitch (right) of the S175 original and modified hull shapes
72

Table III: Original and optimized seakeeping performances of containership S175
Configuration Heave Pitch Heave Improv. Pitch Improv. Mean Improv.
Original 1.320 0.640 - - -
O #1 0.878 0.628 33.46 % 1.91 % 17.69 %
O #2 1.220 0.554 7.58 % 13.48 % 10.53 %
O #3 0.912 0.592 30.86 % 7.50 % 19.18 %
- - - S175: __
O
S175 ; O #1
10
5
-10 -5 0 5 10
- - - S175: __
O
S175 ; O #2
0
10
5
Y
- - - S175: __
O
S175 ; O #3
-10 -5 0 5 10
0
10
5
-10 -5 Y0 5 10
Fig.7: Original S175 (dashed lines) and optimized hulls (continuous lines)
0
73

Fig.7 compares section lines of the original and the modified hull shapes. Configuration O #1
shows that a ship with a fine bow and a large stern offers great reduction in term of RAO’s
heave motion peak. On the other side, hull O #2 shows better results regarding the RAO’s pitch
peak value. Configuration O #3 is a trade-off between the previous ones, even if it is more close
to O #1 . In fact, the heave improvement is larger than the pitch improvement.
8 Conclusions
In this paper, a modified version of the MODPSO algorithm has been presented. The method
is based on concept of Pareto dominance, and the original swarm is decomposed in more small
sub-swarms depending on the distance of each individual from the current Pareto solutions. As a
result, we are able to define a different guide for each sub-swarm. Effectiveness and efficiency of
the proposed approach were shown by solving a set of multiobjective test functions. MODPSO
simulations were compared with those of other EAs, namely NSGA and SPEA, Zitzler et al.
(2000). Numerical results showed that MODPSO accuracy in finding Pareto solutions is comparable
to that of SPEA, and higher than that of NSGA. Furthermore, MODPSO proved to be
computationally one order of magnitude more efficient than the other tested algorithms. Finally,
MODPSO has been used to reduce RAOs heave and pitch motion peaks of the containership
S175. Many Pareto optimal solutions are offered to the design engineers, among which the preferred
final design can be chosen.
References
BAKER, C.A.; WATSON, L.T.; GROSSMAN, B.; HAFTKA, R.T.; MASON, W.H. (2000),
Parallel global aircraft configuration design space exploration, 8th AIAA/NASA/ISSMO Symp.
Multidisciplinary Analysis and Optimization, Paper No. 2000–4763–CP, Long Beach
BOERINGER, D.W.; WERNER, D.H. (2004), Particle swarm optimization versus genetic algorithms
for phased array syntesis, IEEE Trans. Antennas and Propagation, 52(3)
CAMPANA, E.F.; PINTO A. (2005), A multiobjective particle swarm optimization algorithm
based on sub-swarms search, submitted to Evolutionary Computation
CAMPANA, E.F.; LIUZZI, G.; LUCIDI, S.; PERI, D.; PICCIALLI, V.; PINTO A. (2005), New
global optimization methods for ship design problems, Techn. Rep. INSEAN, 2005 – 1, submitted
to Optimization and Engineering
CARLISLE, A.; DOZIER, G. (2001), An off-the-shelf PSO, Workshop on Particle Swarm Optimization,
Indianapolis
CLERC, M.; KENNEDY, J. (2002), The particle swarm-explosion, stability, and convergence in
multidimensional complex space, IEEE Trans. Evolutionary Computation, 6(1)
COELLO, C.A.C. (1999), A comprehensive survey of evolutionary-based multiobjective optimization,
Knowledge and Information System, 1(3), pp.269-308
COELLO, C.A.C.; VAN VELDHUIZEN, D.A.; LAMONT, G.B. (2002), Evolutionary algorithms
for solving multi-objective problems, Kluwer Academic Publishers, New York, ISBN: 0306467623.
COELLO, C.A.C.; LECHUGA, M.S. (2002), MOPSO: A proposal for multiple objective particle
swarm optimization, IEEE World Congress on Computational Intelligence (CEC00), pp.1051-
1056
COELLO, C.A.C. (2003), Evolutionary multiobjective optimization: Current and future challenges,
Advances in Soft Computing-Eng., Design and Manufacturing, pp.243-256, Springer,
74

ISBN 1-85233-755-9
DEB, K. (1999), Multi-objective genetic algorithms: Problem difficulties and construction of test
problems, Evolutionary Computation, 7(3), pp.205-230
FOURIE, P.C.; GROENWOLD, A.A. (2000), Particle swarms in size and shape optimization,
Int. Workshop on Multidisciplinary Design Optimization, Pretoria, pp.97-106
FOURIE, P.C.; GROENWOLD, A.A. (2001), The particle swarm algorithm in topology optimization,
4th World Congress of Structural and Multidisciplinary Optimization, Dalian
FUKUYAMA, Y.; YOSHIDA, H. (2001), A particle swarm optimization for reactive power and
voltage control in electric power systems, IEEE Congress on Evolutionary Computation (CEC
2001), Seoul
JIN, Y.; OLHOFER, M.; SENDHOFF, B. (2001), Dynamic weighted aggregation for evolutionary
multi-objective optimization: Why does it work and how?, Genetic and Evolutionary
Computation Conf., pp.1042-1049
KENNEDY, J.; EBERHART, R. (1995), Particle swarm optimization, IEEE Int. Conf. Neural
Networks, Perth, IV:pp.1942-1948
MEYERS, W.G.; APPLEBEE, T.R.; BAITIS, A.E. (1981), User’s manual for the standard ship
motion program, SMP, David Taylor report DTNSRDC/SPD-0936-01
MEYERS, W.G.; BAITIS, A.E. (1985), SMP84: improvements to capability and prediction
accuracy of the standard ship motion program SMP84, David Taylor report DTNSRDC/SPD-
0936-04
MIETTINEN, K. M. (1999), Nonlinear multiobjective optimization, Kluwer Academic Publisher
NG, K.Y.; TAN, C.M.; RAY, T.; TSAI, H.M. (2003), Single and multiobjective wing planform
and airfoil shape optimization using a swarm algorithm, 41st Aerospace Sciences Meeting and
Exhibit, Reno, AIAA 2003-45
PARSOPOULOS, K.E.; VRAHATIS, M.N. (2002a), Recent approaches to global optimization
problems through particle swarm optimization, Natural Computing 1: pp.235-306
PARSOPOULOS, K.E.; VRAHATIS, M.N. (2002b), Particle swarm optimization method for
constrained optimization problems, Euro-Int. Symp. Computational Intelligence 2002.
PERI, D.; ROSSETTI, M.; CAMPANA, E.F. (2001), Design optimization of ship hulls via CFD
techniques, J. Ship Research 45/2, pp.140-149
PERI, D.; CAMPANA, E.F. (2003), Multidisciplinary design optimization of a naval surface
combatant, J. Ship Research 47/1 pp.1-1.
PERI, D.; CAMPANA, E.F. (2005), High fidelity models and multiobjective global optimization
algorithms in simulation based design, J. Ship Research, to appear
PINTO, A.; PERI, D.; CAMPANA, E.F. (2004), Global optimization algorithms in naval hydrodynamics,
Ship Technology Research, 51/3, pp.123-133
PINTO, A.; PERI, D.; CAMPANA, E.F. (2005), Multiobjective optimization of a containership
using deterministic particle swarm optimization, submitted to J. Ship Research
SCHUTTE, J.F.; GROENWOLD, A.A. (2003), Sizing design of truss structures using particle
swarms, Structural and Multidisciplinary Optimization, 25/4, pp.261-269
SCHUTTE, J.F.; REINBOLT, J.A.; FREGLY, B.J.; HAFTKA, R.T.; GEORGE, A.D. (2004),
Parallel global optimization with the particle swarm algorithm, J. Num. Meth. Eng., 61(13),
pp.2296-2315
75

SHI, Y.H.; EBERHART, R.C. (1998), Parameter selection in particle swarm optimization, 7th
Annual Conf. Evolutionary Programming, San Diego
SHI, Y.H.; EBERHART, R.C. (2001), Particle swarm optimization: developments, applications
and resources, IEEE Congress on Evolutionary Computation, pp.27-30
STATNIKOV, R.B., MATUSOV, J.B. (1995), Multicriteria optimization and engineering, Chapman
& Hall, USA
SRINIVAS, N.; DEB, K. (1995), Multiobjective function optimization using nondominated sorting
in genetic algorithms, Evolutionary Computation, 2(3), pp.221-248
TAN, C.M.; RAY, T.; TSAI, H.M. (2003), A comparative study of evolutionary algorithm and
swarm algorithm for airfoil shape optimization problems, 41st Aerospace Sciences Meeting and
Exhibit, Reno, AIAA 2003-102
VENTER, G.; SOBIESZCZANSKI-SOBIESKI, J. (2003), Particle swarm optimization, AIAA
J. 41/8, pp.1583-1589
VENTER, G.; SOBIESZCZANSKI-SOBIESKI, J. (2004), Multidisciplinary optimization of a
transport aircraft wing using particle swarm optimization, Structural and Multidisciplinary Optimization
26/1-2, pp.121-131
ZITZLER, E.; DEB, K.; THIELE, L. (1999), Multiobjective evolutionary algorithms: A comparative
case study and the strength Pareto approach, IEEE Trans. Evolutionary Computation,
3(4), pp.257-271
ZITZLER, E.; DEB, K.; THIELE, L. (2000), Comparison of multiobjective evolutionary algorithms:
Empirical results, Evolutionary Computation 8(2), pp.173-195.
76

!! !!! " #
!
$ ! !%&
8(
*#
5
*# 6
7
(
5 6
5
*
%&'$ (
) * &++, !
# ! (- *.(- */
$ ! 0!
(- *
!"
( #
)1) # !
! (!
$ *! )1)# &++,
2 # ! # 34 !!

)1) :! (- **
!;! !;
!(- *
(' 5!(-
#
& !
,

B"
(('B"-A CB" A
#
-
)
-
&&%
!
&,-#
&

(,32(! B"
(,=2 !
(,92-5(
(

)0
) 5
5
5 5
5C$
5
- 5
(
)
5!
%$$
%3'(- *
(- * !# !'
! !(- *.)0)
55 5- 5/#
# !(!$ *.)5
! / ( # ! !# # '
!!!!!
(- * ! # # !
!! ! )1) !# -!D*)D5B !
-()*@%# ! (- * !)1)
!# '
2 !!
2 ! ! # ! # !
2 # !
2 2! !'# " !
# #
(- * ! A2A ! #
! # # !
B( ; ! . ! /
! (- *
D D #? (D-@? *D# -$*' **G *G
$ %
@ ! !
H!(! !#
H'
9&

2 !! # 0 ! 0 !
! !#
!
2 5 # 0
2 ! ! !
( !! H
!! 7
!!!
$ #
(! $ * # )1)
! ! !! ! !! "
( !! !
!#'
2 !I
2 !! I
2 !!H
!! !!H
./) !'
2 !!2# " I
2 !I
2 ! !!
) !!H +234J
! !! !
@ ! !!
# !! !
!! #
" !! #
7
!!
2! ! 0 !!
!:
!! !
2!(!
,44, ! ! !#$%# #
; !## ' !
!!#
# ( !
#
!! "! 50 ! !!./ 0
! '
(
=
& =
&
= =
=
&
'
&
=
&
'
&
# (Σ' C
' )!
& C!
C !
.&/
9,

7 ! . / 0'
*& +
.,/
# C "!
%!#! 0'
=
=
&
=
=
&
('
=
&
.&
⋅ +
/ = &
+ = ⋅&
+ = ('
+ = (, + .

=
('
=
&
=
(,
=
1
α
⋅ %,
(,
( ! 0
1 ⋅ %, 1 ⋅
α
α
%,
&
= &
+
= &
+ &
= &
+
.&&/
(,
(,
*!# # !#! !
'
1 ⋅ %,
α
&
= &
+
.&,/
(,
# (,C
#!! %= !!!
!# ! !
$ !
!! 0!!!# !#
!!!!
6
.&4/
5
pi/Oi
4
3
2
1
0
0.0505
0.0446
0.0401
0.0359
0.0322
0.0287
0.0256
0.0228
0.0179
0.0139
0.0107
0.0082
0.0062
0.0047
Bankruptcy probability R
0.0035
0.0026
0.0019
0.0014
3.2000E-05
%='!!!
#
!
#
!!# !
! ## !
93

&
&'"
? (- *
!! !! 6
!250 (- *!"
! ! !# #
! ##!
#
!
!# !
"( !!#
! #
!( #
! *
( H!!#
1!! !#0 '
2 !! !!H!I
2 !HI
2
I
2 !! ! !I
2 !! ! ( I
2 ! # H 2 H
( I
2 " !! # # # H
I
2 " !! #
:!I
2
2
! :! "I
!! "
!#
!#
-
#
%>'(- *
9=

5!! !# !1!!
# !! ( !!
! !!
! ! !!
# !0 #! !
# # ## ! #
# # # #
# ! 5@) L,BB DB
) 5@)#!
DB ! L,BB # !
# !! (! ! ! (- *
# %> ((( # # !
!
((('-!!
# %
! !
B # 6 ;!
-
-
&! %%
? (- *( #
AA ! ! !)!
! " $! *G * $*G
*G @ "
( # # 5@)
!!!!5@)!!
! " @
-## M? # !
! 5@) ! !
DB L,BB !
(1
(1' !
*! L,BB DB
'
5!? B ! " !
! #
5 ! .
/
L*
L
'
L*
L*
L
'
1*
L*
'
)* DB
5@$N) M
# L-5 )-@DB
()
!! ! ! !
" # ! *!;!
!;!(-
*
9>

!#! ( '
2 !2 # # !
2 !(- *#!!!
2 ! !
* .* / (* # !
.% 2) / A 2B" A ) !
!# !!
!# !! ! !#
!(- * !!
!! !!!
! #
!
# !! #
!
# (- * ( #
;! ! #!
! # ( !! # #
! # (
! #
# ! " #
? ! !
! : ; " % " 5@) !! 0
!
$! DB !
# DB !? #
*
D@1(*EO I 7)D@1) $I 1(E@@1) BI )F@P(D 1 .,44

!"!#$
!"""#"$"
"" """%&#
$ """"""
"""$"
"""""' """
" " "
"" " ""
" ("" "$ " "
" !""#"""""
" " "" " " " "
")"""""""
*"""" $""""""
" " ' " +,*#,* " "
""""" ""(""
" ")"""-
!""""+,*#,*
".,//'0 ' " "
" "1""""$
$"""""""""
("" $ " " 1 "
""$ ""-""
"$ ""
" " " 2" ' %
"""*""
" ' $" "" "
"-"" $" "
'"")
" ""
" 2 ' "$ " " "
""""" 2"
" " 23 " ("
"""" )
"" " " "" " " "
""1""""""

"#"""
")-"
"" ""
."""""$""."
" ""'""$"
"("
2" " " " "" "
$"(" " " " """
""")""""
" 5 " " " " "
) "" "$"" "
"0""
! "#
."" """("
""6$" "$"$"
"$"" 25
⋅
( − ) 8 = 7
$
≠
= γ ⋅
⋅
6
=
=
−
=
%
9%:
; ""$""$"""5
( ) <
( )
( + ∆) =
( ) +
( )
⋅ ∆
+ ⋅ ∆
( + ∆) =
( )
+ ⋅ ∆
9

$
'"" "".,//'0==5
Integer, parameter MAX_DATA=100
Integer N
Real, dimension(MAX_DATA) x0, x1, y0, y1, z0, z1,
+ vx0, vx1, vy0, vy1, vz0, vz1, m
common /planets/ x0, x1, y0, y1, z0, z1,
+ vx0, vx1, vy0, vy1, vz0, vz1, m, N
' $" ")" "
$"7%$" " → + ∆
5
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
7
%
7
%
( )
= 7
8
>
=
( + ∆)
= %
8
( )
= 7
8
>
( + ∆)
= %
& 7
&%
& 7
& %
) """"""" ""
)""""5
[ ]
[ ]
[ ]
5= %
5= %
" ≤ $ " ≤ $
= 7
= >
5=%
= >
[ ]
[ ]
[ ]
= 7
=
" ≤ $
⋅
−
.
= γ ⋅ ⋅(
−
)
6
= +%
= +
>
= +%
<
=
+
⋅ ∆
+ ∆
< ⋅
>
=
+ ∆
= +%
" " " "" ? $
""
47

$
2""""5
##
! %
9%50:
#' 5@"A
#
5B6C
#
#9# 5:
5B6C
#5
#"95:
#5D*
#.9# 5:
#0)" ( )
#"$0)" ( )
-" """""
' ( " "
" 5' 2) '
2 ' ( 2 ) . "
" " " " "
) **")+* ,- ""
"*""")
"
"""""" ""
"""") ""
"5
B"5D*55"95:
{
→'
{
→0)"9:
}
→'
{
→"$0)"9:
}
"' (" "5
4%

B"5# 550)"95:{
5 = 7
→→' {
=
+ → 9 :
}
5
→
<
= → + → ⋅ +
⋅
⋅ →
→ 5=
→ + ⋅
→
}
B6C5# 55.9# :{
( → =
→ )
{ 5 = 7}
→ ⋅ →
( )
5= γ ⋅ ⋅ → − →
→ − →
}
'$$ $ "5
B"5# 550)"95:{
{ 5 = 7}
→→' {
=
+ → 9 :
}
5
→
<
= → + → ⋅ +
⋅
⋅ →
→ 5=
→ + ⋅
→
}
<
<
4

&$"$$"
$ 2" " " " '
""#$""
" "" " " )"" ""
D""""""' ( "".)
""" " 5
! %
!
#'D #D
#
' $ 2" " " "
$.+/001-1"$""
"""1""""
2 $"$1
2 "" " '
"$ " ) " "" ' "
""""" "$"
&$'" "$"
" " " "$ #
5
% - " 2" " $
2""+EEF$
< ' """ " " .,//'0 " "" "
"$
2"""" ""
2 2"$"-""
2'"""""
""""""-"$"
29":" " $"
"$" ""$" "
." 2"""""""
"" """, 2"
" " " " " " "" $"
" #$ " " $" "
"+"".,//'0"""'
" 2" " """
46

2 " " . ) .,//'0== "
-"""" 2"".,//'03+
$"""
$ """ ' ""
""$*""" """
" "C.,//'0
+EEF$ " " "
C" " $ " """ "
$'"$"$1
"""""1""
" " 3 " "
" " ) " +< 0
"9.,//'0:"
2"9+EEF$:" 2"'
" $" $"
; """3-".,//'0$
+EEF$3."""
$" """$")
$*" "$""
"""
$-" 2"$"")"1")"""
$")
) $ " +( " "
""""".)"
"$"""+D1"+D
" 2 " " ) ""
$ " 2"
,"$ """"$""
" " " " ) "
" " " " " ' "
""" "
'"+EEF$9 2":""
" " "" 0 +EE 1 $ "
""""""+EE""
" +D - F$ " "
" " """""
""""""$'""
-"'$""
) " " $" ' " "
"""$"" """)""""
1"" "
-"""C"
"""""-"""""
" " " 2" 2" "
""
&$ ( )*)+%
; " 2" " " .,//'0 $"
" $" 3 " " " .,//'0
# " $" " 2" $
".,//'0- """ 2
""-" 2"
4!

" " " " 2 2" )""" "
""1"2C$
" 0 *
)""$ " 2"".,//'0"
&$( )*)+,,
-"""""""
5
Subroutine xyz_new()
Real : a,b,c
Save
A=0.0
B=0.0
C=0.0
return
Entry xyz_delete()
…
return
entry xyz_calc(u,v,w)
…
return
end subroutine
$ " " ) " 2 " "
9 :""9)G>)G>)G>:
1 $" " " $ "
""" $"""$" 2C"
2 " " " 1 "
"$$" "
""""$)"$" 2""$
""""""""1"
"""""
&&$$"! $
""" 2("
"$","""
"$" .)' "
-.,//'047""""$5
type MyClass_type
integer :: i
real :: a
end type MyClass_type
0"" "5
Type (MyClass_type), dimension(MAX_OBJECTS) :: MyClass_data
"" 2'"""
"
4&

Logical, dimension(MAX_OBJECTS) :: MyClass_isUsed
' """"".'I* I$"
"""")"" 2
' ""5
Function MyClass_new()
Integer :: MyClass_new
Integer :: I
Logical :: ok
Ok = .false.
Do I=1,MAX_OBJECTS,1
If (MyClass_isUsed .eq. .false) then
MyClass_isUsed[I] = .true.
MyClass_data[I]%i = 0
MyClass_data[I]%a = 1.0
MyClass_new = I
Return
End if
End do
MyClass_new = -1
Return
End function MyClass_new
' "")
"$" - 2"5
Procedure MyClass_delete(id)
Integer :: id
MyClass_isUsed[id] = .false.
End procedure MyClass_delete
-' ""
""5
MyClass_dat[id]% = …
- " " $" "" " "" "
"" 2""
&-"# %$
- 2""""""","
""""$" "1"
"""""""""
2""" 2-""" "
2("$'"")"5
type ChildClass_type
integer :: parent_object
real :: c,d
end type ChildClass_type
4H

"" 5
ChildClass_data[id]%parent_object = ParentClass_new()
'5
Call ParentClass_delete(ChildClass_data[id]%parent_object)
." "5
Procedure CildClass_(id, …)
Integer :: id
Call ParentClass_(ChildClass_data[id]%parent, …)
End procedure ChildClass_
'" """ " 2"D
$" 2 $" 2
- 2" ""
- $)""""'""
-"")" 2 2
$" "")"" 2"""
"""5
function ChildClass_castToParent(id)
integer :: ChildClass_castToParent
ChildClass_castToParent = ChildClass_data[id]%parent
Return
End function ChildClass_castToParent
""""" 2"""
"" " 2 "1
2"" """"
""5
function ParentClass_castToChild(id)
integer :: ParentClass_castToChild
ParentClass_castToChild = ParentClass_data[id]%child
Return
End function ChildClass_castToParent
Function ParentClass_newFromChild(child_id)
Integer :: ParentClass_newFromChild
Integer :: child_id
Integer :: id
Id = ParentClass_new()
ParentClass_data[id]%child = child_id
ParentClass_newFromChild = id
Return
End function ParentClass_newFromChild
0"
" "" " " " ""
)"""1"" ""
4=

&.$"/! "
'" 2""""""$""'
$""""" ""$
"" $",""
" "" " 2 "
D""-
"""" $"""1
"""
$"""$"""$""
"$""""""
"5
D = GeneralShip_getDisplacement(ship_id)
-" .)"2
".)" 2"
".) "" )-
2"""""" "
$"'"$
" "
"" 2""""
" """-" "(
" "5
Integer,parameter :: GeneralShip_classNo = 1
Integer,parameter :: FerryShip_classNo = 2
Integer,parameter :: TankShip_classNo = 3
…
" " "
0)"""""""
""5
type GeneralShip_type
integer :: child_object
integer :: child_classNo
…
end type GeneralShip_type
0"".),2 "5
Function GeneralShip_getDisplacement(id)
Real :: GeneralShip_getDisplacement
Integer :: child
Real :: d
Child = GeneralShip_data[id]%child_object
Select case(GeneralShip_data[id]%child_classNo))
Case(FerryShip_classNo)
d = FerryShip_getDisplacement(child)
Case(TankShip_classNo)
d = TankShip_getDisplacement(child)
Case default
d = -1.
4

End select
GeneralShip_getDisplacement = d
Return
End function
0 " " $ "
"'" """"-"
" """ "
-
1"$""
"" " " ' "" 2 " " "" $
" "" " .
"""$"$""""
"" , " " " " ""
)" " "" "" ' " "
9" "": "" " "
"""""$"
)" $ , 2" " $
""
; " " .,//'0 2" " " " "
" " " ' $ "
" " " " )" $ "" #$ " "
""" "" "
"" 2" C" " ""
""2"""'.,//'047
) """"""$"
""""2"")"
""
)
'##' 9

!"
#
!"
$ %
$ &'
%
$
! "#$%
&'' () * + ,% - &.
*!- # . ()
( )*++,- ! # #
% * . *++,- #
!/ # 0 %
, 1# % ## ,# $ !
# 1# ## # #
! # % #% %
% % #
##
##!23$4*2 3$4-%#
! % # #
*# 5## 1 5 #
# ! ,# - 23$4 , # 2+5
*25-## #
6 7 ,#%
%
# 5 # 1# #
# !
##%%
23$4%##8 ##*8-!
# #
23$4 # # !
* , # ,# #- 5
# ! *#
-#23$4
0%# % #
9% 23$4 # %
# # #
# #

23$4 %#%%
# # %#
# 5 % )/00*- #
8 ##*8- # 0 51
2)*+++-###
# # * #-
#0 #
%##1# !
5%#% % #
# #
#23$4 1##%# :
#% 0 % # ;%
## #0 #
#%
% !#
1 #
1# #23$4 < #
#%
!"#
! 0#1# %#
# 1 !)/003- %#
06#+ 7
,# !##%#
+ % # 0 5 4 )/003-
# #='()#1>=
>++' ## !
,# + + 5 % #
# ?@#2)*+++-
55)*++/- ##0#
+ ## ##
+ # ## #
+ ## # ! # #
% +#9%%
# !% 67%!
# )*++*- ,# #
# # %# #
# # 8
# % #
67 ## #%
#1 # # #
%% 5##+
# ! %:
##0 #
#%#! #11
# (1#
0!,# %1
677)/000- 8)/000-
%## ! %
#1*%##9*++,-3#%%

6 )/00*-:)/003-:")*+++-:
( )*++/-:")*++/-:9!)*++*-:1)*++*-
.)*++*-% , !
##% ! #
!#8 %
$%&' %
23$41 #%% ##52*
5 2 - . )*++,- 23$4
#23$4
#!# !
% %#!# 1#
# %
23$4 %# 2 A ? !BB #
C # + ## *
.*++;-25
%$8! #% !
%' # #%D, :#:#:#
0 *!- #
: # # #
#D 7::
#
23$4
% % %#
! 1 # % E #
# %
D23$4 #
( & )
7 ! %# #
# ! #
! # %# ,
! #
%
2% ,
,
%
F #
%
5 %
( #+
#0
!
2%
#
F #
G"
%##
#
# 23$4 % % #
*.*++,- (+ # %
#%
# #%
&

##5# 23$4
#%<
#
#$ 05
#5
5
, #D8#(#8# .

5
()1'()
#
.
()1'()
(1#
6
!
! !
+
K
()1'()
#
7
=
J
()1'()
(1#
!

#% %!#<
= 3 # # % # + + %
3 0 !3
# ##
$
%&*
23$4 % # #
!2% )/0?0-
6 #0 ## #
## 7
%# 23$4 1 !
5# :%#
%#* 1# #

– #F
• #3*#! -D
– 4 L ##
– @ !% #
MN!
• D
• 6 @#1&!
,- 6
.H ? '.
& & N &N
. =& & ==
= . .M ?N
' & ' .'
? & & ,+
H &= & ;B
M &= = BC
N .= &M B*
=M =. N
O()
. &&= . +
#*5 -

D4!2 3 #+!
Sum of Sum of
Container Terminal
Distance Ship Turn -
Management Policies Ship / Traveled by Around
Bay
Scenario
SCs in Times in
Stowage meters Hours
Config.
Berthing
policy
Scheduling
policy
Stacking
policy
Sum of
Container
Ship
Operational
Profit in
Euro
Scenario 1 BCSP HEF Dest. Random 2760759 44:07:00 € 226 500
Scenario 2 BCSP HEF Dest. Fixed 2698905 42:03:00 € 221 755
Scenario 3 BCSP HEF Ship line Random 3067510 45:59:00 € 223 000
Scenario 4 BCSP HEF Ship line Fixed 3050050 44:19:00 € 217 570
Scenario 5 BCSP FIFO Dest. Random 2781045 43:51:00 € 212 540
Scenario 6 BCSP FIFO Dest. Fixed 2753205 42:45:00 € 200 220
Scenario 7 BCSP FIFO Ship line Random 3090050 44:15:00 € 220 200
Scenario 8 BCSP FIFO Ship line Fixed 3005045 43:22:00 € 206 560
Scenario 9 STTP HEF Dest. Random 2763045 42:38:00 € 198 800
Scenario 10 STTP HEF Dest. Fixed 2725450 41:28:00 € 185 040
Scenario 11 STTP HEF Ship line Random 3070050 43:07:00 € 205 550
Scenario 12 STTP HEF Ship line Fixed 2984655 42:34:00 € 200 250
Scenario 13 STTP FIFO Dest. Random 2763045 42:31:00 € 196 800
Scenario 14 STTP FIFO Dest. Fixed 2704050 41:10:00 € 180 750
Scenario 15 STTP FIFO Ship line Random 3070050 42:57:00 € 205 250
Scenario 16 STTP FIFO Ship line Fixed 2984655 42:07:00 € 198 450
0#1 2 "
1# 23$4%#%1#
! 8
% % ! #
, # 23$4 G" !
! ##
#% #+ %
! #% 0 #
#% !#
##! #
# , %*.*++,-
#% #
1# 23$4 !
#
#% #%
23$4
#1 !
# 0 1# 1#
! #
##%
23$4 #
1 ;% 23$4
N

# ! #; #
% #%
0
# # * # - 23$4
%
# 1
#% #1

;(J((I F : C (4J(8 < : 85A8$J 3 *&.- $#9 ( (
& ! !# 5##
2*!$23/.-;K
5 2 : ;5I5J ( : K;$ < *NNN-
Q38 UF2 .=
##..+.==
F(5;4)2 Q: 54F(4K F *&- 7
3!# ! !!Q
F( +C : 3 J+ : F(( 8+C *&&- 9 ! "
1 (52(&&3 !3 5
2(
254!$J)F *&.- 3 ! 4# &. K L Q
&.2 4 F
2FF(4 *&&-JA5 )#
J;2)45( :255 :3535824$) *&-6
(# Q$# 4.##&M&+&N&
$Q5F5F *NN&- (
5 <
3(4IJ< *NNN-

-3
5## 15 !3! (,# 8%#
! K P'
2!
P&'
P
!
P?
4< F P.
2TF
P'
3, P'
D254!$J)F3 ! 4#&.
K LQ &.2 4 F
5## 1 3

!"
#$%!&!
'
#(
!"! #!
$% ! & "
# ' $ $$($
( ' #
$
) #
! " *
$ +
! #
! ( ,
# !
!
)*!
! "!!! #$% !
# ! ! # ! ! ! #&
! #' ' ! ! #! ! #
###! '! ! &
# !! !!!! !
( #!# #! #! #
! !' ! ! )
! !! (#!! '
" * % # ! ! ! # ' +
# #! !!# # )!
,# #!#'!
# ! ! ! !'
#!#!!,!,!!(
#! , ! ## ! ! ! #
' '! & #
%#!!# # !!! #
( -./0./1 ## 2
!# 3') ! ! ' # 3
!! ! '%4
!# # )( '#
!#!./ !
! ' 2 ! !
!

-+ !#
#! ./ # #! # !
%'##'" ./ !
!#! #!2 !'! !./
! ' # #! #
#!+(!! #, !
##'!! *! %#! #'
' ! ./(!
## #!! ## './
+*!(!
# !!! !6!! 2
' ! 01 #!
./ ! '!0! 7#7##1
! # !!!! #'!
'# ./! !#2!#!! #!
#!! #./ 0 8' 91!
'! -: #!!
! ' 4! #! , # ! '
% ! ! '! ( ! #' ! #
#! ,'!!
! #! ! #
!!! ! ) '# ' ' #
./
( #! ! # 0 '1 # ##
-. /00/ ' ## !
4! ./! !#!# # ##
5

-:+4!! !
- ' # ./ ! % !
! ! ! # ## - ! '
!! #!! # # !
#! #! !!3
# ! #! ! ! !#
! '0 # 1!!!!,
#!' ' # (!! #
'## !# ! !',!
#! ' # !
! & #
-+2! # ##
# ! '! ! ##%
!!#!
###' # #!#!'
!! ! ! !# ./! ! #
;

# ## # ! ! 2
''( ! ' = #'
####! 3
" ##! '+=
3 ' !!
!> #
" ## #! 3
(3 ' ! #
!
,*
#! ! ./ ## # ##! -
## # ! ! ./
#!# &# '-5+
-5+>#!
,*)-. !
#!!!%'+4#
' ! '#!
'#!
!! ! #! #!
!!! ! ##
! !! #./ ./%# #!
> ! ! ! ' ' '
'3(3! #4 ! #
!! '###!'!'
! ! 3 % ! '! #
#! 0;1!!
# (.? 0' ( . ?' @ -#!
* 1 # ( (.? ! ' #! :; % :; A #

#"! 2 ! ! : 0 1 ! ! # < -
!! : # ./
!# ! #(.? #
;C# #"## ) !
#"!B;%:; A
,*+.
( # #! ! !
! # # # # ' + =
! # # 0 ! #
# #! 1# ! # #!
#(#! ! 3! '
! #!)1 /002>!
! !#!
# % #!! # !+
!!
!
#
,#! #
!## ' '
!# ''! !
'#! ' # (.?
' '
,*,-!
D #!# ! +-
! ! #"!'! #
'' !2 ##
#! ! ## ! !
!3 # # = ! !
./! + ! # ! #
# ! !' ' ! ' ! !
'% 012# !#&'
!! 2'# ./
! ! !! ! ! ./ !
#! '3(3 2!
! '# !
# ! 2 ! #
% !' #4 #!!
"# '?!''! #"!
/* 0
2 !' ! ! #!,
! #!2-; ##! !
3(3 ./(#"!#
+ ##! !! ##!#+ (
!# ! ! #
! !#
B

!!# ' ' # ( !!
-;+3#! ./ -

-B+.+H! %
-E+./'#
. ! # #3
!! # #= ''#
!! #!2' ./ !#!
'#-E#!! +
01. #
# ' !#
2 # #
#
0:1. #
G

!+H! !#
01('
(!:## ./
051 ' 3(3
! ' #!## #!! *
!! ! !!##! '
./3# !# !!#! '
!'
' # #! ! !!
./#!2' ( !#!
' # ! ! #
#+
,2
' 3 ! ! ! !
! # '+
# ##! ! !
! ! 6/>-2 086!
/)2 91!-.5/00/
# # ' # ! # ! !
# # !#- ##
! ! ./ ! ( # '
%! 63H 06!3H 1
#!
3
.# ! 3 !
##! '! #%'# # !
# "#! ! ./ ###
' # !
# #! !#!
' % # ' !
!6 #!#! #
./ # # ##!!
!###!! #!!
! ! ###
!! !' #3 !
!!!#! #! ./
!'
./ #
0(
$# ' '' '
#'! # #! ! '
./ ! # #
!!./! #
#! ! ' #!
!# ! ./ #
#!# ! !!#
:C

= '# '#!01./#!
2' ! ! " 063H#63H##./1
0:1 './# !-.5/006
4*. !
# ! ! ! !!
!! !! !!
!#! ( ! '
!!! './
!#!'(620##!# !1
# !# ./ ! '#
% ! !!#' #
!##!#./ !
# !!
-G+2!
-C+D#! #!!
:

( -G !! ./ ! 0 ./ 1
# ! 2! 63H
(3 !! '#'!
#'!!! !
! 2 ! ! !!
' !! # ! # # '
! ! #!! #
-C #! #!
!
5*!6
( !' #! , # # ! !
!! ! !./!
# #!! # ! !
#! # !./ ' !
+#! 2
#!'#!!!
! # ! # ! ./ ##! ##
'!# "#!#
2 #!! '%
!!./ ! '
###!# #!(
!./#!2'
4/3?(I>2--?60:CC1 = $J
-/($>-?/260:CC17 8(!
$?3?**I-/2?3?= (D3(IK?/*?$0:CC51$9 (
2&$($*(5B ##:;:<
$?3?** I -/2?3?= (D3 (I K?/*? $ 0:CC;1 9 (
2H ::CC;4##B:B;
$?3?** I -/2?3?= (D3 (I K> J4 0:CC:1 * 1 $-% :
; # 2+ (D4( 0?1+
*+
.>$ DK(* I *D? I (LK( I *?DD?/ HI = >D- ( 0:CC51 * $
**!!50:CC515/ !##5G;G
::

!!!"#$%& "
!' !!' !()
! "
#
$ $
%&' ( $
"
* ! ! + ! !! !+ %%+ % +# !
+! ! #" %!+ ! !++ ! + #
! !! !#! # %, ! ! # !
! # ! # %!+!# # # )*+," - # !
#!++ #.!! ++!+ #/!+
+!#! !!"0#+#!! !%%
! ! % # ++ ! ! - .//." - .! #
! !++ ! # % +! # 1! ! 2" 3+! % !,!
+ +!! !+#! !!! !+ 4 #
% # ! ! !4 # % # +! ! ! +
+!#!# "+!!!+,+"0123-
.//.%!!#!++%+!+! ! !"
3+! % #!+ % !# !+ % ) #!# .#!" !#
!!+#! )# !"! !# !!+!#
%)+!+"+)!+#%!+
#%!+!!!+!!#!%)+#
! . ! ! ! %# ! # + % ) +# %
" ) ! + % !! 5!+ 3! $45 .//6 !
!+.%)! !!)!
! # !! % ! % #!+ % ! + !
!!6 1! !/ % ! ! ! % !
! % # , !! % ! #! % )
% !2$45.//6 "7!!+!!#+#
% ! # ++# !" 8 ! +
!+% !!!)!# !+!
!!!.++#"
"" # $%
- !+ % ) % ! ! %!+ + ! +! %!"
5+#7 -.//8% !+ !+%)"!+

!!" ) #! % ! % # + + !# ! ! %
!!+!+%).//," + %
)! !%!++!-9:
;: $45.//6%+, %#!"
! # !+ + # !!+ % ! ! %%+ %
+#!+!!+!+%+! #!%)$45.//6"
:;%%+#! !! ###!+!
?@A!!! !+! !!#%!!"0#!
!!#!++"
B%!#!+ ! !+#!++,!!
! ! #" ' +!# !! ! # + #+ !!
#!" C!! . !# !+ # % %
# .+%+##!%+!#!#!
#!# # ! # .+ !+ +#
# #!!#D#!++!4 ()**,-
!+ ! !!# !!+ % ! ! D%D! % !#
!++ + ! % .! # ! % % ! ! ! %
+!%+ #!; &)**+4 ()**,"'!+
% + !+ # !# ! ! !! % ! !+ !
!#! #!++!!!#%% !#!++"+!!##
!!+# !+!+!++%
##+##!#!!!4 (
)**,"
"&' !()
),)%!!+! !#!+!#
% ! # )D, ! +! !" ! + % ! E !
+ ! ! ! " ) .!# !! ="" E< # +
+!=+!

)%+!DD !!#!DD !!#%
#!%%++=.//.")! ##! ! !!! "
7 .//,!)## %# #B8,!#
! % ! ! % ) ! # !!# #
!# + +!" .//, ! ! % ) # ! ! # %
7-+!"3%!!)##! +!! !+!
#"8!!#! %#!7-1+!++2!!+!
# !+!#"1+!2+!%#
# ! # ! " !+ %
+ +!!+ +!+! !!%%% !
!"
"*+
!+%!+ +! +% !!+!!!!
D!+!%+ +!"!!! "
# ! ! + ! "
7-+ +!+!! #!+!! !!! !
! !!#!"+7-+ +!! #!+#+#%
#.+!"0#!+D!+!!
!#!++*#!4!%!+###%#+!7-
+! #!% #!">)**

&
0!1 #2+!.#!%)!O3+!!!!#
!+!%## !%+!!+!!
%+#&.///"@DG ! ! +# %# !! +
! ! %,# +!+ 880 ! ! ! # % DD + +!
+ !!" ) % !! + ! ! %+ ! ! +%+
+ # "
!#!+!!!% #!+
+!%%+"!#9%%+=#+!! !!+!
!!! ! % !#!"8! # !%
+!!%% !!%! ! + #+!!#!
!)+# ! !%%+"+,+!!! !
!#+! !!!BDL++"
) %+ ! # ! ! # ! +%+ +# ! !% !
!!#+ # P ::"%!##!
+%)!! !+!%+"+
%!+!!#! !.+% +%+!+!"
!:!9!%!.+!%% !!#
) !" #! ! + !# + +F
!!%!! #!%)F!%)D!!F%)! !+
% ) F !!! ! !!! % ! )F ! % ! %
)"%+!!!!!+ #
!.+%!+!%+ !%!##!!#+"
!# ! !+ ! %! !+ ! ! !!! %6
%!#+%+%%!++!# !%1>+ !.2!!!%%
!! !!"-! #!)
#!+ ! " -
# ! DD + +! ! !
!+ % ) !++" % ! +# ; ! !
#!! % !!#% !#+!!
>+"
*, -./0$
! ! % !!!%%+%)7-+ +!"
)D7- !!# !%.! #B8#)"G?=

) ! # !++ B8 = !# ,< 1 #% % !
.+!=""+!# !!!# ##7-"0#%! %+)!
1+!# !!2!!%#7-!%%+!
!" ) ! %!+#! ++%# 7- + +! # !
%#:=.//).#+!#+!+!! %
+ +!")+ !) !7-+ +!!+!!%
)!#!!6
)6 # ! +! # ! !! + ! ! ! %
+ !4!IQ J"3 ! ! ! !+! #!
!#7- %!!!!!#%%+"4#!!# !
# !#!!%!#"=9=

*6R#4!##4#! !!!#
!+"=9=N

7- +! #" % !> % ! +#! ! ! + ! 7- +! #
+!!+%+"
*&
)# #!)!%L+ ::9,!#! %##"
+! # 4!4 # % ) ! ! !++
% ! )D% 7- !" 8 4!D4 #
#!+ +!++% !" #!+!+!# %+!"0
)D% + +! ! !+ ! #!
+! #! !" 0 + +! .+! % + % !
!!)D !!"3%+! #!+7-
+#%!!!% !"P+ +!+
+ %%+#+%!!)"++! ###%
! !!+!%+%+=!
!!

%%"3!#+% !7-!#!!!! % #/
+!+% H#+/H!/+!#61%!!#
!+!!!++!#.4#2=9=@

! !!% !#% !!!!++#%)"'
# !#%!!!!! +
! " B! !# ! ! !" ) %# + %
% !M#.#+#!! !M!!!#%)D!"
)#!%D !!!!% !!!!#%
"B!% #%4!!#%#++!!%%!4+! #
" %#+!!+#!+ %+ +!#!! #
! % ! % +! +" +! ) #! # + +! M
!+ !+!#++%#!!!#")# !
+!!!#!>!# + #!+ #*#
!"% !!#%!!#> ! ! %
+ ! !!" +! ) % ! ! !!# #!
!!+%+!!+ +!!+ #+#!!#!
! !H+/"
)!# !.#!!!M!!!!!
! #!M !4! !# !+#!!
=! #! ! ! % # ! !! +! # %#
!!!!! #!!%!4!"8%% !
!!! #!!!!++!"+#!#!
"% !+ !%% !)D
!!% !!#6
)6E!++!+#"4!! "0!+!!!! !"*
!$IU#!UJ")"IQ J0!! OL!!#
"3#+!!!+!$O=9=

!!+ +!%#!!#+!#+#0123.//,0123
;.//8"
2'
))!! #%#!%% !=!
!!#+ #!*#!)% !

+! ! +!!!+!+"(
!!##!!+ +!!+%!"
!!%)D% !
0 )D% ! ! ! !+ + "
!!!! !%##'*L
! ! + + # # # % !
!%!+!!!!! !"0)% !#!
! > ! ,!# % ! !% )D
% !"
B! %,# .+ ! !# ! % )D ! +! %!# =

#+ % ! #O )% ! # + % ! ) +!#
# "
-! #%.!!D%+!#)#!#!
+>+ ! ! ! %!+ +!# ! # !
!+!%%+"
$4
%!+!# % B+!# B! -! !%# !+ #"
0 !# ! ! # !+! ! +! # !+ # !
#3E%B)"0!!# !
% !# # % ! +! # # % #+ % !" !
!!%!#!>+8 #3# +!!% "
,
))P5"7"=::9

6 ""#"++Y+#::9." #
WV7X- B"7"F L'(('5 "0")" =::< 8 R 0!+6 ) ! 3 S"
P!!;;=

The Design of PDE Hull Surfaces Using Genetic Algorithms
Abstract
Tim W. Lowe, Cranfield University, Shrivenham/UK, T.W.Lowe@cranfield.ac.uk
In this paper, the automatic generation of a range of flat-sided hull forms which satisfy constraints
on various primary and secondary geometric parameters is considered. The curved
section of each hull surface is generated using the PDE method forming surfaces as solutions
to a partial differential equation with appropriate boundary conditions. The method enables a
wide range of smooth surface shapes to be represented using relatively few design parameters.
The design parameter space of the hulls is searched using a genetic algorithm to locate regions
satisfying the geometric requirements. The designs found could be used as starting points of a
functional design optimisation as demonstrated in an example.
1 Introduction
The preliminary stages of the design of a new vessel often involve specifying values, or a range
of possible values, of various global geometric properties of the hull. These properties, often
known as form parameters, include the primary dimensions of the vessel, the displacement,
the positions of the centres of buoyancy and flotation and various non-dimensional quantities
such as the block and water-plane coefficients. Whilst some initial work can be performed in
terms of such measures, it soon becomes necessary to find a hull surface having these desired
characteristics. Ideally, this form should be as close as possible to the final hull design to
minimise the overheads arising from subsequent design modifications, hence supporting a timely
and economic design cycle. The hull form should also be represented in a manner consistent
with the computer-aided design tools currently used.
The two possible approaches to the determination of such forms are to distort an existing hull
using, for example, Lackenby (1950) transforms or to generate a completely new design from
first principles. The latter approach has the advantage of not restricting the hull found to being
close to an existing form thus permitting the generation of novel, possibly improved, designs.
The interactive manipulation of geometric models to generate new hull forms having specified
form parameters, for example through the movement of surface control points, is however, very
time consuming. Recently, several automatic approaches have been suggested.
Peacock et al. (1997) obtain a hull having specified values of certain form parameters by first
finding B-spline representations of various traditional characteristic design curves, for example
the section-area curve or the design waterline, which correspond to the required form whilst
simultaneously maximising a simple measure of curve fairness. This is achieved using the decision
support problem technique. A similar process is then used to form hull sections based on these
curves.
Characteristic design curves are also used by Harries and Nowacki (1999) who again generate
them by maximising a measure of curve fairness subject to the satisfaction of constraints on
the values of specified form parameters. In their work, this is achieved using a Newtonian
optimisation scheme and the constraints applied through the use of Lagrange multipliers. Harries
and Nowacki use these curves to obtain hull sections and hence a B-spline representation of the
hull itself, by again maximising a fairness measure. In later papers, for example Abt et al. (2003),
the geometric generation of hull forms using this method is combined with the optimisation of
the hydrodynamical properties of the vessel to find functionally optimal hulls.
Birmingham and Smith (1998) by-pass the use of traditional characteristic curves by directly
seeking the control points of a B-spline representation of the hull surface that possesses the
136

equired values of the form parameters and maximises a measure of fairness. This is achieved
using a genetic algorithm (GA) to search the design space.
A similar GA search is performed by Islam et al. (2001). The GA used is initialised with
random variations of a single hull form matching the required primary dimensions, instead of
the more usual general random population. This form is based on historical data and adjusted
to the specific problem being considered using a neural network. The GA is used to find a
hull matching the required secondary parameters. Hull fairness is maintained by fairing each
individual in each generation of the GA before its merit is evaluated. This seeding of the GA
improves the speed of convergence of the algorithm, but may also prevent the discovery of forms
far removed from the base hull since the variation in the initial population is reduced.
Kawashima and Hino (2004) take a different approach to the problem and represent the hull by
the set of curves bounding the surface together with lines defining the hollows and ridges within
it. Sequential quadratic programming is used to vary these lines to find a surface matching the
required form parameters. This procedure starts from either an existing hull form or a set of
basic hull lines drawn from a database.
All these methods deliver a single fair hull form satisfying the design requirements. However,
in general there is no reason to suppose that there exists only one hull possessing the desired
properties. Indeed, the fewer restrictions placed on the hull at this early stage in the design
process the larger the number of possible hull surfaces that satisfy the requirements. Lowe
and Steel (2003) used a GA was used not to seek the single form that possesses the required
characteristics and maximises some measure of fairness, but to search the design parameter
space for those regions which contain hull forms satisfying the design requirements. Surface
fairness was ensured by means of the method of surface representation used, namely the PDE
method, Bloor and Wilson (1990a). By generating surfaces parametrically as the solutions to
an elliptic partial differential equation, a smooth surface without superfluous humps or hollows
is guaranteed.
This approach to design generates a range of possible hull forms that can either be taken as
the basis for subsequent geometric modifications by a skilled naval architect or used as starting
points for an automated optimisation of the vessels functional properties, for example wave
resistance, Lowe et al. (1994), Markov and Suzuki (2001).
This previous work is extended to the design of flat-sided hull forms satisfying geometric requirements
given in terms of either specified values or a range of permissible values of certain
form parameters. The use of the designs found as starting points for a hydrodynamic design
optimisation is also illustrated.
2 Hull generation
The geometry and main dimensions of the hull forms considered in this work, together with the
Cartesian coordinate system used, are shown in Fig.1. The hulls considered are symmetrical
port and starboard, and hence only the starboard half is labelled. The region within the closed
curve BCDE is flat. The remaining curved surface is generated using the PDE method.
The length of the deck is denoted l d and its beam b d . The deck parallel section (BE) is of length
l dp and its mid-point positioned a distance x dp aft of the bow. Similarly, the lower boundary of
the flat side (CD) is a distance d f below the deck, of length l f and its midpoint positioned x f
aft of the bow. The keel-line (KH) is of length l k , centred x k aft of A. The draught of the hull
is denoted T and the freeboard f. Note that if either of the length (l f ) or depth (d f ) of the flat
region of a particular hull is less than some small tolerance, the flat region is omitted on that
vessel.
137

z
✛
✻
l d ✲
y ✛ l dp ✲
A ✒ B
E
✲ x C ✻ ❄
d f D
F
G
✛ l f ✲
b d
f ✻
✠
❄
✻
T
❄
✛
K J
l k
I H
✲
Fig.1: Hull geometry
The PDE method generates surfaces parametrically as the solution to an elliptic partial differential
equation (PDE). Information is specified around the edge of the domain of solution (the
surface boundaries) and a PDE solved to generate the surface in the interior. Using an appropriate
parametrisation of these boundary conditions, a wide range of hull forms can represented
using relatively few design parameters. This property is advantageous to any automated search
of the design space, since it reduces the dimension of that space.
In the current work, following Bloor and Wilson (1990b), the hull is generated in its two symmetric
halves. Considering the starboard half of the vessel, the curved surface is bounded by
the deck and so-called flat-of-side curve (ABCDEF G), the bow and stern profile lines (AK and
GH) and the keel line (KJIH). If the surface is represented parametrically as
X(u, v) = (x(u, v), y(u, v), z(u, v))
where 0 ≤ u, v ≤ 1 are the surface parametric coordinates, the boundaries of the parametric
space can be identified with the boundaries of the curved hull surface, Fig.2. The u and v axes
are oriented such that u runs from the deck to the keel and v from bow to stern.
0
deck profile
and flat-of-side
A B C D E F G
1
✲ v
bow
profile
stern
profile
1
K
J
keel
I
H
❄
u
Fig.2: Surface parametric space
The upper boundary curve (X(0, v)) is formed from:
138

• A cubic parametric curve AB in the plane z = 0, having tangent at A in the direction
(α db , β db , 0) (and thus a deck entrance angle of 2 tan −1 β db
α db
) and tangent at B parallel to
the x axis with magnitude t f
• A quadratic parametric curve in BC in the plane y = b d
2
with horizontal tangent at C
• The straight line CD
• A quadratic parametric curve DE in the plane y = b d
2
with horizontal tangent at D
• A cubic parametric curve EF with tangent (t a , 0, 0) at E and (0, t t , 0) at F
• The straight transom line F G of length bt
2
The lower boundary curve (X(1, v)) is the straight, horizontal keel line KH. The bow profile line
is generated from a cubic parametric curve with tangent (α db , 0, γ db ) at the deck and (α kb , 0, 0)
at the keel. The stern line is similarly generated with tangents (α ds , 0, γ ds ) and (0, 0, γ ks ) at the
deck and keel respectively.
To provide more detailed control over the form of the surface, in addition to these positional
conditions, the tangents to the surface ( ∂X ∂X
du
or
dv
) at the boundaries are also specified. These
vary smoothly around the surface boundary between the values illustrated in Fig.3. The surface
tangent along the keel line is constant between J and I, a length denoted l kp the midpoint of
which has coordinates (x kp , 0, −f − T ).
β db
B
E
β ds
A ✒ ✲ C
D
F
α db ❄ ❄ G ✒ ✲ γf γf α ds
❄
γ ks ❄
γ db ✒ β kp
✒ β kp
✒ β
✛ kb
✻ γ ds
α kb
K J
I H
Fig.3: Hull surface tangents
The curved part of the hull surface is obtained by solving an elliptic partial differential equation
subject to these conditions. Since conditions on both X and its normal derivative around the
boundary of the domain of solution are specified, a fourth order equation is necessary. As in
previous work using the PDE method, the equation used to generate the surface is
(
∂
2
) 2
∂2
+ a2
∂u2 ∂v 2 X = 0 (1)
The parameter a is known as the smoothing parameter and affects the extent of surface over
which the boundary conditions have influence. Varying a changes the “fullness” of the surface:
large values of a give a surface lying close to the centre-plane of the vessel (whilst, of course,
satisfying the imposed boundary conditions) and small values give surfaces that are far from it.
In the present work, equation (1) is solved numerically in the u-v parameter space using the
finite difference method. A solution grid having m points in the u direction and n in v is taken.
The banded nature of the discretised system of equations permits efficient sparse matrix storage
and solution methods to be used.
139

The hull geometry is thus characterised by the 29 design variables l d , T , f, b d , l dp , x dp , l f , x f ,
d f , b t , t a , t f , t t , l k , x k , l kp , x kp , α db , β db , γ db , γ f , α ds , β ds , γ ds , α kb , β kb , β kp , γ ks and a. Note
that not all combinations of values of these parameters lead to valid hull forms. For example, it
is necessary that the length of parallel deck side (l dp ) is not greater than the length of the deck
itself (l d ), and that it does not protrude beyond the bow or stern. The full set of constraints the
parameters must satisfy to give a valid hull are:
x dp − 1 2 l dp > 0
x dp + 1 2 l dp < l d
x f − 1 2 l f > x dp − 1 2 l dp
x f + 1 2 l f < x dp + 1 2 l dp
x k − 1 2 l k > 0
(2)
b t < b d
x k + 1 2 l k < l d
x kp − 1 2 l kp > x k − 1 2 l k
x kp + 1 2 l kp < x k + 1 2 l k
3 Geometric design space search
The geometric requirements of the hulls sought consist of both specified values and permitted
ranges of various characteristics. The example requirements considered here are taken to be:
f = 1 2 T (3)
T < 15m (4)
V = 26000m 3 (5)
1 < b w
T < 4 (6)
0.55 < c b < 0.65 (7)
0.75 < c wp < 0.90 (8)
1% aft of midships < l cb < 1.5% aft of midships (9)
|l cb − l cf | < 0.5% l w (10)
140

0.3 < A f
A s
(11)
where V is the displacement of the hull, b w the waterline beam, c b the block coefficient, c wp the
water-plane coefficient, l cb the longitudinal location of the centre of buoyancy, l cf the longitudinal
location of the centre of flotation, A f the area of flat side, A s the hull surface area and l w the
waterline length. The constraints were chosen as being typical of a generic cargo vessel. The
last (11) is included to ensure the hull forms generated do indeed contain the flat side sought.
The individual form parameters are calculated by interrogating the surface X obtained by the
solution of equation (1).
Note that the first constraint (3) can be satisfied by simply removing f from the list of design
variables, its value being determined by T . This reduces the number of active design variables
to 28. Hulls satisfying the remaining constraints ((4)–(11)) are found by searching the design
parameter space using a genetic algorithm.
GAs are heuristic search methods inspired by the processes of Darwinian evolution and natural
selection, Holland (1975). An initial randomly generated population of individuals, in this case,
a collection of hull forms generated from random values of the design variables, “evolves” over
time by seeking to optimise some merit function through the use of so-called genetic operations.
GAs have been described widely in the literature and the method used here is described in Lowe
and Steel (2003). For completeness, the method may be summarised as follows.
The “fitness” of each individual in the population is first assessed using a measure of merit, F .
Here, this is taken to be the average of the square of the amount by which each requirement is
violated:
F = 1 7∑
c 2 i
7
where c i is size of the violation of constraint i. Low values of F imply a high hull fitness.
Individuals are then randomly selected to form an intermediate population, with the selection
being biased towards the fittest individuals. Each of these individuals may undergo a genetic
operation, the probability of selection for which is a parameter of the method. Here, two
operations are used: simple crossovers in which the values of the design parameters subsequent
to a randomly selected parameter are swapped between two individuals, and whole cross-overs
in which two individuals are replaced by two new individuals lying on the line joining their
corresponding locations in parameter space. Finally, the resulting designs are subject to random
mutations in which one parameter value of a selected individual is randomly replaced with a
value from the permitted range of that parameter. This process of forming a new generation of
individuals is repeated a specified number of times.
In the present study, it is not a single hull form that satisfies the imposed constraints that is
sought but a range of hulls representative of the regions of parameter space in which suitable
designs can be found. As the GA progress, every hull discovered that satisfies the requirements,
that is, has a merit value less than some small tolerance, is thus recorded.
Due to the stochastic nature of the GA, different results may be obtained each time the search
is conducted. For this reason the whole process is repeated a number of times to sample the
solution space more widely.
A consequence of representing the individuals within the population using values of the design
parameters described in the previous section is that many of the hull forms considered will
violate the geometrical constraints of equation (2). In the previous work, this was accounted
for in the design process by assigning an artificially low fitness to any forms that violate the
conditions, preventing the GA selecting them for the next generation. This, however, degrades
i=1
141

the efficiency of the method by effectively reducing the variation in the population from which
individuals are selected and modified. In the current work, search parameters are used that are
related to the geometric variables of Section 2, but chosen in such a way so as to guarantee
the satisfaction of the constraints of equation (2). For example, instead of randomly specifying
the length of the parallel deck section, l dp , the fraction of the deck length that is parallel is
given. Undesirable hull forms, such as those whose sides descend below the level of the keel
before turning to meet this boundary are, nevertheless, prevented by assigning an artificially
high merit function value to these individuals.
The search space is non-dimensionalised with respect to the length scale of V 1 3 , this being the
only constant length scale of the problem. The limits of the search space are taken to be those
for which the non-dimensional search parameters lie between 0 and 1, except for a and the
non-dimensionalised equivalents of l d , b d and T . To permit hulls of realistic dimensions to be
accessible to the method, l d /V 1 3 is allowed to take values in the range 0 to 10, and b d /V 1 3 in
the range 0 to 2. The range of T/V 1 3 is specified so as to ensure satisfaction of constraint (4).
The smoothing parameter, a, is permitted to vary between 0.01 and 1. Although hulls can be
generated with a greater than one, as explained in Section 2 these have a surface that remains as
close to the hull centre-plane as the boundary conditions permit. Such forms are not desirable in
this search and are excluded by this choice for the range of a. This again improves the efficiency
of the method by reducing the size of the search space. The lower limit of 0.01 is necessary to
avoid numerical difficulties that are encountered at very small values.
The process described above yields a large number of hulls which possess the desired geometrical
characteristics. Due to the nature of the GA, many of these hulls will be similar, or indeed
identical, to other forms found. A clustering algorithm, Thorp and Pierson (1998) is thus used
to identify groupings of the hulls found within the parameter space, and to locate a single design
representative of each of these groupings. It is these designs which are characteristic of the
various forms found that are presented to the user as candidate hull designs.
4 Results
The finite difference mesh size used in solving equation (1) to generate the hull surfaces was
m = 20, n = 100. Preliminary computational experiments indicated that such a mesh permits
the geometric parameters of interest to be calculated within 0.3%. The computational time
taken to calculate the surface and evaluate the properties of an individual hull form was typically
0.02 secs using an Intel Pentium 4 Linux workstation.
The genetic algorithm used 100 individuals in each population and was run for 100 generations.
Any hull form with a merit value of less than 10 −6 was recorded as satisfying the constraints.
This process was repeated 5 times before the hulls representative of the design clusters found
were identified.
A total of 2656 hulls were recorded as satisfying the geometric requirements which may contain
multiple instances of various individual forms, and 6 cluster representatives were identified. The
entire process took 21.0 minutes.
Figs.4-7 illustrate a selection of the hull forms found. These show the body plans for each hull
together with a perspective view superimposed with hull sections and buttock lines. Whilst
the perspective view is scaled appropriately for each form, the scale used for the body plans
remains the same in each figure. The primary dimensions of the forms presented, together with
the values of the constrained quantities are given in Table I.
A range of hull forms have been obtained which are representative of those regions of the
142

design parameter space satisfying the design requirements. The small violations of a few of the
constraints seen in Table I are a result of the GA being governed by a merit function F which
is the average of the individual constraint violations, and the fact acceptable designs have been
recorded on the basis of small values of this function. An alternative method would be to accept
a design only if each constraint was individually satisfied. The errors introduced due to the
scheme used are, however, small.
Fig.4: Hull form A
Fig.5: Hull form B
Fig.6: Hull form C
Fig.7: Hull form D
143

Table I: Geometric properties of the designs presented
Hull A Hull B Hull C Hull D
l d (m) 123.8 187.2 193.6 230.1
l w (m) 108.9 179.1 179.6 224.1
b d (m) 31.2 21.5 24.0 17.7
f (m) 6.3 5.9 5.5 5.0
T (m) 12.7 11.8 11.0 10.0
V (m 3 ) 25968 25996 26020 25995
b w /T 2.46 1.82 2.19 1.75
c b 0.603 0.572 0.549 0.652
c wp 0.880 0.889 0.902 0.855
l cb (% aft of midships) 1.08 1.28 1.19 1.24
|l cb − l cf |/l w (%) 0.40 0.48 0.31 0.23
A f /A s 0.31 0.30 0.30 0.30
Across the range of designs found, many of the constrained parameters take values throughout
their acceptable range. The exceptions to this are the water-plane coefficient which tends to
take a value in the upper-end of the permitted range, and the ratio of the area of flat-side to
the total surface area of the hull which is close to the minimum permitted value in each case.
5 Functional design
The hull forms presented above were created purely on the basis of satisfying the imposed
geometric requirements, with no regard for the hydrodynamic performance of the vessel. This
aspect of design can be addressed by using the forms found by the GA as starting points for a
deterministic optimisation scheme to improve hull performance. As an illustration of this, the
wave resistance of hull form B has been reduced using a Newtonian optimisation scheme, namely
the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. The search was conducted using the
same scaled design parameters and parameter space limits as used for the GA. Constraint
(3) on the freeboard of the vessel was again satisfied by removing f from the set of active
design variables and constraint (4) by the prescription of limits on the permitted values of the
scaled design variable related to T . The equality constraint (5) on the hull displacement was
satisfied by restricting the search to being over that surface within parameter space on which
the displacement takes the specified value. This was achieved using gradient projection. The
remaining constraints ((6)–(11)) were incorporated using penalty methods. Further details of
the methods used are described in Lowe (2001).
The functional design search was guided by the need to reduce the wave resistance of the vessel
at a design speed of 20 knots. In the present work, this was estimated using thin-ship theory,
although a more sophisticated method could easily be used. Table II gives the parameter values
of the design obtained (together with those of the initial form taken). The wave-resistance
coefficient c w was defined with respect to the water-line length of hull B:
c w =
R w
1
2 ρU 2 l w (B) 2
with U being the vessel’s speed and ρ the fluid density. The resulting form is illustrated in Fig.8,
with the body lines of both this and the initial hull being shown in Fig.9.
The design optimisation reduced the wave resistance of the hull, as estimated by thin-ship theory,
by 90% whilst maintaining the required geometrical characteristics. This large reduction in c w
144

is partly accounted for by the inappropriateness of the initial hull form B to the specified design
speed, Fig.10 (where the Froude number F n is also defined in terms of the waterline length of
hull B). The functional optimisation has increased both the length and the draught of the vessel,
both properties known to reduce wave resistance. As a consequence of the constraint on the
displacement of the vessel, the beam has correspondingly fallen.
Table II: Hull parameters of the functional optimisation
Design Initial Final
(Hull B)
l d (m) 187.2 198.0
l w (m) 179.1 186.2
b d (m) 21.5 18.6
f (m) 5.9 6.7
T (m) 11.8 13.4
V (m 3 ) 25996 26000
b w /T 1.82 1.39
c b 0.572 0.560
c wp 0.889 0.810
l cb (% aft of midships) 1.28 1.10
|l cb − l cf |/l w (%) 0.48 0.34
A f /A s 0.30 0.35
c w (×10 −3 ) 2.156 0.212
Fig.8: Hydrodynamically optimised hull form Fig.9: Lines of optimised hull (—)
and initial form B (· · ·)
3 x 10−3 F n
2.5
c w
2
1.5
1
0.5
0
0.15 0.2 0.25 0.3 0.35
Fig.10: c w vs. F n for optimised hull (—) and hull B (- -). The design speed is indicated.
145

6 Conclusions
The use of a GA to locate regions of design parameter space containing hull forms having
specified geometrical characteristics has been demonstrated. An example set of geometric requirements
was used, consisting of both equality and inequality constraints on parameters of
interest. Further constraints are easily incorporated to remove excessive design freedoms, for
example by restricting the length or beam of the vessel.
The hull forms considered were generated using the PDE method. This permits a succinct parameterisation
of the geometry hence reducing the dimension of the design space to be searched.
The PDE method has the additional advantage of generating hull forms without superfluous
surface ripples. Surfaces obtained using this method cannot, however, be directly imported into
current computer-aided hull design packages. This can be circumvented by representing PDE
surfaces in terms of B-splines as described by Bloor and Wilson (1990c).
The designs discovered may not represent every region of parameter space that satisfies the
design requirements; further designs may be discovered if the GA was run more times. The
forms identified are also restricted to those hulls representable by the PDE method using the
boundary conditions described. This, nevertheless, is seen to be a broad class.
Whilst the GA has effectively searched the design parameter space for those regions of
interest, the disadvantage of this method is the number of individual hull designs that must be
considered. Each of the 100 generations of the GA required the calculation and interrogation
of 100 candidate hulls and this was repeated 5 times. Since the computational time required
for the calculation of the hull surface and its geometric properties is small, this is not too
burdensome. However, the use of such a method to optimise more computationally intensive
merit functions, for example wave resistance, would require significant computational expense.
A more computationally efficient approach would be to use the GA to find those regions of
space containing valid hull forms, and beginning a deterministic functional optimisation scheme
from such points. This approach has been demonstrated above.
Acknowledgement
The author would like to thank J. Steel for writing the genetic algorithm library used in this work.
References
ABT, C.; HARRIES, S.; HEIMANN, J.; WINTER, H (2003), From redesign to optimal hull
lines by means of parametric modeling, COMPIT’03, Hamburg
BIRMINGHAM, R.W.; SMITH, T.A.G (1998), Automatic hull form generation: a practical tool
for design and research, PRADS’98, The Hague, pp.281-287
BLOOR, M.I.G.; WILSON, M.J. (1990a), Using partial differential equations to generate freeform
surfaces, Computer-Aided Design 22/4, pp.202-212
BLOOR, M.I.G.; WILSON, M.J. (1990b), Geometric design of hull forms using partial differential
equations, CFD and CAD in Ship Design, Elsevier, pp.65-73
BLOOR, M.I.G.; WILSON, M.J. (1990c), Representing PDE surfaces in terms of B-splines,
Computer-Aided Design 22/6, pp.324-331
HARRIES, S.; NOWACKI, H. (1999), Form parameter approach to the design of fair hull shapes,
ICCAS’99, Cambridge, MA.
HOLLAND, J.H. (1975), Adaptation in Natural and Artificial Systems, University of Michigan
146

Press, Ann Arbor, MI.
ISLAM, M.M.; KHONDOKER, M.R.H.; RAHMAN, C.M. (2001), Application of artificial intelligence
techniques in automatic hull form generation, Ocean Engineering 28, pp.1531-1544
KAWASHIMA, H.; HINO, T. (2004), A hull form generation method on initial design stage,
PRADS’04, Lubeck-Travemunde
LACKENBY, H. (1950), On the systematic geometrical variation of ship forms, Trans. Institution
of Naval Architects 92, pp.289-316
LOWE, T.W.; BLOOR, M.I.G.; WILSON, M.J. (1994), The automatic functional design of hull
surface geometry, J. Ship Res. 38/4, pp.319-328
LOWE, T.W. (2001), Variable-complexity hydrodynamic optimisation of a yacht hull, Mathematical
Engineering in Industry 8/3, pp.253-274
LOWE, T.W.; STEEL, J. (2003), Conceptual hull design using a genetic algorithm, J. Ship Res.
47/3, pp.222-236
MARKOV, N.E.; SUZUKI, K. (2001), Hull form optimization by shift and deformation of ship
sections, J. Ship Res. 45/3, pp.197-204
PEACOCK, D.; SMITH, W.F.; PAL, P.K. (1997), Hull-form generation using multi-objective
optimisation techniques, 6th Int. Marine Design Conf., Newcastle, pp.405-419
THORP, N.A.; PIERSON, B.L. (1998), Cluster analysis after a partial genetic algorithm search
Engineering Optimization 31, pp.225-246
147

!"#"$%&'(
! "!"#"$$%)
#
! "#
$ %& '
( ( '
) $ %
( )
*+
"
$%
*+ *
* * * * * *
**
,*
*+ * *
(** (*
* **
* '
* * * ** *-
*
&
. ** /%01* *
2* %0, ) -.//013
) -23301*** 2
, %02
3** * * *2
, ***
( *' 4 5 *-
**
6 ( 7 )) ) 3 *
4% 85960!3 :,
*((*

2 *: * *
*!*' **
(< -23321
3*'+ */=1
*' *8* *
,*<
*7*/=1
* *
*&$ -23341
, 7%02
• 62
) *: *
* *
+** +/,1** *
' ( *3,( +*
* * > ) ? />)?1
* -23341 * -23301 *
(*:
*
• 02
3** **: * **
* *
** *3 * ***
* * *** ***
** ) -23301 3( . @60 ?"
)*>)?***( **
( * * *: : (
5 -23301
, #%02
) * * ** '
* * *3
+(*
*
!+ >)? *
* *3 *
< * *
* -23341
'"
'$"()*+,
* ***
!"# " $ $% > !"# " 0 $% *
"*/ 1
$>A,< *
( #.
+* * ,
< *( * *
+ : * <
* *' * +
**/ *B$*1
;

2*!"#$)
>A2$CB# -23341
'&"
'&$
3* * */
##, < *1
, ( / *1
* 2 * * *
( * '$
* ( * * 9 ,(
* < *.
* * * 4 *5
2* ,
4*5
*
< *2##,
*
CB

! + * *+ + *
* < * * * * (
* < * A !
* * *
'&& +
. * * (*(24'59
( * * *
** 4* **5**
*/4'5,1( D
'*
4'5*E ***'/
1 * (
*/4*54*5,1
* 4( 5 <
.
( > ' *
* /
(1) 2*
/*1* *'
E *
* / '1 * *
/ 1 * ** * 3* *
** ' + *
>D *
Current production planning
Machined parts
Machined parts
to assemble at
shipyard
Production
planning
Drawings
BOM’s
Plan and
coordinate
machining
Material
request
Planned &
resleased
job
Collect
material
Controled
parts
Planned &
resleased
job
Machining
Machined
parts
Assemble in
machining
centre or
Store parts
Machined
parts
Control of
machined parts
& X X
Machined parts
for third parties
Outsourced
machining jobs
Change of job and/
or planning
>D20*
** 4* **54'5,<
("-( /
1 * * /
F 1
( *
*!
) <
** ( ****.*
+* * (
A 3*+*
D ?' *
C

'&'
* * *
* * *
2
* 2
, !*2
• 3** *
• **
•
, ! *, 2
• +* * /1( <
( * (
3 * * ** ' 3
* 0,7 + *(
', C /9)1**
-
-$"(!
$,+*** G
* 4 **5 ,, H ,
* * ( 0,7 ,
* (**
( +* *,4 5/4'5
4< 54*51 >*(#DAA
*3 6& 7
/ 14'5/*
(,, 1. *
6%7>CC
.',./..12.',
! *
!..**/ 1
/1.'/A1
.'
' !', *
* < (
*+ -233.1
C 9)29) 2+* !
* + /0,71
45* + /
1) < (4'*5 +
/ 1E ****
G * !9>B!9>D
5 *-23301
H 3+* < ,, *>D
>
3 / 1! **
*
CA

20 *
. 4*5 *
6%7 >C >2*
' 4
*5 ; !4'5< 6* 7>C 7
4'5( 2*
B (** 'E /1
( *4* 5*'
* *
-&%
* * ** A /
*( 1
*!* **
0,7*
* ** 2
, 7 2 * * * *
, 7/**12< **
, 7/*'12
* **'0 /*1
* *' 3
< * /1
; 0 *2*
>C
B * /*
I* * I* *1
$* * 2/*1(
( * ( ,
* (* **4* 5*
*
A . * * ' /*
*1
CD

C2J *>
>C2J2* (*
>C2* **(/+,+2,+ *KLM1
!* * *2
, !** ** ' +*
, !'
, ?*'
, 9 *
, #*
, % * * 4*5
, * *
C

-'.
-'$.
!* * 2
, 3*****
, 7 **/*
*1
, 7 *'/*
1
, * / * 1
, . ***(
>G2? *2'
>G2?2(+*
-'&
* (**/0,7
9+, >C : *
* * *2 0) 7' >
*/4'5,1'
' (?3*
CC

* *( **>G+
*/4*5,1* **
* >G ! * *
(
-''
! * * ** * *
* /1!(+**
*
$ *'
, * !
*<
< < *
3 *
(* *
#< *
*
/ !
3( * **
*
/$#!
> (
* ** * *
* >*'
*
, , (
) * (
*< :
>)?* -23301 787
" D &$ -23341 > (*
*!#, *!
*!#, * (
* /701/8 23391
* **
/&#+ .
) * : < **
!#,**. * *!"#$
* **.
*** .
, ,
* * * *
*2 ( * * * /
(**-*1
D 787" 7 ,7,8 " * * *
< * N * *
*
CG

* * 0 *
4* (5 * * *
( * 4*
5* , (
* <
/'0
> / 1 (
$* * *
*
* * (
! ,
+*
* '
"+* 4*5
* *:$
4
*5 *
# < *(
* (
1
7 ****< *
** *+ /* 1* *'
* $* ( *
** * *
* > +* *
< ( (!
* ( * *<
*
E * ***
< *
0 ** * +*
**
"(
* (* !#,**
$*** !
**
( * *
*** **
367"9"O?P3O!9"!)OE 3?@#/ABB1# %
9 *)* 8*#, 6
367"9 " /ABB1 # % : ) ;
* % / 1
CH

$3667/ABB1 ! *
*2 (Q*
?P3O!9"!)OE 3?@#/ABBC1 -1 :
( #.07!ABBC"
!"#".663/ABBD1 93.0 * !
*2 R* CBR*
&$)!/ABB1! ?$ @
7.7&. 9)O $3863#" # /ABBD1 ! %= # *
*2 *% R)**
)9!"398 /ABBD1 :
< #.07!ABBD,H0ABBD" **ABD,AB;
)9!"398O"9!9030/ABB1*( ? "3)33
ABBB**AC,AH
)"! @?O 699 &&O E .. @"O &!0 E O 699 @"O &!0 )"O 738& @PO P!0 "
/ABB1) % * & & * , * @
)*7 ABA**H;,D
8.P0!/ABBA1* $ 2. E
@ ABBA**,A
C

!"# ! $
$ $%
$ % &
!
! "# $ % &'
! "#( ) %) %
*+
%%(& ),-.
),-%%%
/))( ))
! "# % % ! '001# 2 *
"32%)()) )
% / () )
)))
"
"#$$
4))
% .
)) $
)))()
) )).
%%) *
%
56) )
'56))

89$)4
++. +)
.( ) .
% /.
.%4%). +:
89$4:))
""%$ &
))'/
) ( )%
%; () )
; )
"- %
);%)
%.8)
) ) ); %
4%%
) /%.
"'
) * 1 % ) % % %.
%. 6..
% . ) ( ? )
.
! "#
)))%)@5
• % 88)%%
• %.).
%)
• % %%
• AA )
) ,-
• %,B-
15B"C! "#
D5
70

*5! "#
?) E0 B 6BB
+ '70 7
$. 7 D
&1 '1
6% 0D07 " '00&0.F
) ''. " '1
? 100
6 'D&
'# $ $
4 % %.%) %
) ( % ) /
%))A
)*%)%*G7D
,'000-5
B6%6 5 1
B 5 D
G.5 D
"% (4
))%A
%.%%>D
)%)
% )
%)
)
) %. 4 )
%%/%
. ) (
%% )(5
• >(5 A )' )1
HD HD ) H7 H 2
• B(5 ' 1
%)
*);%
;% ) ))%
7

(")
+ %) )
) I.*/
% / % (
/%$%
.%(5*/ '
,-1 D ,-
%
5628"$.
(
* ! !+ !
4)%)) ) .
)) %
4) ;
)%)
) %%.
4(7% 4(E2A
/ )I(02A
('2A7 ) ) %)
% )J())
& ("
%).EED
H(,'1- 4
%,-.1%
M.E. Vib 5: Cylinder Station fore
y
75"
&5 ))
),-
7'

) % H.1%
)
%)%%7 H
% ()) 1
*%) I
) ) 4 ) %
; /
*%
)()*
% )(
*)%H)
/I
*
)% %
E5.
5 *
% 7
)J.%
(%)))
) )) >"
)@ 2%)
% ))%
%%)
%)
, ! -!
, -
@)
%.)@A/)
>"%%
%
. %
%) %
71

," -!!!!
) %/
>
)
))% . ;)% 5
• 4 5 ) .<
2
)
%
• F 5 2 %
) (
• F 5 %
) )
%
4)%%.
;%
*)%%
$ ) % ;
)0 %%5
% %7
05>
%
4
% . ! "# 4 %
/
( ))
),-)/ )0'2A
))
%% )'10
%%'0% %
' ) ) . 11
)I% @
7D

.4))%
'07
56
'56 .
(
* 2%
)) %) ) ))
) 4 )
/)% )
4))%
4 4
)%%
.#!
@. (4
% )).
) ) )
) )<
)% (
)/>)
) / %
)(
/$)(
$ %
7

!
"# !"
" !"
$%&
#$ %#&
$$ $$&$ # '
% '$ % $ $ &$($ &% #
%& ) * (
$+ '$ $$,
$& #&& &
( & -$ + .% $
% !"###$ !"##%$ !&'''$ *
$ & & $$% & &$
#& %$$ &$ $$!
% # %%$$%$ &$
$ %() !&'''$
/$% $(&&$ *%%&"' !
"-' %0
o 1&
o +&& &2
o * &&$%$$2
# ' & ( &&$
&3%,$ & ,$
$ ( $$
$$% #&,&$$
$ & $% *
$$%,$ $%
&-$+.%%
-$ $($ $ $
$%$% * $ &$%
% !&'''$
# $% $% $( &&$ & $(
& & && &&$#
$ $ $&$$% & %$ !
%( !&''*$( !&''*$)!"##+$3 $ %
/. &$% $$ $
$ &% &&$!"###$

5 $. /$6,- !
, &'$ 1 &
$ '$$ $$&$7$!
%$( &&$%$ !
6,- - &&. /$%#$ !
,$ $ $% '$ !
'%
-%$%,&,$ $%. /$
6, - $ 3 $ # &
$% $$%$& $% /.$
$ , # &%&
7% , !&''&$ # / 1 % - $ /
.$ % $ % $ %
!"##%$#-$- & 0
o #/1 %- $ 8/ 9
$ & %
o #6*&- &$% :3 !
$;:-%;:# ;# /.$
($'&$$!
o #-$%- %&
$%&&& 7$!
$ $ %%%&
#6,- & -$- $$
# $$ % %$ &,$0
o &
o 3 %&
o 6&&
# $ $ $ $
7 %8%$%&$%$9 "
8 9 8% $%9 # $
$ ' 7%<
# $ % /.$& # &
$ & $ #
$ $$%&& " &
% &" # &,%
3%$ &" $ $ % %$
$ # & 3$% *
$% & $ &%" $%$
/1 %- 8/.$9
-$-
/8/9
1 %-
6*&
-
-$%-
6
+$$
6,-
/+$$
.+$$
3
-$%+$$
6,+
7%05 && $%$$
4

! % , !"##-$ , !"##+$ 5 $% $
$$&$ $# $-$3$%
/3$%
# $ &$$%& & 0
o $
o '$&
o &
o $$
$$ & $. /$6,- 0
89>$& %, !&''&$0
* &&$ $$'$&* %!
%&'$& & &&$'$ "
#'$ &# '$&
& &&'$$$ #&'$ &
, #&$'$$ '$&!
& $'$$&& $
89+ &%, !&''&$0
# & $$&$ $
$ &( $,& #&(
% #$$&
$ $ &&& $ $
%$ #& $
& $ & & %
$%?&$%$ $%
893$$%, !&''*$0
#& %$ &
#% %& % !
#& & %$ &!
3$ $ $ :$; $ $
%% & $ $
(%!
# < &&$$%,&
,$%&*%$ & !
Product1
Product2
Assemble
Product3
Assemble
Product4
Product1
Product2
(1) (2)
Assemble
Product3
Storage
Assemble
Product4
Assembly1
Assembly2
Assembly1
Stockyard1
Assembly2
Operation Model
b) Operation as Relation
Product
Place
Time
Operation
Product
Place
Time
Product1
Product2
(3)
Assemble
Trans.
Product3
Storage
Trans.
Assemble
Product4
Target Subject Content
Assembly1 Stockyard1 Assembly2
a) Operation as Object Event
7%

)
)
B
B
B
3$$ &
%0
C
#%-"+&
C
3 %
C
/&
6
-$
B
B
B
.
+
/$%@
B
B
B
B
)
>$
D
7
1$%
7%E- & $& $%
& - $ $&
%&& $$#& & $ $
$%$ 7%E#$ & &
&$$%&' $$ $
$ %)!"###$0
o #$!/ $$$ $
o >$$$'$&
o + &
o 3$$
o @$$$% &&$%$
# & ' & % $ & &
$$$&& $$. /$6,!
1F 0
&G
3 %&/
/&6
%0
.$
1
/.$
*
+$
-$
-
6
*
6,
%
6
+ .$
/
.
3$$3 &
6 0
.
+
.
-3
/3
/$%@
>$.$
@ .$
7%H05 &. /$6,- $%$%
A

- #$$&$ $%
&&$%$ % #&!
$% $% 7%H * $
$& $$% &"7,
$%," %# %$ &, 0
o 3$$&&$ $
o 3 %%
o -'%
#," 0
o . & %& $& %$
&"
o + &$ &"
o /$%@ $% &&$%$%
# $ "%%$%%
($
*%+
*%$%+
#$% %" & !
$$$* '&$% &$$!
$ G $$ +$ /
.8+/.9 %&$$!&'&% $ %.
!"###$ % $$ %
$* $ && %
$ #" $& $
$* $$&(
% %( &
, !"###$ * && & $$% (
'$ & && $$( # (
% $ $.+$-$ &%
$% %,!"###$.!"###$.+$ !
' $$ $%(&$% &
%# ,$% 3
":/$%@ ; '&&% $
/$%@
1$&6/
J
5&&%/$
6
*$
6<
6E
6H
#
3 $
-%
3 $
-%
3 $
7%K0/$%@ .$
4I

# $$ $ ( %
# $ $ !
& '%$$$ # & '%!
$& & $$$
& & & $&!
#$% & $( !
% && & $
$* $ $&%%$ %&!
7$&& $ % &!
# $ $,$$& $
$ &$$%
*%'%!
# & $ #$ $!
( & % $$* $
$ $ & &$ $ &
#$ &$ L# #!
$ LM#M % (
$L$$* $ /8-95&&$ $
$. $#$%&$%$- /
.- $ &$$/.%0
!&''&$
#$ & 0
<
−
.
+
−/
1
( / 1
−
<
σ
/ −
8'H9
.
8.
9 =
⋅ (
<
σ
/
< Π
.
+
( /
1
11$N-D%&G$%$NF
(-Nσ
F-F
3& && !
&#$&& %!
(($ O %&
#$$ 0 & 0
−λ⋅0
809
= λ ⋅
8'H

$ #& $$ & $ !
$ $$0
89+ $& $$& $ $$
'% %# $$ $ & &!
#" & $$ &$$ 0
&
8
9
= 89
89
89
8'HE9
+$
-# = P + ? + Q
( − −
+
4< ( −+
4
(
0
3−56 8.
≤ ( 9 = 89
89
89
I I I
(=
-%
P?Q $$ &$&
$6/ $ $$ &$$ R'HHS0
$ &$$( %
&
0 8'HH9
8509
= 03
−56 ⋅ ( −
0
)
#$$$$ $ 0
8'HK9
0
= ∏ 0
850
9
6/=
6
# $$$ $& *
$ % ( %-$%
$ $ $7 !
%$&($$
8

$ $$%$$$ && P?
Q R'HS$$ &$&7$$
' R'HES $!
#& &$% &&%3$ %
& &(&&% &&!
% $ ' $$ &
8509
= 8'H49
0
0 3 −2
0
= ∏ 0
850
9
8'H=9
6/=
6
5$ & $ $%
& G$& $$"
:/$%@ ; &$$ 0
7 = 0 8'HA9
+ 0
* " (,#&/$%@ .$ %$
& , '& $% '$ 8%9
.+$-$* $'$
$% & /$%@ .$
*%(&
#@ .$ &" :@ ;:1 ;"#:@ ;
&& &&
σ$& λ&%#%
&:@ ;" &7$$%&&!
$ :@ ; $%$&
& :@ ;" $,$ $$
& & #$%&$%$ '$$
$:1$;:5%%1;:%1;&
$ $ G &
:$1 ;:($1 ; $,":@ ; &
7$$$ "
:@ ;# 7%
#/1 %- $%$%&$ &!
$$ $$ # %
%&$ $$&% %
&7%4
#&&/3$% $&$%"
#/$ & $%E1 $$ &#$$
E1 3 && %0
< < <
8'HI9
= + +
4E

3 $6
5%%U%
D%&$%$
<
1
1 7
@
σ -
µ -
78(9 -
λ 5
78#9 5
/81$9
/85&&%9
/859
$1
($1
+$
-+$
$1
@F$
σ 1$
µ 1$
6"
-+$
51
#
λ
/
G$ / +$
6" I
6"
J
6"
&
6"
IJ
7%01$&@ .$
7%40*&$% &
*%*%,
#/$%@ .$ & %&.+$-$%8
!&'''$/!"##9$3$% $ $$
& $ µσ
$ & & # % %
5(!.$$ & & $ %0
!&''&$# $$ &.+$-$ !
3 '# /$!
%@ .$ %$ & $7
$$&:/$%@ ; $7 $ &$
",$+K&.+$-$ $ !
EIIII $ & & $#$*
$ & # $ %/$%@ .$
$$ $$&$%.+$-$
3
5
+
1
#$*0+ &/$%@ .$.+$-$
.
81$
9
-26.73
-8.00
-14.61
-72.57
138.61
.+$-$
-%
8 9
12.62
21.13
20.48
37.38
11.24
3$
/$
8$WXI9
0.97
0.38
0.61
I
/
.
D%8/$%
@ 9
@
3%
/$
#/$%@ .$ $ % %$ $ #'$
# $$$ & $ $$
V/$%@ :%7,/$%& $!
$/$%@ .$
3.17
5.93
3.49
1.44
4.49
'
H
(
$
K
+
@
%
/$%@
'
K
(
$
H
4H

&$% &&$ &.+$
-$#%& /$%@ .$ $$
, $3#&'$$$ &$&
& &,#/$%@ .$ &$$%
:/$%@ ;& $$$$+K#.+$-$
& $EIIII$$ ' 3$

$& $% %!
$$ $ $ 0
o # & % %
$$$
o #$ &&
3 $*
-*
3 *
-

* $%% %! ( %3$$
$ %" &$$%%
@ K
Cost/Risk
@ K
Makespan/Risk
Cos t
Cost/Risk
M ak e s pan (s e c.)
Makespan/Risk
4 9 14 19 24
@ I
Planning Risk
7%I0+ $%
4 9 14 19 24
@ I
Planning Risk
7%0. /$%@
3 $/$
-/$
3 /$
-

3 $*
-*
3 *
-
-E
-

$$$ & -%$ !
$%)
!"###$0
o #$/ $$$ $
o >$$$'$&
o + &
o 3$$
o @$$$% &&$%$
+$ & , ($ "
8 $$9 , &$$ 0
o 6,%$ %$" %
o #" $$% %
%
o * ,%$$% $$
o *+ . , %$,%$($$
",
# /& # 6.6#6Z,36?3.3& &#
& /.$-613-
36?3.3 ZN 6.6#6 #N 3.313 ZN #3Z+* - 8AAA9 :
*++3-[AAF$+%

Z..@3N*DD--38AAA9/

!
"#$ %&!" #"! $%
#%
!"
'(
& '(""##'%)#
' *( %'
#* %" + # ' #
# '(" $ #
(' $# %
"'# #" $% ('
' # ## ' '(
"',%'#-./0"
$ ' ' " '' '' "
''1$ % $'# $
'
)( *%%%
)('(+%%
,2"3% 42'(#$$$##
" %2#$%&&%'5 #"",
""'$' %
#" %6#&""
'
6""" % $4
• %"%"$'
• ,' %"
• , %"$"
• )%''#"7#%#
• )%"
• ) #$"
6"8' 9%'%"8" 9&
" " % # "
##%#, % 8' ##9
$" # - ''0 ' $# $
:$ % " , #" "
%'%"$%#"6#'
' " " $" % ; %" -0
&-0-' 0

&""%7"%7" #"
' &%7" - "0 $ #
" # " '' # #; ' -
#0-0%
$ '"-'0
Process function structure
Functional decomposition
energy
information
material
Processfunction 1
Task 1
Task 2
Processfunction n
Element 1 Element 2 Element n
Fulfils
Fulfils
Relations, forming the structure of
the (sub)system
energy
information
material
Task 3
Fulfils
Principle / technology
6#46$"
" #"
"#%$4
• $''%"$" $
"*
• #*
• *
• %$ *
• $$
)()(%,
&" )## '" ' 8 =
#"= "##"
# "9&")##'
)))

Customer needs
Requirement analyses
1. Analysis of objectives and environment
2. Identify functional requirement
3. Define performance requirements and prior design conditions
Analyse loop
Process management
• Risk management
• Interface management
• Requirement management
Functional analyses
1. Decompose sub-functions
2. Define performance requirements and prior conditions for sub-systems
3. Define functional interfaces (intern and extern)
4. Define an integrated functional architecture
synthese loop
Verification and
Life Cycle loop
System syntheses
1. Transform functional architecture to a physical architecture
2. Define alternative system concepts, configurations- and system elements
3. Select preference-products and process solutions
4. Define physical interfaces (intern and extern)
Product design
6#

%'$$'-%0"$
#'$%"
" '%##%7"$' "#
" '$%"% '$"%
$ ' ' $ '" '% $ "
''%%''#
'#' /012$%&&' #"4
• %%#; "-%# "7
''0
• % % - (' $"0 ,/& ' -7+ 7
#7%70
• %%-0$'-#7%"
###0
Whole life cycle of functional object “pump with tag 130P01”
Functional object :
pump with tag 130P01
Part of whole ”realizing
functional object pump 130P01”
Pump of manufacturer A
Serie nr 34562
Pump of manufacturer B
Serie nr 3A_4562
Pump of manufacturer A
Serie nr 104562
Begin of life
end of life
Part of whole life cycle
6#D4@ 7"'"'
)(.(
, " # #; ' "
## ''" " % (' E $
'%"/"/-//0@-0''% "
##E-';#0' + "## +
$%$

6#E$''$##$';#
(; %# # %+ ; -7
% 0'$# ('%#
' ) $%&&' '' $# #
# " $" #;
$#$" $#%"$
%"(
)(/(0!%
#'"",'' %"
+"++"+$"'
%#'%;%" "'#"
,''$'%'"7'"-#0,
' ( '' + '' 7' '
-'" # ## %# # #0 ) '
'$"(%-%$'
'$%$'$''#;0
(-%$'#;#
'0 %"(
'$'''''
' '( # " $ $ % #
$,'%" "
,' %$' $#8#9(6#G4
• .4 $ 2 3 2
$'3'$
• .44'$'"',
+%
• .'4 $" ' # $ " " #
+''''%
(
Requirements
People
Projectmanagement
Risks
Interfaces
Profit
Technology
Processes
Functionality
Product
skills
Methods
performanc
Geometry
Planet
6#G4('
.'%'''''
'.'%;%"#".
' % ; %" #" % %"
E

'' /012$%&&'6#'$"
##''"#%
'(" ' #% " '
# +" " $ (
- '0 ' $ '(
#"7#
)(1(0!2 %
.+% $"4
• '" + ## ( $ '
+%#%"'''% ' "
%### #%
• '"+## ' +%
#%"'''% ' ''
"'$'"+##
($'
• C# + $ ' $ $
##'%
6#H$'%$$#' $"
$' '$" "#"
'%&'#'#%
+ # % # %"
/" % ' ' +
5 ";#' $+ #"
$" +('%'
%% $"';+"
+ %" + (
;'
Viewpoints…
Experiences…
Terms ...
Objectives….
Solutions…
client
subject
specification
2
Implicit
information
3 4
4
3 4
84
3 4
3 4
7
contractor
5
5
%
6#!
+
0%#!
explicit information
%%
%
6#H46'' (''
)(9(0!
%##%%"' #
"
G

6"$'4
• , $" ' $ -# #"0
'% *
• /# '*
• /# $ " $ -''
''0$"" -%'"%0*
• /#%$ *
• /#$$*
6"##$'4
• +#*
• ? #+*
• ##+#*
• , (' $ ,/& ' -$ ''0 #
*
6 "$'4
• %" %#
$"#-#+7#7%
7'0
6%##$'4
• .%" (# #
%$'$#"#
6'$'4
• .%"-0$'*
• %"''*
• #*
• $''*
• ##"#
• ,$" +('('
%'%% %"+
• ,$" '-# 0
'*
6$##$4
• ,$"#; $#$"
$#"$%"(
• , (" " $
%
('$"'''
'%$'"# "'-6(%"
' '" ' 0 &
%" (%$"(#'%$', #
'( &
'("'%4%""%""
%"' ,%./"'$%
($''% $
# "
-(0!
-('%% !
,";#$'' ;

# #" $3445' $ ' 8.
. . F$# /#9 -A.F/0 $ 6# A.F/ $
($#"%"%"
",#$ ''#$ 4
% % ' -0 ''" -0
- #$'0 ''#$#
Information
objective
function
Information representation
life form
process
activity
System
content
geometry
relation
System
behavour
physical object
System
structure
Collection
Property
6#46$'
)$'%"$';";%-
%"("0 '%%"$
6#I A.F/%"'$'%"%"
## @%"-@0 "%"%#
$ $ % % % - %
'%#''$$"0 #%"%
';%%6#I$"
1?,
View model
level
Business object
level
Specialization of Business object
(library object level)
Specialization of library object
Objective process objective a for human acceptable inside climate
system objective climate control
to avoid entering of smells into other spaces
Function process function realizing desired humidity
realizing desired air quality
realizing desired inside air temperature
system function HVAC system function air distribution
regulating air quantity.
circulating water
controll system function
remote monitoring and alarming
Physical object system HVAC system
plant
proces unit
proces unit section
air-conditioning plant
air handling unit
chilled water unit
filter section
heating section
cooling section
Property absolute property exhaust capacity
return water temperature
minimum ambient air inside in winter
principle system principle single pipe
direct-on-line
6#I4& $%"- $$#1?,0

&%$%$$+%"'
6#>$'' #%$%$
$$""'"%-''0%
$%%",''%
('" &" $ $ % 6#> $
%2''"#"3-'"0 $ 23 '
'-'0' '

7>E
Pump 45P1 is valid since 01-02-2000
Pump 45P1 is referred on P&ID 45
Pump T345 represents pump 45P1
Pump T345 is of manufacturer xyz
Pump T345 is valid since 01-02-2002
Pump T345 is terminated at 29-01-2005
Pump R654 is successor of pump T345
Pump R654 is of manufacturer abc
Pump R654 is valid since 01-02-2005
Pump R654 represents pump 45P1
6#A4)('(' "
-(.
''% " $#%%('
7$#$' '$";#'
%# $6#< (' "
%% ' '' ")"%
% # ' $ '%# #
'%#'%#@ "%% 7
$'%##'' 6#D4
'/( '''
-#&:%"0#%"';'
I>

' $#$
%+-##$0
concept template chilled water unit
Business generic definition of a
chilled water unit
Development
Re-use
class template chilled water unit
Description of a specific
chilled water unit
by yard for building nr xxx
Development
Re-use
Instantiated class template chilled water unit
Description of a unique
chilled water unit
by supplier for building nr. xxx
6#D4 #''%'%+
''"%%('"'% -
'0%%$%# $
%%$%('%"%
$"'("% "%%"('% $
#%#$#;%"%
-(/
(' $A.F/ $
%% 4
;"'*
< %";%*
A ; # *
D # $ ' ' $
+% $$#
-#'0
"## %%"$ A.F/
%"4$-0%%%"%
"#';A.F/% " %"
%%(#" '""%# %
''%A.F/%''$
%# # $ '7' % % '
# ## # #
"% '$
.(
.('"%,0#
A.F/ $ % ' # C % -C 60 C
## & ).% " & ).% % ' 8 9 ,
( & ).% (' - (' + 70
'# $ % - 7 #7 %0 %" #
"' C ##-#'06#E( $
%%%"$"'$)%$' (
'
I

has UID
object
grammar part
has UID
object
Fact-ID
Lefthand object
Has relation x with
Righthand object
“main fact”
has context
has description
:% 6 ."%
6#E4 $A.F/ $*!J+
1 2 101 60 3 15 201 65 9
which forms the connection between
two remote locations by means of a
1010829 10430 piping route 1146 is a specialization of 1483 route
sequence of piping components.
3/16/1998
1130271 130207 pump impeller 1191 can be a part of a 130058 centrifugal pump
which is a set of rotating vanes within
an enclosure which is used to impart
energy to a fluid through dynamic force
in order to generate a required head or
pressure 3/26/1996
1130956 130207 pump impeller 1146 is a specialization of a 130144 impeller
which forms part of a rotating assembly
of a pump imparting kinetic energy to
the liquid being pumped.
3/26/1996
1910911 911231 shutdown procedure 1146 is a specialization of 910002 procedure
to take a facility out of operation.
3/20/1998
1194089 192495 heat transfer 1146 is a specialization of 192923 unit operation
transport energy and entropy from one
location another. Typically the
exchange of heat between two 10/19/1995
1521473 520876 winch 1146 is a specialization of a 731016 machine
for materials. hauling or pulling; especially: a
powerful machine with one or more
drums on which to coil a rope, cable, or
chain for hauling or hoisting.
2/12/2002
6#G4' C % -C 60
6#H4 7% C 6
I

," $#'4
• &
• &
• .%" - "#0
• #
• @## 7%-7##%0
) ' % $ 6#E $ '
& ).% $ C 6 6#H 0 $%&&' )# >
'#$>K%K
& ).%7"$6# %##"
(,+*35.;,*.;

% & ).% -% >>>>0 $ A.F/ $ A.F/
$ & ).% ' % %" # ';
& ).%$$A.F/'%"A.F/-$%
%%0(%%%& ).%%,"
%"%$"6#I;''
.()7#!
,(' $(#'
'' 1?," ""; '$
'" 1?,
$A.F/ $#'#%7$"#'
# 6#< , ' ( $ $ #
% % $ ' & ' %
)((#%$',$" -"0
' L/@ $" % $ A.F/ "
''L/@, @%"-@0& ).%%
8 9A.F/'%"-'' '0,
'%"''@%(%"%-'
0'' %''
Reference data library
for shipbuilding
(standard template’s
and objects)
“chilled water unit” object information model (template):
chilled water unit is the whole for compressor
compressor is of type semi-hermetic
compressor is of manufacturer Carrier
chilled water unit is the whole for condenser
condenser has property cooling medium
cooling medium is qualified as LT water
LT water is supplied by client
chilled water unit is the whole for liquid cooler
liquid cooler is the whole for circuits
circuit is the whole for pump
pump has function circulating the chilled water
pump has property pump capacity
pump capacity is qualified as 50% of the unit capacity
liquid cooler is the whole for starter panel
Exchange of product
information, based
on object information
models (templates),
exchanged by XML
or excel sheets
Sub-sub-system definition,
requirements etc.
Sub-system definition,
requirements etc.
system definition,
requirements, etc.
Electrical contractor HVAC contractor
Yard
6#4.'(#'
) '" " ' '%" ' $ ##
% ' @ # ' ##
'" #'$##$
'-$' "#''06# %
4
• "'" '
"*
• !#; '
% *
• ,$"'' 3$"
$'' '" %"
• # % % $ ' '% '
% " % ' #
ID

(%
A.F/ $ - ''% " "0 7 -
''70 $ '%#
%'""%#%''('
$"%"'%""'%$%
""'# "' %"##"
'' " # # %7 + " ''
'''''A.F/ $
###%# (%"
$#''"5 '# $
''A.F/ $)('$"
% % " % '' " , '
'"7%#"$ #%
$ A.F/ ' % ' . " $" ''
$ ' 7 A.F/
%
?)@M3->HA>GEH
F::))C11-II0&I>>DEA07&I>EEID>EE>
:&)->D0&-:&)7 .7>A7>G7>

!
"#
!""""!#"" ""!$
" " " " $% " & " $ " #"
!"'' ""(
• &" ) * " '% +!" " $% *
$ " ! +"$ " " &" " " * ""
" $
• , ) * " "" * !" ! &"
""" #!" !!" "&"""
*""# ""$*"'
• )")*""!" !&"""
" " " "!"&"""
*"""" "!"$"! "
- "$ " !""" $"'
"."*""!* "#"""""!! !$
"*!"$"(
&""#"( −/"
−0*" 1"*"$
1
1$"!23 4
−/"""!"
&""( −,"""
"#"( −)" " 15
1
1$"!
−0!"$"
−0*!" "
"( −,#
)""#"( −)" " 16
1.
1$"!
−)"!" "

)""( −8"'
−,!
)""$!$#"#!"'
*"(
1
1
1
)#$"!#""""!#*" !"
'. - !. " "! " # *"' , ) ,""
)*"')"),)$
-!" +'.""" "
" " ' ". " " " +!" "
!9"""*
'.*"*$$"*"""$
)" ) - ## " " 1" # '. "
"""!:"
& " $ !9 #!" " ! "' $"!
#""" "$"(
1
1
1
- "" " " " "
-#""!!" " "#!"
-# "'"#2" $*!"4" !"
#-""" " !"
-"##' "*!"'$"#"!$
"""*"'""""";)! "-"
*" #,6)$"!*" !""#"
" !"""
$#%
$#"#%
" "! ' !" " * ' $ " #
"" " "" " "" " * "$ "' "
#!" ""$"! $# *"" "
"1$"!6 "'""# "" "
(
1
1
1
1
1
#!""#""""'
" " """"$
#"*" "!'"!!" "'
" !" !"""$"$
#!!" "
* * " * '" ' " !#!" ' !
!"*'""*"'" !#
**"!!* !"**$ ""
$#$#&'( %!)*
-"*;)8"'"!"$"""*"
"!" ""-!*""" "'.
7

*#" "*9""*" !" !"!"
" - ! "" " " ! " '
,"" ";)"!""","")!""
!" " *.' " " " "
"#*"$"!$" ""!"*"
" *""""* "$'"""**".&
"'$1*" ""'."*#$"!-""!
!""!"" ""!"!"*#$"#
**""!6"#" ;)"!!"
#"!""" "###1"!""!"
! 2"" " ""4 & " '$ "
"* " " ! - # ! !"" '" $"! '" 1
"*"""
6!* $'*"!#" """ !
"-#""""!"*#
!"$ *$ "$ ' * $ " "" " "
!" => "! ="> !*" " =&"!
8">'""'""'&"!""
!"*$!"#"" !$ "!
"'."" "$? !"
"" ";)""!"* - "
"**"*$"""!"*#*$"
/(;1! *1*""!""

"" " * " ! " " " !
( .*.&"$"!" "
*$ ! @ 21 ! " 14 A " " !
"*(
1 6" " !" """
1 " +"$ ". " !"$ " !" " " !
1 " " !" $" " !"
1
""!
&" "" !" 2 '* ! " "4 *$ "
" " *$ " "" " ' '" " !
&""*"'"!"".""'!""
'"
6 !"" "" " $"! " 9"" " ' "" !"
" $""!" $-!#" " "'
!""""*""1"""!
"!" $ " " ! !" :" *$ "! & " "
" " '"9" ' $!!!."" "
! " " '. $ '" !"$ 6 " ! " !"
!""*"""*!" !"!-!'
+!" " "$ ' '" ! !"" ' *'"
+!"B6"'.*# ? 6"'.
$#&#!%!+
+*
? " "*,6),6,6$"! "" !""
!9"$ "$"!#! " '"""
!" !" " 9*'$6""!"!""!*
'.!"$"! """% !"&
""+!""*"""*""" !""$"" $
&" $ " "* ' " " " ""*" !" ' "
"$ "* ' # " " !" " !" "
!' ""*" "!")"$"*""
" "$ "* "" ,6),6,6 $"! '" !! "* '"
""*#*"-! "'"
'"''"*#*$"6" ""
*"$""!" !"" *"'""*-
"#$!""B6*""? 6''."$:"
! ""- *:"1""*"" '$"
'$ " " "" $ *" *:"1"
"**$*" "!!""*
$#,#+*&'( %
*++
6 " " "!$ " " !" ;) ! " *
!"'"1"" """"!"A""
!""* " $'"1" "
":"!"6""""!"" *""
!" "" ,6),6,6 $"! " " !. 9"# "
""$"""A!#" " ""
'" ' * / " " !

"" ' $ " " '" " ' " " !"$ !"
* "!" $ " - !" " " " " ;)
""!* "!"$ 6"!""#"'
*!"$"$""" ""*-##"
" *'" +!" ? 6 "" " '. !
#"
/C()*1*""!!'""
$#-#
-.$" $ "'"' "#!"" "*
" " "$ " # !" "" *"' " "
2# '. $4 9*"$ " *! " # "'
" '" " " !" !! - ! " " *
# """*"'"(
1 6:"!" " !" " " *"" "" !"
"*!""
1 )"""*"!"
1 .*#
1 "$
-'$ !""""*"""'$ !""
*"" " " " * 5 " " " $ '"
""*#!"*#"*" " !"#"
"""'$-""*"""
" $" " " * " " $" ""*" '" "
""""1"!"-"""$
. " !*. "#"-# ""$
CDD

!"$*"""*"8"""*"#"""*!""
&"#!"""""! $.$""*"
#
-*.*# "!""""""
*"'"6"" !""* *.*#
" ' *# " *. *"" " "" "" " " *.
*"" # "!" " " ' " *. *"" ! ""
"" *. *"" ' 9! " " "
#1" ""
/;(.*"" """"*"
/E(0!"
CD

6!""""" """"$"-
"$'"" #"$#-""*#*$
"' " / " - " * #" ""
#""$"
)','*""!" $ !"! "
"""*"".""!3 *"!" $""'-
'.""'""!" "!! "'
"!" $"- " $ '"""
'! "#$!!
/F("
$#.#/
6 ="" "> " " " !" 2
" " ".3 4 "" !" " "" * " !" :"
=""">' *"*""*$" "
"$"!"- """' "
"" " "#"""
&" =""">'""+"#' "" "
!9" "!'=""">!!"
" """"61' "" *"*#*
:"A"*#* :""""":"
*$""! !"*$" "$!"
CDC

(8 "
/7("'
CD;

$#0#1!23%
&""*#!"""#!""!""#
*"" " " "" "! !$ +"$ :" # "
! :" " " $ . ' 1 " :" "
"$ # .' *! !: - * #"
'..'#"'"*#6#$
:" # " * * " $ " "
"$""!""*"A$1' **"
$!* *$"1' *#* :"-
'$ **$"$1' 9!"#*".
" #* "$ "" !" " "$ 1" #*
"$" """$ :")' *"'
'$ 6 " "" " ! +" " .
"""""" "' '$#"*"$
=*.>""#!!9"
1
66 &A 2CDDD4 ! "
,A8&-8"!
6BAA/G,ABB A6G0AH6G A) &0@H62CDDC4"
&,,6%CDDC
A) &0@H6G0AH6BH,G0@ 6&GAB6AB2CDD;4#
$ C ,A8&-5!*
A) &0@H 6G I&IA G I&6,@6 6 2CDDD4 % "
,A8&-8"!
AB6ABG0@ 6&G @-82CDDD4 !E"&/&8
? 0FC? .J'&"#,6)J&,1E@,? $8!
AB6A BG 0@ 6 &G @- 82CDDC4 ! K/!
J'&"#,6)"J'&"#%@,L? $24
J'6!8*
6BAA /G 6)@L6 ,G @- 8G 06 ,&6 BG 6I6HA &G I&6,@6 6 24
& &"'();1E;
)@ 6 LG 8@H6 LG 6BAA /G 06 ,&6 B 2F4
"$"* $+ ,6)68MF
06 ,&6BG/ 6)HIG-A AL6L2E4 "$" $"
""*'(,
CDE

!"# $ #
% &%'
!"# $ # '' &%'
!("()%'*
)'&'
"
! "# $
#$%
+" "" ),)'-' "# )'
). ' *%' ) "# #
) $ )" )%' ' '# " ' " )'
" ) & ")")'/'#$
" )%' ). # )' " ) )
)#) )""
0 *1'))#0 &)'%#
% &''(" & )'' /'*' &
' ' )')' #' & &% '
%')" ) " &+)#)
))
1 #')&' /' " )
%)' )$ &'')"')
/' ' '#)) "# '
)& )% '#) "
) % #) &##
&" ' ' % % )
+ /' # ) "' '
* )++("+ '# "#'))
) ')) "%%"" )
' )# ) 2 1*$ *3 41$35 )
& )'$#" &'
)"')' " ) '
0 & 162 ) " ) ' ) ') $
! !
"

" ) & )%')
) )' )# ) ' 4 '
&%&))8 5 &)
')) ') ) ))%'9
&%'% " ) %')%#)#
)")') $%#)
) %"' 4# ) 5 ) )' )
)1 &4 :)')''5,) ''
% ) & &#+ '
%' :
1"' ) % ).-
1"' /' )" &)'-
1"' ' %#) &#*
4,)#)' '# &#5-
)" ') ) -
1"' )") &")
4%&% ' ' % ))"
' & ' %" )%'-
1"') ) )-
)" %&))#)')
$ ) & ) ) ) ' % ) %# :
')' /'#;' '" &*
%% ))%'):
$) %# )')%"' ) & #)')
& )' &'-
$ ,%# ) )'&
)))
&$%
&$#$
% &''(" # ,) '
"%#) )%') #1""#" %"& #
) )''3 %" 162)
< )< ) +" %&
"%&) %&#'%* '))"%
" "'.;=
>? " ' % ' $
) ' ) )
# $ ' ) %& )#
)* &>1? " & '
/' )' * ) '
& ' %# & )' + )'
), ##'%#4 ) ' '
')) " ')# '5) # ),@#) )&
# ) ' '# 4 ' A5 /'
#') B#")' ') ,
%' #))%' ) #'
& " % ) &" "# ) # &#
.' # ')'/' )')#
/'"
7

Process model
Process owner
communiqué Process yard communiqué Sub-contractor
Start
project
Preliminary
study
Feasibility information
Feasibility information
Attributions
to preliminary
study
Attributions
preliminary
study
Generating
program of
requirements
Tender
request
Start
project
Advice preliminary design
Sharing
expertise
Evaluating
offers
Adapting tender & specs
+ updates (x times)
making
Preliminary
design
Tender
request
Start
project
Project phase
Making
Shortlist and
choosing
yard
Contract design
on main features
specs & price
Contract
owner - yard
Adapting tender & specs
+ updates (x times)
Tender
request
Making
contract
design (x
times)
Start
project
Detail engineering system design phase
evaluating &
choosing
engineered
systems
components,
layouts
Evaluating
working
drawings
Main drawings for
approval and system
schemes for approval (x
times)
approval
Drawings for approval
approval
Making
technical
(systems)
design
field
specialists
Making
working
drawings
Approved
engineering
package
Adapting tender & specs
+ updates (x times)
Contract
yard - subcontractor
Suggestions for approval (x
times)
Suggestions for approval (x
times)
;=:2 ')#
Making
contract
design (x
times)
Making
engineering
for approval
Making
detailed
engineering
Approved
engineering
package
&$&
1 ) # % ) & D)' B
# ) 1,) ' ' '
" ) ) ' )) & ' DB
' 2% ' # ' ' 4)5
& ) ) ) '
'# #" /') "))&
&%"' ' "
, )++-"" ) '% & )' " ) )
& ' '* '3 ' " )
% & ) /' ' # # ' ' %
'% "#&1)):E$ ' *)
& ' )%%# %# ) %# "& ,) (
,) '" ) ' "')
C

% ' "' " ) '' "' )'
" )) 4 &') # ')"%#
5"' ' ', "
,) ' & ' & %" &
)'%'# %'&' ')%'
' ' ?
+ ))&'%#%# . &'''"& )) )%*
% '))% ' )
3 ) )D #)B
$ )' #, )
"G" .# )
' ' 4 / )5 $
'/''%# % ),# #
+ )) ' )
D@ &# )* ,'
',) /' )) # ' ' ) # %
&# "%# # ) B%#
&''(" $ ' %# ')) & "' ))
$ ')' %#'D ) B
% )

'' #" %5%# ' ,)&
&& ;) &
)%#% , )
+)%# ;%) 0 )
,4) "%# '5 )'&
) & 4")"'5$ ) &
&/'&&"#+,)'>
' '% )K@?$& '
"& %# ' ' % ' # $ )
'& - )0 )
# ' ') '&
"$ ' )43 3)= 3)5
%# )%%# %' ) ! " )
&) /' 45&; ,):%#
/' ' & "
$) )H#)'))')
) ) ' ' )%%# %' )
'% % ) ))$
)') )*)

*#
"
!
+
Not OK
*
!
OK
$
!
+
ok
&'
()
Not OK
Not ok
Not ok
- +
.
/
"
#$
%
;:1,) )/'
Task: SP_FO1
OK
,
Not OK
*#
Not ok
Effort required (hours)
8
7
6
5
4
3
2
1
y = 19,719e -0,3313x
0
0 2 4 6 8 10
sum of parameters
;6:%& )
&#"%" ) )%%#%'
) ) )) "
' )) L= ' #)''
& ) LOL # ' ' &;
,)& ' #''#% '6&%
" &" & ' &
" L;36 ' %# %' '
&) % )
=

3#)"%')# %&'
'#'"%' $ ) %
) ) # # '
"# & ;' )/'; )')
) & # &" ) # # /'"
"' "% ; ,): %& # ')) "# %& %
$ /'""'/'%#,)
=* =*64) )5$/'% %
' '? 6 ) '%
)5$)/'# ' ,)%)
,)"%'% ",))
$ ) ") ''# %
'' ' $ ) #':
# 4"'% ))& )
#"#% '5#)4" )
# "# % ,' 5 + "# )
)) $ &) &":
* -
* ) -
* ) ;'3)')-
* #

'$'-
H % )) ' % " $
%&)') ) )%%#%'%
& )# )"%# &" )#
% ' )" %# ' %#
) ' " & %'
'"0 '& *)') ""'
)" ' ' ) &%' 'H "&
& ) " % "' ) & '
'&)'"')0 " )
%&'"'%' '"'&' " "#
#)%%#%' ) '%
& 0 ) ' "'
%' ' & ±P ' "' $ ' " %#
'% ' # ) " '% ,)
" ' % %
.
0 )) ' & '% ) ' %&
& , '# )'%'
' ) )'$')))
& ' &"$' :
* 1"' ')') ))O=-
* 1"' ' )' 'O
.$#%
+) %&# " ) &" ) &
)'"#')') % )'" )@#
)') ,%' )) %#()
0 0 &''(" + )' ) : E ) '
) & " )' #E + )' #
') )' ' ) '%*# 4M )'
) 5H ' ) )' )')
'/' ' )' /'$' )') &)
) )) ) )' 0
0 &''("* )++("
;O:+)) &+*) O 4 ':&&&" &
&&&' &&& *' 5
& ' $!( )* +!,--
.!,,!,-- /!)* 0 %'"
=

; ))& ' /'#) ) )) /'
$/' &)' %
6+)' 162 &":
* 1 2
+ ) '' )%' '))
) %# # '# # ';# '
' :
o '% )& #-
o $%&'%/' -
o " )/'-
o )& #
+)' # # 3 24325 $)& #
" %' % '% 45 ) @
):
$%:322';#
32*+ 32*H 32* 32* 32*;
945: 6 7F C7 FO J=
0 45: J == = =6 =6
45: O 6= 6O 6C 6C
()4 5: F
$ 2 & C ==C =6 =J
40 5:
)
4 5
OO FJ ==J6 =OF =OO
&: F OF F C F
#): (
''
#
9
''
("#
"
;#
)
"
)
"# "
"#
H ,)"' # '%:
o '=4 32

"# )') " )') )') ' )'# '
)) /') $ ) # &
.

.$#$&$
H # ' % )' )
)"%; )' )%
'&=)$'JP "'"& *
& =P "#' "%
%1# &''(" "'
% ' )' ) )) & '
% 'CP)) ) )$%$ '
',&) /' ) #=
$%:;#= /'4,5
() 32*; 32* 32*+ 32*H 32* $ 1 ;#
3* ) = F= J= F=F F6 O6F
2') )) = C6 FOC C7 CC O=6
G'4P5 CC C C C7 C
$%:;# /'4,5
() 32*; 32*+ 32* 32* 32*; $ 1 ;#
3* ) = J== F=7 CFF F= O66
2') )) = FOF C C7 C6 OF
G'4P5 7F C CJ C7 C
;' % ' #"%''
,' "&$' ' #
" ) ' )' ) ))
# ' ' + # ) )
D )') B)%%#%
occurence (%)
35
30
25
20
15
10
5
0
69 - 70,6
70,6 - 72,1
72,1 - 73,7
73,7 - 75,3
75,3 - 76,8
76,8 - 78,4
78,4 - 80
80 - 81,5
81,5 - 83,1
83,1 - 84,7
Engineering Effort (simulated)
84,7 - 86,2
86,2 -87,8
87,8 - 89,4
89,4 - 90,9
90,9 - 92,5
92,5 -94,1
94,1 - 95,6
95,6 - 97,2
normalised time categories
(total effort)
972 - 98,8
98,8 - 100,3
100,3 - 101,9
;:;/'#%', )= #=
101,9 - 103,5
103,5 - 105,0
105,5 - 106,6
106,6 - 108,2
108,2 - 110
Ship 1, oneoff/product
platform
Ship 2, one-off
Ship 2, product
platform
=

.$&
+ ) )# *' &
" ) &" ) ')' '4

) ' # )% ' '+)' '
' &#
!4'% ''# '5:''
)' ' & ' '% ' '%
'') #B '
95 4 ** )##5:
% ' ' )' ' ' )
4& , ) 5#
* 5 : ,) '%* &
),#
&%
.$&$#
+$%;7 &,)% "D)' ' B
7PJP 4 ' "5%4 '
'5)"#; DB4 ' " %&'
)' ' ' %# '% 5 ' '
,) " =P ' $ , ' ' %# )
' ,))#"%##$,)))"
)#) ' %' $' ' & '
#%%#) #,)4)5' %
) % ) " " + )"'# ) %
D B"% ' ;C%'
'' &+ # '%#) #
' ) ) '' )'
' '%#
$%:)' ' /'4,5
%
, )
))' '
JOP J=P JP
frequency
16%
14%
12%
10%
8%
6%
4%
2%
0%
71-73
77-79
83-85
89-91
95-97
101-103
107-109
113-115
119-121
125-127
131-133
ref
case a
case b
case ade
indexed engineering efforts
;7:;/'#%' ' )' '
=C

!
$' &%# ') ##
)) & & ) )
# " ) " ' 1 ) '
#% "') % &"&)))
& -;' # )#" )$
%, ') ) #'%
% %#( # & )
#)/' )* ''
&% )*&$# '&% '
& %# )) ') % "%

1!0 1!(UU1!(!4O5:
6 3@2$('.))=J*6
1!0 1!(UU-1!(!4O%5:
OF O'%"))OO=*OO7
1GHG+1 +- 1U1 20 - H3($+19*H93 0 4O5
!"# $ #
=J

!"
! " # #" $ # " !" # "# ! " #!% "&
" '" " % " # % % # %
" " % " #! " (# " # "
" ! ) " # % # # "
") *!! $ " ""! !! " ""!
" (# %!! #+ " #" % " !
" " ,! ### #" "
!"
# # " ##!! ")!"!
## "#!" ""!" #$!#%&%!#%'(
)&*++,'
+ '$%)!! "- ! #" !!$ %)!" "
""#%! "&%! ! )"
#" " " !
# # #" $ ! )")!!
+ ) " % - (# " #" " ! "
+$ #(# "# # %!".+
# ##
+ $)!"%"-(# " !% ""%# !
#) # " ! # % #) "%
(# ### " " $## %%!
. (# "#) )" "!")!"$
+ %% !- %!# %
# " " )!"$!!#"
!#) # ")!" , %!
+ '$%%!-# %!"%# #
#) "" # % ! % # " '$
# " "! "" % # / %
#) # "$" )!"!!
+ '$% -!!" "" "% $0
" # " 1.

+ 3&! - # " " " "%%
" # #""$ ! "# %%
# " )" "# (# & "4) 5
"# "4## " ) # !!5##) )
#"!$%"#&
# ) # #!! !" 6
+ / ) ! % +! " - (# )!) ""! ,
")")!!) ")!"%%
+ / %"""%-""%# !) ")!!")!"
%% %% !# # #!")%# " .
% # # !! " + 7$ $" 8 #!"
! % # # " ! #1 #
"# $$" %!! "% #
"
+ 9% -" "# +! #"%"
# " " % (# %" % " ) ! "
.%# )!"% 3) # " "##"%
# %!"# ## !
+ :"" #-/" %!#!" ! )#
" %! " # !! " #
##!" "
+ !# %% +" !-%% ! "%%
" #"))!!
+ +" " ! - +" " ! ! # " .$!
" "% ,"" ! " %#
# ! ! ! # .$! " " " )" # % ##
"# $ % ""
+ !" -(## )!! # !
%,%# " ## #" (#
!" ## # # " ") "%% %#
%##" ,
#
#$
; #"! % ! %"%
# !! " $ "#/ "# ) ! %
# #) ! ! # # ;# "
!" #"!!# "!)!! "
# %
/ ! " # " ## 7 %% 8 #
%!# ! "#7! # #% 8" %% %
#!""# !7# $!#28(# ) !")" "# #! #
#+# ## ## %!0
,! 6
;?$ 2 ,' ,,/, @
;# 6
;!## #
$ 2 %% " " #&"
2

' ! # "!
/" # " $
!$ %%
(# %% $ 2 !!"%#!")# %!" )!
%' /" % ,#
$ 2 ?;A7' ,,/, @ 8
(# ! # ,## # " "# )!"!! ;7$ 2 %#
" !8
##&$
! # "" # !## # (# !## # ")" "
# #% #"+""# !!## #(# %
! # !B+C "
! ## ##02&#$'6
Light-ship Weight
Equipment
Hull
Machinery Remainder
026,! !!" # #
!) !) %)!#;$$"# %! ) !")" #
#0(# # # #02" ," "! ) !%" !
!#""% ! " "# ! ,%# #"# ! ) !%" !%
# " # " ! " " !
# %! " %% # ! % " "
$ %# " 7 )! 8".%! 7
%# !8 ,! +" " # #; #
Light-ship Weight
Hull Structure
Propulsion
Electric Plant
Command
Auxiliaries
Outfit
Armament
Engineering
Assembly
06,! )!!" # #
#' () )
(# ! ) ! % %" 7 8 % # # !# 7;D8 " "
!" )!""$ ("!! )" "#
) % # " # # ! " " # # %%

"" # " ) % # +! # # # !
%" ! ) ! % # " " !! % ! # # !
# " %% ) !") %%" ! ) !) #%"
! ) ! )" .) # # )!" % # # ! #
%" ! ) !".$!" # # # ! ) !! "# %# $
%) +" + ##
;#! # "# """ ) !!"" " %#
%" %# (## # "#; # %"% ,#
)!! # )! %# """ ) "!!# (#!!!
)" % )!# )!"%# " #(# """ )
" # !)!
'
'$
(# ! # %# ! %#"E
## !!! # #"%# ) "! !!
!%!!"! $&)*++,'
' %
# # ! "## #
%!" %% %#!""# !0 #
%%!6
+ :!-:! # "# #""!" # !
! " ) )" " +#" !
!" "!
+ '-' # #%#" ! # #
(# # !" % # #"1 ! "
) 7 ) # "!"8
# % # %! !" ! %% " ! # ,!
+" " %"0!#/
'#&$
!# "" # !"!#%"# #
7# # ! ," " !" " # "
"!8(# # # # # ## #"
!# #"
* ?$ ,;
;# 6
* # %# #!!
$ %% " " #
""! %% !" "# %!%# "%
$#%!" # %!!6
+ :!# # 7 " # % !!8
+ %! " ,# # 7 % # #" # % %
8
+ /%% " 7 % !!! ,! 8
C

+ " %%
+ / # #%# !7 #!! #!8
# ## %% !!"%#!"#
%! " "!!6728!" . "78!# "
) %# #!! %")!" # !$%)!! "(##!!
,"# !$%)!" %% ;#! 4 5 %% !" ,# #!"
%!# %!#"##"#!"" ) ! %% #
"# . "!(# ! ) #
""%###" %% " ) "3 ,! F
#" $ ) + " C/ ! " ! #
#" ) 7$*++,8
'' ) )
% # " ) % # .% #
%" ! ) ! % ! !# 7D8 (# ) % #
% " #) ! % ! !! # " ) " !!
# .(# #"" )# "
) !!%" ! ) !%# ;D"D"## ! "
*+)),
0C " # " " ) " ! # #1
#"## #" !#!" %"
! ) !
Weight Estimating
Coefficients
Cost Estimating
Coefficients
Ship Characteristics
- Length
- Beam
- Shaft Power
- Fuel Capacity
- Others...
Weight Parametric
Formulas
Cost Parametric
Formulas
Initial Design
Cost Estimate and Level
of Confidence
Weight Confidence
Levels
Cost Confidence
Levels
0C63) ) %!" #+ "
(# % # # # 0B +" "
!!) !! (# "# !!% ) !6
+ # "## #"-" "!
" ) # % "# "!!
+ %!- " #!#&" "
) "# )
+ : % " " - # " ! " %% " " !
!"" " ! ) !##%% " !)!! " ) !"##
%!#!"" " # .%"!! #
.$" " "%! # %"
+ %%-# #"%! %#
# %!%" ! ) !" " #"
B

-) )
") """) %# #"!#) # "% "" ) ! "
"# %!!
-)
+ (# #"! !! " " 7# %% " %!
)!""8#!")" " "!
+ (# " %$# ## #! % ! !!
+ (# # ! # #!$"! ) !%" !
+ (# #"%% .$#$! #!!!%#
%
+ (# #"!"" "
+ % "# # !
"##) "
-)
+ (# "") #"" ) ! %! %% "%"
! ) ! ")!"" )!! # #"
./ $
(# %!! ,! ### #; #% " #"
# 0!#/ ##; #"0!#/ !
%) "!" # ,! % # "!# !
" (# ,! # D!!+AD!!+%%A ) ! 7D,8 " !
" (# %# # "(!
(! 6,! D,#
! 01 2310&4 &5 +( "(3
(!%" 7G8 @B
"#78 C
!$ %% @=
/ ## / $78 / 2=@
/! 7 8 /! 2BB
/ ## :/ $78 / <
/ " #7 8 / C

(# "#; #% #% #: %#
%# % ### ! # ! #!%%0B0# % #
%% !!" " "! " #!! # # ! %+#"
%0B" %# "! "E# ,! !! "
) !!"%# 0#) # %% $ 2 " ) " 27#
# #" # 4I! 5 ! % # ! # #+#" % 0B (#
!## # # !!"# %!## %# %6
;?$ 2 ,' ,,/, @
(# # " !!!!# ## # #
0B6'## # #; #
(# !!" # !! " / (# !
! , !! "##!$# %(#
%0@## D,!% (# ! %0@ " !%#
##!#" 4'56 ")! ## "
H

0@6,! # "" !%! #) !!
(# # " # #%# D, ,! #
# ,! # # # # ! ) ! # 0H / " # ! ) ! % " !
" "# # # # ," """!! ) !
0H6,! #!" # #
>

0H ! %# #"! ) !%# # ###!#"6';27. %8
;# "! +!$ " # ! ," # # 0> ## "! #
%!!6
• %6 "/
• D !#6 )" " % # 7 8 7% ! JK #
,! +""8"'7# #"% 8
# !# # %!!6
o ,-# !#%### )! " ) "
o I! -# ."!% , # ,
o L/ )- " )%# 7# """ )
"%# +" % " #"! 8
o / )-# !)! %# " )
o D!!+" -# "%% # )! "# %# )! %#
,! ! ) !# # #(# !!+" ! # # ,!
! ) ! !" " !! " # ! ! ) ! !"
! # ! ! ) ! )! % ) " " ! " " #
%!!!"# !!! # ! ) !(## #
" "$ # # +) #
o 4; #5!6'M(MIM-'"!) ") !
%)!!"!# #")" "% %
# # % ! ! " % ! * # % !E #
%#" )# ! )%!
0>6; #"%%D, . "
=

6
(# ,!! #"% #"%# !" %#(#
#" "%" %! ## %!" ""(#
"%! %% "%" ! ) ! !! "# "
!!%"%!#
!$(
$
I-"$#$ $$.$

!!
"!
#$
!!#$
! "" " "
# $%&!'(()$%&(*+,-
. / % , $ % 0 % ),$%0%* & !
1" #1
2 0 /-)0/-* 3
4 $%&( / )+,&* ! 1 56 ! "
# +, 3 "
"7! "
5
" 1 0/, ' ! # "
"# !" "8
" !3 3!
!
9 "! " 0/-! !
3 " " " !
+ "! ! #
! :! ! !
)!*! #" !
3! ! ! )!*
;3 " !: 0/- 4 ! !
! ! 1
&! "
"! "
""" !: &
" 0/- !: 4
" 4
0 / "" 3 " 0/-
+)+!*&"< ='
' 4""0/->! ! %)0/,*

='?+&"< !0 /%"&'''
" #
4!!:! ! " 0/- "
"! ! 4
!!
1 "!:9
!3 3
& " ! !: !
! ! # # # !
! 3 "
&$-/)$-/*
:!
% !13 @
- ! #
" " ! !
1 , ! " ! !
! ! ! "
"
4#! ! " 0/- "! ! !
" 4 " )! # *
! " )3 !
'

* )
*
$ " 0/-3 "
" !!
! !3!
4 " 3 2 ! 3 !
! " 9 ! 0/-
! 3#;&%&0-,&.%$,09

4 ! ! ! ! 3
!"= !9 &9
!5359 3" !
!" ! :! ! 3
" ! 9 & 3 =
!"9 9 >"
!:! 2 !
MassItem
id: string
mass: decimal
xcog: decimal
ycog: decimal
zcog: decimal
boundingbox: boundingbox
TankItem
density: decimal
freesurface: decimal
ContainerItem
slot: containerslot
=?+-< !9 4#9 -9
= 1 # )! 3 *
4#9 !9!! 1#
! ! #3 ! 3
-9 !9! ! !
2 3 9,$ (E''' B 4#9
-9 5:5 " ! 9
=
< ,/& "C! = FG
B# - ,! 3-&%,4&;" !
" ! : !
! " ! 1
$ )
4 ! ! !
! )! * !
9 ! ! ! C!
) ! C , -*
! ! " ! 30-,&.
= ! ! 0-,&. C 3 #
! # C % !
C"!!4 !3?
- C< B
- 0:, )C,*
- CH)CH*
$*( & +
C< B !C )0 4*

55 ) ! * #
I"-GG4" !C,

4 ! #3" " 3 CH
& C,4CH3:3 ! !! 3
3 2 ,
3 " !
-9 C 4! 3
3 !"0-,&. 1 2
!) !
"*= !! 3#
4! 3"CH !=A /
:3C% 3 3
!?4A )K9 *L
K '?M)'N )K9 **"'
K:'?M)'N )!KK9 K NK :*"K '*"'
K'?M)'N )!KK9 K NK *"K '*"'
K2'?M)'N )!KK9 K NK 2*"K '*"'
)K 'K:'K'K2'*
O@
=7?- ! 0-,&.
-
CH
%
=J&! < 9!
J

& ! !3 ) #
* " 4
! ! ! !C 3"
!
, CH 3 ! ! ! " C
! 4 ! ! -
0-,&." C !3=74!
!CH =J
= "C,4CH"1 !
C !C,43"3! !
! 3 CH "
!3
/' 0 1
= !!" ! "
! !3 0/-4! !
3 ! !!:
& " ! ! ""!3#
:! )Q ! 3*
)0/-Q " * 4 ! !
C "
, 33!!" 3
4 !
!! ! 0/- 1#
! !
&0;9,-I)*123,-44,&567
4&/.9;-
&/$

!"#
! $ %& #
"
#$ %
'( #% )"* % #)
# + , "#% # ( #
##"+ -.% # %
% %+ )#% # # %
# ) # %
# + )# , ( # # %
&$ '"
+ % # % # % #
( #% #/ "## #
#)#" &# %#
% ## #%# "
#### + )# ###
# % 0 (# 1 %
2#)#%%# %
#0"%) # " (#)
& ( " )
#& # #
* " %# )"
# " ##
%#+ % )13/#%
)# # % )
##
($ )*
+%% ) ## #%#
$ #% # )# "#% , # #

"# # 5 # ## %
#
($#$+!
/# #% #) %) ,0
# #,)##( #
1, %6
!"
7
= ( 7
−7
+
)
879
7+
7
#"
+ ( :
+ $:
) −
7
− :
−
=
89
:
+ $:
+ 7
$"
$
= ( −
7
+
− −
7
) 89
7+
$
+ % #### "%6
! ## #%#%#
! ###%#
! )89#%#
0 "% ## " %# + # #) #
+ # " )
#+ ## ; 7 %
? @ "% &! +
25#%%##) ###
5 # )' 7
%
")#)%
2 )") ) "%&!&# &! )
#(%% ") ! + ")##
()!") )0 #")#
%
+ "% % 8# 9 # )
#+ ) &! ## )
+ %##" &! ## #/%7")##
4

% # )##@
−7
$
$
#)%
&#
$ + 7
$
8
−7
7
9
8
−7
8
7 9 9
%
9
8
7
/%76$ *%
/%6'( ##
"
/#)% ) " #"
# %# ,)%0##)
%#" #+ # %
## % ##%
## -% #.#-%.#%
0 # %
%# + %
3 ) # + # # )# "%
6
")#)& #")###
+ #+ %+ #
%# % #+ #%
)# %$")3#%&
"# )% " +
# % #)% %##% %
% % #! #
+ # % % % #
##()#+ ## 6
A

! 5%()# #
! C%# %
! @%%%## #
/ % # 1 " # # #)#
)#
"!!#%1#
##(## % + "!!##
")#" )#"
## % + -) .) ")) #
+ ))## ) %#,%#"
/%"(+ # # %+ ##
% ::#)# 4+ :< )#
%+ #)" %# #;:
# %# 74:

%;" #% + ##
(0): )%)(#%
#0 :(### # "+
#B;+ 1#
/%6"
/%B6* %##"
/%;6%#)%####/%B
-$ .
0 1% )""####*
%# # #%(
(# %)& ####
"# )+ #% %
## #%
B7

+ # # % % #% "
# ## & % # %
#")#+ % "+ )#
# % (% ## & #)#
#)# %%#"&"#
-%#. (# ) % 2!! +
## #%"#)#2 # #)
%") %#%"")
/
+ E # ) /# '# $ + % #
*#%
*'@'&F+ CG *0H0/ 87AA49 ' ( ) $ #
$ I#
&/0F8:::9; &/0FF%#FF0)%
J0&@HFG/C0+87AA49* +,*5 !K%
@2'00G0K@2G52H$'@@CGD0@$'@HC8:::9%%
$*$%
$'' &FC87AA9- 0##!
$@L'J587A49 %F7B;
+0K87AAM9- . 0##!
B

!" # $ !%&'%
( ) & ! & ! * '
#
!" #$# % !#
! #$$! #$!# #
& '!( # $ $ !$ #
$! ! ! # #
!$ $ ! !$ ! $!!
! ## $# $ ! !! $ ! $
!! $ # !# # !
$ ! # $ ) * ! # $
#$ ! $ $ $ $ # ! $ #
*!$#! $ *$ $ #$ $
# ## $ !!
! # *$ $ + ! , $ !$
!$! #!$!
$ $ # $ ! !
! $$$!$!##
! $ ! $ ! !,#
! !$! +(,--.*! ### !
! !!$ -./$$$
! ! $ # ! ! -01
(,--/*! $ #! !$ $
2 ! $ $#$ # !$ $
! $ $ # ! $
$ $ ! + 3 ! ! $
!$ $ #! ! ! # ! !
$ $ # $ ! ! $ ! !
(/001*
!
! # # ! # # ! # $ $ #
4 ! # #,#
!! ! # #$$$!

# # $ $ ! # ! $ #*#5 !
# 5!! !!# ,$
6 # ##5 $ ! !
! $ # # $,, $
! ! $ ! $ ! $ $
!#$$# # !# # !
# # ! $! $# # $
$# !# $
! + !# *$ $ *$ $ !
6 ! $ # # 3$
!# # $ ! $#$ ! !
$ # $ ! ! ! ! # #
$ $ '$ ! ! ! !
# # 6! # #$#$ !!
! ,! ! * $ $
##5$#$ !!
# $# $ ! ! !
! ! # $ ! $ $ !
$# $ !
"#
! *# $ 6 # $ !!$
!$ #$ &,## 6! $$$
## $$ ! ! # $$ ! $##
#$ ! % !$! ,## #$## #
! !!# *! $$$7$ *! $!!$
##$$ # ! ! &,
## # $ $ # $ !
!,
! 6 $# ! # !$ &,
# $ # $ $ * $ #
! #+ 6' ! ! ! $ ! !
## '! ( # ( $ #$ ! $ $
!$ #$$ ! $
6##! *! ## $!
$! 8 #*## ! $ $!
! $##6# !#$#
$ # # '##
$ ! *! $$$ $
! $$ #!# $! ## $
#! $! 6 ! 5
(, ##6#!
!! $ $# $2!$ $
!$ !# !
$! # ,## ! # ! #
$$ $! ! $#! ! # ! !
!!!# *#! !! $ $

$%&#'( '
6&9(49 :6 '! ( # ! &*$ $ (# &;
+$ $! & $ ! (&
! # !!! #$ $
# # &2 (/000* ! # !
#,!$$$,$$ #
$$ $#
)&
! !$! 6 $
$!! # $ ##
7
; # !# # $
;$ $$ #$$
;$$!:#?!$;
$;!# # ## #
; *$ $!,:# $ *! !$!$;
! $ ! ## ! $ $ ! $ $
#$$#$ $# # ! $ $!
# $$$# $3! $$
6&9(49 ! $ $ # $ $ $ # *! $
#!!$ 3$$
! $#!$ # #6 #$
4 ,$ # $ $ *! $
! 6 #! $$$$!
# @0 ,$ $ $ $ $ 6
$ 6 $ # $ *! $
!!! # A B!!! 6 #
! #$ $! ! #
$ $ *! $ # 3
3#$$$ $
M o b ile A g e n t s
D a t a E n t r y A p p le t s
O O D a t a b a s e
M id d le w a r e
IN T E R N E T
S u p p ly
C h a in
S h ip o w n e r S h ip y a r d S e r v ic e S u p p lie r M a t e r ia l S u p p lie r
@074!! $ $#,#
/

D# ! # $ $ , $ $
$ # #!$
: $ ! ,,! , $ # !3 ; ! $ $ $
$ #$! 3# $ #! $ $$
$ $# $ $ :
!$;$ *! #!$
*! ! $ ! $ $ # ! $
'#!!! !$ #$ $
$ # $ $! !$ 4 *$ $!,
$ # ## $ # ! $ !
# $ $#
! # ! ! # $$!
! $ 4# # ##$$ ,#
! # 36# #* $#!
#!, $$! $$ $$ $
! $ # !$ 6 $$ ! # ,#$
$ # ! !$! ! ! $ *
$!4=##6:4=6;! $ *! !!
$ # ! $ 6 $$ ! D
D :DD;#$ $E(F! # ! # #$ *!
#
'
D6
@0
6
(4&
@
@
@
(
( !#
@0?# !$
@?$$ #$#
@?#,!$
@?!#
@/? *$$!,
@/
=9
@74
! ! ! #$ ## $ *!
# $ # $ ! #$ $ * !
$ ! ! $ ! ! ##
+,$G484$! ! !
! *#$$ $!!! 4=6! !
! # # !#$ 6!
! 6 $ $ $ $
! # # ! ! :$ ! ; AB ! # !
!' # # ! !:! ; ! $
! ! # ! !! !
$ $!!!
C

# # ! ! # # ! #$ 6 # #
$$$ ! $ $ $:! 3 $;! $!
@! ! #$$$ ! $ !!! $
!# $$ $!$&!$ $
!! ## $ # $ *! ! !
! $ ! !6#3$ # $ !
!:!# $ $;$!
! $ &! *! $ ! ! !! ! E(F
!! $ !# 3 #$ ! E(F $
:D6($;!! $ ! $
! $ $ ! #$ $ !
# !#$$#! $!#
$
6 =
E(F
4
)
)$
D&*!
'
D)
'!
%
D6
$
D
4 +
E(F
#
$ +
6 =
E(F
+
D6
$ +
D
@7I ! 6&9(49#
*+
! $$$! +7
− '! $ 7J# ! 3$ $ ! !
! !$! ! ! 36 $ $! !$#
$$ $ ! $
− ' &# $ D D7 )$ ! ! !
!$! !!! # =$
$! !$ #! =!! !$
*# $ 6&9(49 $ # !3 $ ! $
! #! ## $
− (, '=7!$!!+!!
$ &! ! ! $ 3 6&9(49
$! $$! $!
!$
− '! ' (7 ( ! # $ # ! $ !
! * $ ! # 6#
! #$ $ ! ' # ! !
!
H

− &*$ $ !,9 7 $! !$! !
$#! !#! ! !:$# $# $
$ # ## $ ; 4 ! $$ $
## ## !
,-./.
! #$ $ ! *$ $ ! # ##
##$ @#! !
! # ! #$ $! $#$ #
! *$ $ $ ,$
& J#$ , $$ #
#! 8#$ $ ##
$ !## D
!! $ ! ! $ $ $
*! # $ ! # ! #
## # (& $ $ $$ $# $$ #
# ! $ $ $# $# $
: $ *; ,$ $ $ $ $ # #
*! I ! # $ 3 ! $ $
$ $! $# 6$$! ## $!#!
$ ! !!! !
! $(! * $$ $! !
#$ *! $ # * $ !!
$ ! ! $
0&12
! $$ $ #$ 6 ,(= !! $ % $
($= '!:I$ K&3G=$! #
3$! ( # '!;"6 ,'!!$ % $
'## # ! :$ $ $ "
! $ $ $ ! # ! !$ # !
; I ! # # #$ ! ##
! ! !! $$ @ ! ! ## !
6&9(496 ,'
!$!$!! 3*5
$ #+! # #$
# ! !$ $ $ !
(&! #$ !! $
# 9 $# $ 3$$$#
$ !, ! $ ! !, # !
$ $# 3# $ $!! !$7
− &#7( #!$ $$! B#!
−
!#
I7 ! $ * :* ! ; !$
$ ## $
I! + ! # ! #!#$ !
#$ * # $! $ !
(&#6,#$!
6'$ # ! (&$##!! (&
$ # ! $ $ # ## 4 !
+ # ! # ! (&! &
.

Main Shipyard
= XML Interface
Shipowner
INTERMAR SY
Planning DB
INTERMAR SY
Planning
Application
INTERMAR
Collaboration
Application
Receive Enquiry
Request Details
Req. Quot.
Submit Enquiry
Receive Request
INTERMAR S/O
Planning
Application
INTERMAR S/O
Collaboration DB
Legacy
Applications
Legacy DB
Legacy
Applications
Legacy DB
INTERMAR
Collaboration
DataBase
Subcontracted Shipyard
Receive Quot.
Receive Request
Submit Quotation
I n t e r n e t
Tribon.com
Receive RFQ
Submit Quotations
INTERMAR SU
Planning
Application
Supplier
Legacy
Applications
Legacy
Applications
INTERMAR S/S
Planning
Application
Tribon.com
Application
INTERMAR SU
Collaboration DB
Legacy DB
Legacy DB
INTERMAR S/S
Planning DB
Tribon.com
Global DB
@7'
6 ,(=$ !! &# $$ $ ! # # #!
$ ! 6 # ! 6 ,(= $ ,# # $
# # = ## $ $$ # !
$ ) ,,) ! 6 ,(=##!
#! 6 6 ,(=!! ##$7
− =+7 ! M=+N #$ $ # ! $ $ !
&3K=!KI$ K K'
− =7! M=N#$!$! $
− 7! MN$ ! !
! #$
3
6&9(49!# # ! !,,! , # ! !
$ $ # ! !$
$ !, ! M8 &N !
! #!$!# # #
$ $ $# $ # $ $
#3$
'1
D9&% 9O:110;3&4D !'
(&P

! "#$$
#%&'
!
! ! ! " " # # $
%&"!#!!!" !
'# !(!!
' !!!"!&) #*!
'#!! #""!!#'#'"!+,*!
"" " " ! ## # # ! +-! "
!.'!! "'# !!!##*!
'#""!'#/""!$/.'#'"
.'""'#!
+,0*""!()*++
1 ' # # ! / " ! 2 !
'# ! " ! # ## ' #& "
.' ! / 3 # ! '#
$# 4$5 ! " !'# " / %# *! $ ! #'
/!# !6$#!46$57 # '"%"'
#"%# !%"'*! "!'#
/%###'%"%#

,
2"#
$#
!5:
,-./8149
,
,
A>'
@'#'%
>
"##
>!
*
='#
$##
=#!>?
$>?
(!'#
>
3
3 $*23 $*2
B6% C
C
##
,
)
<
;
,
,
,)
/ 8 !:
+0#!% "",4./5!/!0)***
%&#'
*%#7+D)%!#!+ #'
&#"!!!!'#"!
# *! '" % # " & #' 7 "" ! '"
*!&'#! #!!!' '
!!"!!
*%#70""!
!'# !'#
E! #E ,

=
{ ( ) ( )}
+
!2 G/ 45
/!
, 4θ
5
4 5
6 ∂η
= −,
{ 2
} 2
6
θ 4 θ
+ θ
5 &4 θ 5
− −
54θ
5
∂
4D5
4 5
{ }
, 45 G,"!!'#"!3!%
, = 2
θ θ
53
%!#"!'#"+)-.4D5' #%
&!!'#!%"""*!"#1 #'#%
ρ
1 = 4,
+ 251
= 4, + 25
/ 4
4)5
2 ! " " 4 ! "# "" " # 7**>IF 1 ! "#
"# !'# ! '""!!'#*!"'##'24,H25G,,
+0-&#"&"#
*
*!!'#"/#'#%#'η !" !"!#!'#
"+

*#1 %"'/0
(/ 71 71 81 45
#'!#"#'η "!%#η !! +
'# ! ' ! # / ! # !'# 4 # # !
"5!! #%#!3 "'#!" # 0
4$5>"#
7 # %# # ! # &# ! ' " !
/ %' ! !'# " %# *!"
#" # 0
JJ.
−, ≤ . ≤,.
−,
4

*!%# #'#"##$!%"'4 5
##:"#"!!'#
# # ' # '# ! #" # ' *! #
#!'#!*!#!"!#%
%" # $!'#'!# # !!#.'#%'
!/%%%#"% !:%!=#/%'0
, :
{ }
, : = : = ⋅ &
−
4;5
; 4
5 0
<
;45#/"!'0 < !=#/*!&#
" # =#/ " $ ! ' ! =#/ %'
! !!#
!7##'4 5
7#'4 :( 5
>'#'4 5
("
#'
?#"#K
∆
: =
(
) −
4
5
'
'
∆: <
K
6
!%%#
%=#/"
$
'#'45
&4
− ∆
:
5
>
γ
K
(&#K
(&K
A
+J0$#!"'##!
+J #'!#!"!$!"!!'#'#
#' #'%'%!'#'#
%%#%'"'4=#/%'5$ #'
'#"'%"#!*!'
)

456##' # !#' :(
4,56'#' #'"#'###'"
45>#'#"!!'#'
∆: = − ∆: <
7"∆:=$! #' !%%#",4∆:#
4J5
γ'"'%%'!#,
4D5'!'' !!.'#%'
4)5*!' !!"
- )
( ) ( )
− ∆:
, &
(:) =
> γ
+,07#!'#""!'#4#"54!5
+,!#!'#""!!'#!+,,! !'#"
! !'# " / " # ! ! " # " !
!'#+,D!'#"!7!#"!'%"
#!1#! !"'*! # !!
'%"#" #!#!2 !#'!
%#''#"!!'#7!!!'#!"%#!
"! +,,)$#!'!!#!"! !'!
! # % %' ,L ! # !'# " *! !'#
!!"" ''#
+, ,< ! ! #! % ! / 1 " %! !
+,! !!"%!"!#!/!'#""!
!'# -! # ! # #' ! " !
#!'! ! / #'# &' / # ' )
*! #" # "'! # ! ! " ! +,<
! %!" ! # ! / !'# " " ! 7
! !"!!'#!'!! "!#
!'#"#!#"#''!"!!') %'"!%#
"#'#

+,,/ ! # +,/ !"
4!'#5
#!!4!'#5
*%#77! !"" , : G1 ⋅/!" , "!'#"!
#1 "!#/!'#"%!!'#!")
, !'#"""

+,D0/ !#
45
+,)0/ !"
#!!45
+,0>!'4!'#5 +,!'45
)
$B$674,JJ,5
+$*IJ,*!FFJ
E$$2?-@1(M$$*-2E4,J;F5 >
B#' $1'%#!
E-3 7-?4-54,J;;5, ? 4 665@$(-
F

! " ""#
$%& #'%" #! " ""#
!
"
#
$
%
&'(
#
( ) * # # # ' #* )
# + # ) ) *)* )" * # #
+#*,'*#)#+"( ))##
)*#*)**"
- +# ' *,'* # # # ..
# ' *)* ) # ') #" /* # #
0#'*'**,'*# ..*))##
'#)"$*)*#*
)*# #).,"
( ##'*"(* #
*##0#* *.*#* "1
##,)*,# ..*
"( ..*#'*)*)#)#
*,'*'## )* "
( '* ## ..*#*,'*#)
'*"# ) )##*.'2
*3"* #'*), ) )
#*' * #"(*'#
. *"4* *'#)"
*' *' # '.#) 5"
5 * #"5.

*'# #)
**% &)*++,-"%
##*.)%#. )*++,-"5
)*% ##7 )"89,*.*"
)"8:-'*)%
/) ## " 4
*. '*# %* # ##" (
% & )*++,-" % # ' # '
" ( # * #%# . ##*
)##* '#"(**%
# #) . * # . ## #
#)."
(*% )
# * " )" ' *#
/ )*++,-"
5#. +##)**
''#)# )*++0-"/*#').*#)
% "*#*#
*" * . # )) # +)
%')*#..#"(*
* . )# ,*" ( ' # # '*
%" $ * #
*'). #%" )
#) ,)*'#* #
"
6

)":= *%
*** #'*))
#) " ( )
')* *##0#"(
##*#'# '#.*#'#
* #" ( % ## '
"
( ## % + % "
'. #"(* *.*"4
.*.* '##)
)*) #.*'*'*)#" %
* * .* * ' #. %
#)# *''/
)*++1-"
( ) # "" % ' ) #) ' .
)' )##))#')*++*-"
( .* #) * ) .* " ( .
)#'*#)
#'*" > % ) * *
) .* )'*" 4 .* # % )
*) # "4* *####'*,#"
%) )* ))*'*)'
* # * #'# ) 7* %*9
) # # ,) 23 4 )*++1-" '
) % ) ) "
;

% ) # )"( +#*)
+ * # #' # ' # # "
( ) *) # '% ) #
) " ( # ' '# #.)
*)# ##234)*++1-"
%),#*)*#%
*)#*)*#)#**
*'#)"
!"#
#%)* )*#
')*++*9
89 . : ( ## ' % )
#
9 : )#)*#)
) . # *) # .* *
.
?9 :*
#)
(')##. #'*'
# #*" *# ** )# #
' # .* # . )
" / ** .* # *) .
# #'* . " 4 )# # * #
.#)"( ###) )"?"
)"?:@##)
1 # )'* " *)'
+ # ," /*'*
### ) ##*"-,#'#
##*.# *)#
###'"
( . ) '* # *,'* '* ##
* *##*7.*'*9'*
) # # # *
#))) #.#*&)*++5-"
;8

( % ) )# # )
* # ' '* * #* # *, * ) )* #
* # '*# * ##" * # #
')#*"#.)/% '.**#
'* ,) / 1 ' )*++*-" (
% /. # //. ' #" % *
*)#*) * #* % *#)#**)
*###'#))#" '#
//. .* # #* ) %*# #
"6"7##4)*++*-"
$%#&'&&'
/%/.

'* # ) ) # # . '"
)* #'*# .*"( '**#
##.'*)## "@
*'*.)##* *##"*)#
'+### .# #*#
*#,"
@.)..'* )##
* %" 4 * * .# . ) # ." D
* .#*..#))2#*3&)*++5-"
)#/* *#)
#)"$#'# '#)
'#*'"4 #
'# ')"(## .*'*#*
' *# '*" '* # * .)
# '#,**"(*#. .*'# #)
#"
* /%#/' )""(
*.*"(*.* **.*7**.*9"('*.*
#'#)"$ #'*.
* '
*"
)":/* /%#/
1# %/.' '"1#
//. #.#*)'*%*#/"$
*# . *.* *" ' ' )#
*"4'#.' "4/ **#'
/ ' *"#' '.
."( '%.#/.' *#"(%
/. +*'* *# //."/' *
' #' )" ( ' * ## " ( '
#.#*##' #.#*). #.#*"4*
#*' *# %)('#D #"(
;?

.'*#.*### #"# )##
#* * )):%)*).
'" ) # # % # ' . #
#'#"%)#' #.#*
)# * # " % ) * %"
$* % *# . * % * # #
#)*)# *# "
( '*):
89 4* '# " ( * # . ' ## ' '
'#.*'* 3 %"(
) '#'5# "(.*'*
%#'*#"(.*'#*#
. ### )# %"('
#)#%"7 )";9"('
*% * #)"
9 = ) ##%"4#.*,
#% '**.*%.%7 )"E9"
4*% '## )#' #
%"(##)%)
%#.."/*)*.*
#"$.' *))"
)";:/*8)
/%
)"E:/*)
/%
;A

# %.*# #)'
) ) # ## * # #* # % #
*'" ( ) ' ). # * #.#* '
' *#*'*.*.)*++5-"
( %#'&%'
( % . # / . ''# % ) *
"(*.'#.*#'')
* )# * ##.*'*"
( ) # '* % /. # / . %
) ' )# * " ( % )
'### 5*)"(
# ' 5" * . :
F" -. ')* ## # )# "
% # # * # ##) " %
).*%## *%"(*
# # ) # '* # *' # ## ##
'"1. '*. " *
##" * #)# *"(#*#
'####''"//.'
+# #) ) #*" 1 //. ' .
. # # *' *# ' % ) # *
#%."
(%).*)# .*#
'*"() **#' )*
##*%" %)%)
) #'*%.#)#"
)":@# * /%*5
%) * '##
5"4)'*# %)7 )"9"
5# ' # %"(#
%###* *#'
* % ' ## ' % " ( 5 #
#'*",5# # %
#) %)"@)#%)
)# * # % *# #.#* .) '
;

"5 5 %)"4
%). * ""#"(#
) "#)))#)
%" ( % ) # * # #" ( '
*. # # # '*)) " 4 %
) #* % . "" # , ) ,#
## # ,# #
%#*' '*#"%')#'
% )" - ' . . ' '
#,*#)#"()#).
')# '*. #*
%)"(#*).##' #*'
/."# .#. . *#"(
*#. *.*'*#'# #)"$
)##'* %)#*.#
#.* % ) # ' "
#+#)%)''*)*
))"-.')%#
5"4 +##) .#"
/*.'#.*# %)"()#
%)'.#* '%
*%"(##*.',#####"(#'*
%)# 5 )"6"
)"6:*#*/%#5
)&#*+
*%) ** "(% # 5
%)#)"* .*.#
% " ( % ) # * # #0#
'*) #.* ) #" /
))###'*%*#.*####
#"4))' %) #
*%"*%%) %"%
;;

# .% )#"(%
%)#.*%'"(%' %
)% %7 )"8

)"8#8? #'))(-F8,*"(-F8
)#)%)%))F*F F*F
7)9" ( * ' ) '" ( )
*# ' # ) #.#* ##)
+"
)"8:@ '))* *
)"8?:@ '))* *
'*%#*'# #, # "5,
*#)#')"(# )#" )"8A
,#*' #.*#%"4*
##)"
.. .*'*'. #"4
' ,**(-F8 )"8"(* )
#* .*'*" *,#*.*# )
*" ( .*# * %" 4
* % # ) " ( '
*# %" * . ' # )
)))(-FB##).*#"
;

)"8A:@*'* *
)"8:'*)* *
#'#'*%) #
)#"-'%)*
## # " / )) * * #
) # # # ' #
#*"(@#*'#.*# .# #*# #*#
" # *# # ,"#
# '* # ) # ) ) # ' # # *
* # # # % # # '* ')" (
### #'# #.#*%##
'*"(%)*##%"
*%###*) #)#
#*# % .# . " ( ) ' # * %"
% ' *# . # ' # * #"(
#'#' *# # *')#*#."
,&
())###+ ))"
# # '* # *# "
% # )# %*,
###.**'*"5 ,) #.*#
;6

"
(% #.*# 5.) ***
% " ( +) % "
@) # ,# # # ##" (
).'#),##
)#)#"*+)
'*").''*'#.
' * # # * # . ' '* '*#
## "
4'# * )# 5 ** %
"%.#/..*'#.*#5
# # * % , '
#)#"4'* .#%)# )#'
*#) %#*.#'#
.'#"(#.) .)#)
*'* # '* , % )" * *
/1/%#4-,*"
)'#* . *%)
"4*#% *#
)#%) ' 5"
( %)'%.)
* ') #.*#" *# % *# # '
*)%'.*#"$#
%)')*#"/ ##*#'#
+ # *## 5"
5#*# ##% #')
% #"
)* # *##.*#"5
#.* #) * *" )
) " ) )* *
* ##.* "
-
-5-I"J-5@4-II">"JI=->5$"J 55-""J -4@-55$"7

D1L/"JC(-5/> -I"7

! !"! !#$
%&'(")'*+,
!"
"
! ! "#$%&' !(' %
%
'(
&!'% !
! ! "#$
&! ) * +
&!!,
- ! "#$
)
'(! "#$
&!
-!
# $$" %"""" $ " "$
" "# $ $" % %
& $ " % " "
% " % " % " "
'$ & ( ! " !% "
" )"% $ % " * $ " $
" +%$ "($
( " $ * '" $ $
$ !!%% ("" " ($
" !! % ) " " $ % $
," " % -,.#/ " " $
""
'$ ( " $ " $$ " " " "
" 0)10). $ $"% * . ($%
" "% ",""
" $ " ($% $ " ""% %+23""-2'1,
/ $$ " % " % 1 $%$ $
$ """" *$
% "$ ($
" "% $ "" " + (! ."//01 % $
$ $ "" )"% $ *
" " " $ " " % "
" $ $"% 2'1,4#/2/2%"#0."//$1
#/2/2%"#3 ."//21 #/2/2%"#4 ."//$1 '$ $ '$
$ "$ $
% $ $ " "" )"" $ $

" "%$$ "" ($% !$
" " 6$ % "" " "
" $$ $ ( '$
" $" %$ ""-/$$ "
$ $'$ $"$ 2$0#" -20#/ $
23'0789209: 5'5$""%5 !(."//01$
" (!."//01; " %$ 0).!%$
" "" * $% " $ " $
"" " $$ " $ '$ $
""0)( ( "'"$
" $ $ & " " $ """
$"%
Owner
Operator
Shipyard
Shipyard
Ing.-Büro
Ing.-Büro
Design Agent
Model Basin
Supplier
Classification
Society
6%742$" %""
, $ "2'1,"""$ 794

$ "" $ +23 " % 5 !( ."//01 2
% " " C. * $ $ $ $
%$ ),7B
: $ %$ " " ""06."
$ % )$ 06.!" &
$%$- " 5.$ /""$
$ " '$ $ % "
$ $ " %" ("-"
" " "" /)$ $$ $ % ("
+12 .?6 " $ " $ $ % $
06.!" 6."//$1+$" "$+12.?6%
" % " ($% $ """
" "$ $$
"$ "
'$ $ " ($% " $ " % " %
- "/ " " % " " %
. " $ ),78
$ " )" "$
" "" %$ $ "$ "
" '$ " % ($% "
$ $& % ( $ " ,
($$"$ ""),78D " $ "$
"$" $" %*
2$$ " "" ("
% $"D $ " "" ($% "$
" %"+12.?6" ,"""
"""% "$$ $ % "
" " '$ $" $ & "
%" %$$% $0).-./
" )

" " $ +23 " 2( " "
),E5007" %"" %$$ 0000B"
007""" % $ .
$ ),E5 " "),79
'$#/2/2%"/2.#77$1 $ %" $ "
& $ ($% %!"
5." % $"0%$(" ""
$ $ 5. " " % " 1($% " % "
$ $"$$ ($% "$ 5.""
'$ %* ),E54
," - $ " / , " "% % $%
%
. % $ 4: "$
% : $ % #" $
%6""H"
) -" $ %"%$ "
/
3%"- /
)"-""% !"
/
;"- "/
. %"$%
. %- /
)!""" %$ " %$%
-
2 EE7 $ ), #/2/2%"#$ ."//21 "" '$ $
" ""EE5'$%" "$ "
"" & "" %$$ " " "
" $ $ % %"),79 %" " "
" %" "%$ ,.# +
$ ),G $%$ $ " $ '$ % $
" $ ($% % " % $ $ !% " '$ $
$ % 0). " ,.# 6 $ * % "
%6%
'$ $ % $$ $ """ 4
, " " "% % "
,$ % $ "$$
$ " % % "
," " % " $$ " $ " "
#% "" $ " %!"$%
) -" $ %"%$
$ ""/
+" "
3%"- /
8 % " 4.! 5.!
% " " % " "
" " " " $
"%
A

D"% "
.$ $ - "$$"%/
66
,"" $%$ (" "%
"" "$ $$ "+23
7E5E5
2"$ "
,
2"
'
6%4 $ 6#/2/2%"#$."//21
6%542
'+40),79
007I00A
00BI007E
0077I0075
0079I007A
007BI007
0078I007F
00E
..
0).J " " %J 5. " " $
%"
,.#J " " % % $$ 5. $
% ""
"" %(
" ""
%"%5.$ J
" "
"% "
B

+),79 " " "$00E"%$ $
)+#'++ 0). ( %007"006,.#
00B"008"
-(" ."!!
--
'$ %" "$ $"
),79 " " -)+#/ 6%5 '$ $
-"%% /" "%$"% 0).-2!0)./ % "
$"% ,.# -2!,.#/ + " $ " " < =
" $ $ % % 0).! -#!0)./
%),79'$ $ " "),79!)+#"
" -2'1,!, 7/ -),79/ + $ $ *4
2$ ) 2 , " , " " ' $ $
"% " ),79 " 4 " "
""" % '$ *""" $
$ $ -% "/ % $ $ !% ($% " 6$
" 4 < " " , ),79< 5 .#7741
589:.#7741
product_category
name
label
*product
products S[1:?]
*product_related_product_category
application_context_element
name
frame_of_reference S[1:?]
label
product_context
*of_product
*product_definition_formation
formation
frame_of_reference
*product_definition
*product_definition_context
*application_context
frame_of_reference
(INV)context_elements S[1:?]
application
application_protocol_definition
6%94,"+" ),79
--!!
+ ),79 " " " $ $ $ *
-1/) $$ " "$* %
; ; 6%9$$$ $ "" " "%$
1?,122'$ *;
$ % K< K< K$< ) % % $
),79 " " %$ " '$
" " $ ; $$ ; %
;'$ ; "$

" " -% / ) " (
$$ $ ; ;
--!
6%A $ $ " $ ),79 " " " $
"6$$ ; ; "$$"
": $$" % $ %$I
$ (" + " " $ - I
$/ ; ; ;;;
"+$ $ ;; * K<
$ $ ;; * K<
*product_definition
characterized_product_definition
definition
*property_definition
characterized_definition
represented_definition
*product_definition_relationship
related_product_definition
relating_product_definition
*product_definition
*property_definition_representation
definition
product_definition_usage
*assembly_component_usage
used_representation
*representation
context_of_items
(INV)representations_in_context S[1:?]
*representation_context
items S[1:?]
*representation_item
*next_assembly_usage_occurrence
6%A4,"),79
6%B4,", ),79)+#
--!.
+6%B$ " ),79%" %" " "
+$$; ;$$ $ $ $%$
$" " '$ ;
"
," " " $ % " % " $
" " $ "" 6 " % $ $ $ (
;";;" % "
;
6 " % " $ % $ $ $ 0).!
%),79"$ "%% " $ "
6$ $ $ $$ " ""
" "$ -5. "
/ " $ $ $ : $ $ $ %
$ % " (
+ %$ $ "$ "
""" +$$
;; D - $ /
8

; - $ / " ; - $ /
"+6%F$

: $$ 6%7E$ $ $$ 4$ "
%$ "$ #0). %),79'$
$ $ %",1@+@110)'+)%$"+;
$$ % % " % "
+ $" " $ " " % $ $ $
-% " /$ " "$ %%
%%"
6%84D " "$P@),)2 >""$+.)!2;
1-
'$ ( $ $ $ $ ),79 " " (
"$"% "+$ $ $ $
( $ % " $ $ "
, $ " " $ %
" ""%""
6%F42$$ " "),79""
8E

0$ $"%"$" " " % "%
% $%*"" $ $%$$
< =
'$ " $
#0).",.#'$ "$ )+#" $$
$ 2'1, % $ 9E $ "" ) $ " "
" $ ( -%
& /$ $ $" " % "$
) $ $"% "
-" QR/$ % ),79$ ($" %""
$" $ %"
,&!
'$ "$ "$ 6 " #1"2
$"' $%" %E52?757'$ $"% $ "
$ $ $

(
H3@2)' J S@+1M+@ J T+##1#)@@ # -EE9/ ! %
F $ +2,. %
2$"$ 6%2-,).2/MU
1#2) -EEA/ : $ 1 ! ""
$4 %
1@.12 #J D)21 # -7FF8/ " " , ),79 007 00J 6 .J
."
DVMT1M 3J M1H1 # -7FF8/ = < % ! "#$ &&3
'."
+.)2'1,-EEA/$4"!
+23 7E5E5!E5 -7FF9/ +" " % ! ," "
" ($% !,E54)40%"5." % $
"
+23 7E5E5!79 -EE5/ +" " % ! ," "
" ($% !,794)40" $" %
+23 7E5E5!7A -EE9/ +" " % ! ," "
" ($% !,7A4)42$%
+23 7E5E5!7B -EE5/ +" " % ! ," "
" ($% !,7B4)42$" "
+23 7E5E5!78 -EE9/ +" " % ! ," "
" ($% !,784)42$
+237E5E5!9-EE5/+""%!,"""
($% !,94+%"% 4 "%
+237E5E5!95-EEE/+""%!,"""
($% !,954+%"% 4
+232D+,'1)#-EEA/: $ %%" %$"
$4$"%"" 5$
2D+@032-EEA/: $ C.*2$+"0+
-2$02/$4$"
2')1HM1J#+MM1HJ)S3: ,JS30D'-EE5/& &!'
&!(: "# ' $%026
8

!" !#$
%&'() !" !#$
!"#$ *+ ,!-!#" !#$
%& (.%" !#$
'
!"
#
()*
/!0! ! .-$0 $# !0 -! . !1
$!0 0 !0 ! ! #. !#! .. ## /2 !
-!!0!!#!-0#! #.!#!$!$!0
$.! 3402.!0/.!-5!
-!#2!
3.#.!-//-$..-$0/2.- .!#.!!#!0#
!#. 00 $ ! !#. -! #!0 6,0 3-7 $!
! . .-$0 0 / .! 00 ! ! /2.- ! .-!0 !
/2.-6,.!08!47 &99!!1!5!!# .!##-0
#0! ! !0 ! -!! #! !$ . /2.- .
-:#!!!#!0#-:#$#!#!$!.!$0$/.0
!0 . /2.- #0! !. 0 -0 . .! $ 00 !
/!!0!.0#!! ./2.-00!/0
/2.-;.-/.!!00!-#!$1!$!0.-/.!
!!$ .!!5.!

+)#
+)()*
.!#.!!##./2.- @;00#!..0
=!#.0.!/!0/!!-#!0

. /0 $ . /.#. .!0 $/ . / 0 . /2.- 3 !
#-!!#/.#.0/0-#.!.!$!#20$.!!
$.#.!50-- (!##!!./0#!#!0$$!-#!
/!/.#.2/#!!0!./0$!0##.!!##
-# /0 %. / . 0!! ! !!!$ / ! -0 .0
!!.!/0 .$!$/!!/0!0.

. 4# . -# ; (-!! @ F !#2 F E0 F . B F
=!#!G E2.!!!/2!#.0.#!#20/0
$ . . . !! . /0 $ / .! ! . /
#.;
.00-00!0!/#!.$/

..##-!#!$0!0!-0#0/#!.
B.!.!$#!!.!1#4#$.0#!-!
!#0-0.4##.!.!!0#@>?;
C!1E2.-4#
C!1,4#
B;,-!#!$0##-!0-4#
'!#.! G#!!$$!0 %!

-)
-)()*
!0$.!0.$/4#/.#...-0# 3
##! #! 0 /.! / $ $:# # .! / / #! !0
! /. ! - /2.- . ! ! . 2 0 /. #0
!# .#00.#0!..0/$!!0
-#!0!0/.!-/2.- .-$/..!/!1-
-0.!!#..!1#/!/2!0#0!#!!0
.0.!2..0!!!0F/.#.0.
/ / . . !$#! . #0 ! 000 $ .
$#!/.!.# E/..!$0!0./$.
./
3/0!/..!4#/$!!!!.!$
@G?/.#.//.!#0#!L>?AAA .0/!!;
1 .-!./0!0.-!.!!!!0

#-0#$0$# 3.!.!.--!
#! -! #! ! ! . ! ! #! ! $ -0
0# -! $#! #! ! /. ! /.#. ! #!
0!$$.$!0$#$.$#.!!##.-!!
.!!.. !.-!#!!
$$!0 +-!!.!$#.#.!.!0-!
0#$.
-)+)+)
/0-!#!$0;!4#!/
H !!0!#.!0..4#/..
! 0 . ! -!

-)+)0)%
E#!/0-!#;+#%!0 !0##
.-!!#0!0!##0.!/.# .
!00!/.0!/$0!-!#!.<
! 00!/.!$!0!!.!!#.!#$0!-! !
!0#.!!0 00!.!.!2.0$0
!-!
-)+)1)
.-!!!/#!$0.

L$/./..$!!0/!0!-5!/..
/-!!;
1 5!;>
1 $!;@>
1 #;$
1 (!#;+#
1 ,;)
1 &-#;@B
1 ,&;(9M
1 9!;-@##
L;=.
.0$#!/.!!!$/.!.!!0.$
B J? !0 . ! !0 . / ! . ! ! ! ! #. $
!/.!$#!$#!/0.!.!00!
. ! # !0 . / # 0 - $#! . #!# . !. $
$#!.00!/.#.#$#!00 ;=.&-#;@
L@

E#! @>.!/!0.!

! !0 0$ /.#. #0 $ 00 !! ! ! -# !! ! .
0)$
!$!-/!0/.-5!#!$ .!
0#.0-.0$#!!2!-!#!0
/.#. ! 0!0 0 # .! $ 0-0 ! !0 ! !$
-0##!!$$!0
$!0 ./ .! #- ! /. ! -5! #! $ 0 !0
#!0.! !!!.!#!$$!0!#!$!
. 0 !0 . /2.- .! $ 0 % / ! 0-0 ! . !!# .
0 ./.$.-5! 3!!#../$#!
-5 . ! ! 4# /.#. / #! . ,( .
!!# -5! ! .!0 0- #-!0 /. 40 $0 .
!0!04#20 &-5!!0!/$!0
#-0./!
!-.-5!.

!"
! #!# !"
" # $!$%#&' &!( ##
(#&##! ) * "$
%
! " #$ %"#$&
' ( ! %'()!& *
+ , - %*,-& "#$
. %.&
"
!
&
' $ +, $$ # !# # $ + $ (! -. /01
&# $ " # # $# !( # $ $ 2# " 3 4! #
( # #!#& 5 -51 # . / " -6671
$ #$#!+$(! ##8 # &# $# #99
! $#& $ # $ # +, $! $ $!&" . !( ## #
! # $ # ! + 4! $ $(! !$ # #
$ ! $!4&#"
' $ +, #$ & # 5 :(! % -5:%1 $ #
##! $(! # !# $ + #& ( #$ #
##&; (,-;1". ! # $$#!#+,
$!& # # # !$ % #& # ' &!( ## (#& + +
#$&#5:(!%# #:(!&# $ $ ##
:":666: 5"
&& ' $%
:(! (! $ 4#8 # (! +8# &#
# $ (! #$ &$ ! &#
##$ $!4 #" ! ?# $#(!# &
, +!$ $(!!8+ +, !4$ ## #
$+, ?# ! $$! $"'#$!#&#$#
$(! ##!!&+## $$ &! $## $ #"
$# $(! # # $ +& # 2,!& #(!& $ !&
!&#+#! $4#"#+( $ $$(!( ?$# $

($ !# $ #! ## # # $ $ !& !# " # #
!# 2#&#+!?$#+$(! # $$ $
# !#"
' #& # # !# !& ## @# # 2 $
# $ $ # !#" 3# # #+ !# $ # !& ## #
A # !#! #& !!& # # $ 8, # # $(! #
" ' !# ! # $ # !4! + + $ #! $
2$"
'$$#!#5:% $. $' ! &-. /'1
4$### # #$!# 8$9 ; ( #-9;1"!&
5:% $ #$ # $ ( # ! $ $ ?# (!($ #
$(! # $ + $ (! ## $ $ &
$! !# $ # !& " # ! # $ #
$! # ## $# $ #
!"
5:%!$$! (#(%-%1 < #-'5:%:6

$(&"D ' !# # ## $#!$ # $$ #! #$ !&
$#$+ #!&# $ !##( $$"3##
###$#$ $!#!8&##?# "
$#$ $$#$#!4&#(+#$ $ "
$ + $$#($ #C #"D' #+$$
$ ##! $ # +## #4##!# $## "
&(( * -
%0111& #$ # ! $# $ ##$ #$ # $#!
!# " G $$ # $ #$ #& # $( $
#!##$!# #+ # # #"G$$# $ $#!
##$ #$ # # $# #+ # # !# # # " G !
4# $$ # # !# # !$ # # $ $
$ #" . ( $ # # C! #+,D # # $ $
$# $#!# #+ # # $#($
$ "
3"&##! #+,E
8 5 8#!#&# # 84! &+&
8 , 8##! # ##,!&4# $ # #+, $!##
$$(&!# $
8 '#8 ### #+,#!#+ ! # ! #+,2
-6671"
$(!$ ; (,## !$ #
$ ## !# # ! #+, ##" 3"< !## # !
## $# $(! # ! #+," # ! #+, #+ $
&$ # + ! $ !!$ C#"D ' ! #+ # + #
F

# ! +### #+ #"'!C,D
# # # !# +# ! + , $($! #
$ #+ ,"
&(. %
# # ! ( (!($ $!& !# 4 ( # $
8#& #+," # # # # ! C+ ("D
;4# # + ( # ! $ # # ! ! $##$ #
( #C $D# "
&(.& ! %/*
. (*3( / ! %0111&!8 #$ # ##
#( #+, ## # # $$". (# !
$# $$($ #!,# &#2,!& $!&# # !
I( % 5%" . ! + ( #! +, #& $!&
(!( $ +$!&$#$"
. ( +# $ # ## # $ # $$ (45 ( .
%0116& + !+ ! # # $##$ # ( # # +, #
$ #+ #"+(!# # $$#&!+&#
$#+$(! # $# # +$# $( $( #
!,8#( $#&##+"
3"E'. (##
'! ##+(##+ 3""(($!
$ #( +##(,"'(2#(,
$$( $#, $# $($# #". (# !
($ #4 #$!$ $ ///3/%0114&
'(,# (!9# 9(& $# # -991#
#+(#!#!#(($ $($!# $
(!! (" 9# ($$ & ,& +$ $ # #! ! #4# !+
( #$##+ $ ("9(&($$&#!#&#
4 2 # # ( $# " 3!& # # !$ & #
# ( # $ $ # (!!
# #(,"
H

'+)
'##$##$# #$( $&# $# # $$
$ # #+ 2 %0116& 5!& $$ # +& # (
#$#&# $# (!($#
$& # # $ $!#(!8!( "$#
$##$ #+,####+ ##!#,##,"'
# # # $$ #! $ " ' # $$ ($
#!#& #+ # !#" $ # #+, !! !4! $
"
' J $ !J + # $ $# # (!! #
!4 !#( ! !( " 5# #! ! # !#$ #
$(& # ## #?# $ " ' ( +
(+# $# ++(#!$$#+! #
# $## %0116&
( )
9 $ ##9;; (,-;1
+# $ ##### $# $$+("'!##!#&#
$( $!,# &#2,!& $!&+# $#+ ?# "3
4! 8 (! $ #?# !# #
2 # ! $ ##! $ ( 2# $ # #"
. ##;+, #?# $K!$ (# $
(+# $!#"' # #!## ?# #$
$# # $ # # (!! !# ##A
(#&#"'& $#!?$$! $!#
($ # $ #8 $, +!$ !?$#!##$!"
' 2###9;!$E
8 85# #$$ $ ( #!+
#!$# !#$ ### !&#(
4$"!#+# ! $##+# #$#
###! &!#"##9;($
#+,, $ $ $ "
8 , 8 '$# ! # # # $ $
!#$2#!&##$& #$#$(! #"
# 9; + $ !# ##$ $!& $ 8$ $
$ # # $ # !" $ # # + ( #!
!# #!#& #+ &# $ !#" 9 $
!#$#&#!!$ # # $ !&
#"
8 / 8 !,#2 #!($ $
(#9; !#!&$ #!?$ $$##$(
# # # ## $ $ & +$ (#& # $("
!#!# # (, $!&$ $(
$ & # #" ' ## !+ (
$ $ &(!$! $&#!!#&"
8 " 8#$# !& $$! $!# -/1
?# $(! (!$$$ $ #!#+
# $!# ". ( ##$!# ##!
! &!# !&4$4#!+## $"
( $ (!! $ # , # # #! (!! # #
#@##"
=

8 !8'$#+#(!$$ ( ## #$!#&#
#!$ & (!# # # # $$ " 0# (!$# $
$## -00/1 ## !+ ! # !# # # #
# ( (!# # ( $ $# # !# !## $
" A 9; ($ # & 4# 00/ $ ##
#"
(& '
';+$(!$ #+ $! +#++! ( #
!#&#$!&#$!&## $$ ##$ $ #". ?$!&
+, # $ # $# # $$ ## !& (!!" 2 #!& # ;
# 9;!# &# $!#". (! #$ $#!$
; #4 $ 4# &#+# ## #2$#
$# $" # $ ## # # # #
9;#;8$9;!# $# &#$ $ #"
(&& *-
;!& # % ?$ # ! $(& $# $ $
# # $! # # 0/. #&" ' :(& $! $
!# #5-:051$ ?$#!$( $
( $! $ !# #! :(&8+$" ' !# + # #
#&##+!$($$#!# $! $!# (!! #
#:(&$ #"###&!&!##(!!/#!+##
##"
$(! 998$ #&#### $ $ $
!& + (" ' 99 # $! $ # (
# $ # $ # ! # $# ##" . ! # 99
# ($ !?$##+($# (2
!?$$#####E
8 0!$# (# $$## (($$
8 L!#& $!# #4## -" "&!# #"1
8 2!# -" " 4#2 ##"1
8 5+ $ !#&
; # (!! #$ # ! #& " '& # C #$D
#" ! # #& ( $ ( ($ #
#$"';($ $##(+ !($#
$(& $ # # " , #$ # # (!!
($ ##!# !#!$#+ #,+ "
(&( * -
3"B !## # !# $ ! ; # ! #+," .
$(!$ # ( # ; $ # 2 # # ! !# #
?# ! $"
8 !;-;1K'( !+(($##(!#
!! - C !D1 $ $$ # # +# # #&" '
; !#8#8&#;+ "
8 ; # ; -;1 K ' ( # # ! ?# "
+## ?# #; $$((!$ $#$
;;# ## "'; #;+, #!$+# !
?# "$##$@### $#& #&

8
# !# $ $# +# $#& # # ; #
;$ !# !"
9 #& ; -;1 K ' ( # #& ( ##
(!! # !#! #" ; $## & ? # # +#
;" $$# !& ; +# # $ #! # ( +# #
;" . ?# (!($ +,
$ # #& ; +, $!&$ # ! $#$
#!#! !& $!#"
3"BE! #+,$ # # $ $ &#
#!# $!# ## $#!# !# $
$#+##;+,# !#&## #"5 ## $#
#&( #;$!&$&# #& $# $&##$#$
#&" ! ?# # #!# # ## #9;
+# # #& 9;" G+( & ?# # $ # ( !#
$ ####!# #!$$ ##+"
3"B + # ## #+ # $ #& ( # ;" (
$(! # # !# $ !# ( +# # ; ;
#&;-;1"##($(! #((!!# #
#+,;"'!+## +## # $##("
(&. *$%
$(!$+8$#! $##!+(+ #,##! $
4#(!!# ;"'# $#!!##(+
##$#,+# # &$#(#+#+(#!"(
!$ ## ($ !!# $ !& $# # $# $#
#&#! ## $ ! ## $ # (
$$ "
8 - 8 ;4! $# ! #! ($ & +& #
+# # & #+ ($ $# ( # 9;
+,"
8 7 + 8$(!$!##!##(( #
# $$!&!$#("
8 3 8$(!$! #! 8$#$(
($ &+&#+## &#+#!$ $ 8,
(#9;+,"
B66

(&0 *+
. !#,!#9; ( #(, !&$ $
#$ ## $##,$ + $$#(! ####
(!!("'(! ##! ## !&+&##;8$9;"
+ +(#!!$ #99# ##
#$##(!!"'!+!4!#& (# $#?#
#### $$ #"
. $(!$ ! # ## !+ # !# ( $ #
$($!&"( $#$ #(! "
# $$ + + !# !#! ( # " ' ($
(! #+ # (" ' ( # !!
(" !& $$ +,($@#"' ($!##(! $
!!"' ###$ $ #& (+$
!&?$"
(( 1),2 3
. ! # #& #+ # # #! !# # +#
# #& $ # !( # ! #+ #"
# $ (!& :05 $$$ # ! & #! ! +
# ## ($ $#( $ ## # $! $ !# " '&
! ($ $! (!$# (# $ $## " . ! # $!
4# (#&4 ( $$!##! #"
'+,!$ $ $ (, ##!+ ?#
#! $###+ $ " !# &# #
#$! $$(!!$ (# (!$# $$##
# " '! ; +, +# # # ! # !
# #2 #E
'!E' ! &
14
*
" -
($!# # # #! #& 5
($! ##! #& 5
#8 ##8 # M: MM
#!8($8#8 M: MM
#($(&$# $## :
M
#
# $$$. (! # #&: 5 M
5 8$ $$ ## # : M
!#$ $ #
#N M
I(N
#$# : M
G $#$ : M
$(! #! $4# # M
#$ # # : M
#$ #& $# # M
B6

.
*-$)" -
+, !!& +# # !$ % #& # ' &!( ##
(#& -%1 $!& # ; ##& +, # $ #$ ! $!
!&" ' !& $(!$ & % # # +, # # "" :(&
##$ $ $ ##$#,"%4# (4
$ + # ! $! $ !# & $ +
&#&# $&$$& "'; $!&$$ ## $
## % ## $ # ###&$
$####&((!!"
.& + )%
'#(!&## $$ ###;+##% $$(! # ( #
$%+,$# ##$(!! !####!+ #E
8 '! !# !&2$@#"
8 ' !& 2 # # # (! $# !# $!" '
!& $! $(!$ & # $ $ $ #
+,## "
8 ' # # # !# $ # !& # #$ #8$!
$ # $ # +# # ; +, $ 4#! # # ; #
!# $ "
' ! ! !#$ ## # # # + #$ ! $! !&
$ # @# $ # #$ # %" ' ## #
$!$##!&#?###$! 3/8-

User
Input
Pneumatic
Tube
Launch
Inertial to
Body
Centered
3"7E!
Air Launch
Angle
Conversion
! #$!
Water
Impact
Water Entry
' !# # ! ! # # $! + # #$ # # #
$! ( # # % # !& $ # ; +," # +
#$ # $! # # $ 4 # # #$ $! $ #
#+# ( #"
.&& / $
$ # # #( # # # # # # !&$ # # 8
$!# # "'+ 3"F" &$!#%$(!$ $
(!$#$ 35%'%:" ' # 2 # # ?# $ $ !!&
35%'%: ! # # $(! # $!" ' $! # (#$ #
#! $# (!$#$#! ##35%'%:$!# #&##
!#" 5 ! $! # # #& # # #$ +# # #!
!, ; ( #" # + !#$ !#$ # # # 2$ # $(! (!$#
(# $# #$!##!,$! ( #"
Develop
FORTRAN
Model
Validate
FORTRAN
Model
Covert
FORTRAN
Model
Validate
Simulink
Model
Integrate
Simulink
Models
Run
Integrated
Models
Develop
Simulink
Model
3"F8;4# $!# #
.&( *" - $
' $! # # +# # ; +, ! $!
( 2$" $! !$ $ #$ # # ; +, $
$($! # $8! # # (!$# 2$" # $! ## $
# (! # $ # ! + !# !& # #$ #
#$!"
Develop
FORTRAN
Model
Develop
Simulink
Model
Wrap & Publish
FORTRAN
Model
Wrap & Publish
Simulink
Model
Validate
FORTRAN
Model
Validate
Simulink
Model
3"H8;$!# #
Integrate
Models
Run
Integrated
Models
'!+$!#$(!$$##!## "3#
#,$( # #(# (!$# $$## # !#!$$#;
B6B

( #" ( ###!#$+#(!($!$(!
# $! $ $# # + # # $! (!$#$" 3"H + # $!
# # +##;+,"
.(
'+$# !&?##!###;$##
#%$!# # ( #"'+E
' ; '
< ! #!
#!3 # !#&
# (#$
35%'%:##!
=6G
F6G
;
G+#+!#
G+#(!
=G
=G
'#!

'!0E#4#!#$!! $!# #
# :> ' ; '
< (#35%'%:$!#
'$!E
7$!-P6G$!1
' . ##. #$
3!# $. (

8
8
8
8
1
5 K +# # ; +, ( !$ !# $!
!# $ 8$#$ ## !$ #$ $ $
# #$ +## ( # ! $ +## # #&
#+"
* 9 K +, +# # ; +,
?# !& #! $# 4# $! $ !# +##
4 # !#!#&#&# "
* K! $ # $$ $#!$ (!$# K
#!$&(! !#&$K+##;+, !$ #
(!$##$ #&$(!$+##+, $# $
# +##$(+"
- K! #!&(+$$ &
4#!!$8# $ !#&$8+! #!&$#
!(+ $(!"
! # 5 -6671 , /: * 3 5
; 35.#%#:"58678

!
" !"
!
#$ "
# ""$ %
$ $ ! $
!& ! $!" !
" '
"$ ! " " " " ! !
$( "!
!$ $ !" " ! !
"$ ) *!$
! +,-!"*! $*! $
! !$"
$ .$! #!$/ $
0 "$"
"*! "
$ $1&!"!
! " % !
*! ! !"$ "
! 23-) *!!!")!
!! !" *!
! ! " ! !"
" !" *! " !"
$ " "4!
!! "" !$
$ " " " !
*! & $ !
" "
%$"
( !" 5!$ $
" .6778/" !.99/!!$
$ $ ,!" " *! &
$ !#$!! $ !$
! $$ *!
" ! $ )!
!" !

! ! !
& $#.677:/ .98/ !
!! $ $ ! ! & !
!$;& !"
" " $! !$
" ! )
! "!"$!5*!
-! ! $ "! )"6 + < 3= > &
,? 5&>!
@$ .*! / " " 5& "$ > !
" 4""
#!$
'($)$(*(+
)"6

!$" +3
*! )"9$!0,1(?.99899/ 45
"" *! " " " !
! " ! $ ! 5
!!$"*! A5
+
$ "
− " "" !"
− 3"$ "
− &" $ ! $ !" $$
− " " " !
!" "*!
− !$
""! ! 5"$-"!
!!" " $" " "$!
." !" !
!/ 5 . "&
$ " / ; *! !
"!"5$ ! $
(+ $ $ ! $
!$ $ "
" ! !
*! #
" > $ !
7

$)! !! $ ! !
& !"$$ $!"
! (+ "!$"H!" H!
! $ 3!" " 5 " $
! ! )" & ! $ "
6'3*-)'121'127/-/
)8/7/*($
(3(//1+73)$.)'('*/
9(*(+$-'1*-)'
1'9
(8-'-*-)')8/7/*($3)$.)'('*/
86'3*-)'/
7/*($/*+63*6+(
/(2(3*-)'
)+$621*-)')8$1*,($1*-312
$)9(2)8/7/*($86'3*-)'-'0
:')42(90(;1/(8)+$-'0
5 & $$$ $
! " " $ "! (+ '
!
$! .98/ & !"
" !"!$"
, " ! $"%
&! )! ! .6729/
% .677/
""" "$!
" ! "
! $ " ,
6

! 5"$
! !!*!! $" !"
!" ! (
$ *!! !" ""! "!
!! <
C IJϕ 6 .&6&9/ϕ 9 .&6&9/K
.&6&9/"!Jϕ 6 ϕ 9 K $ !
&6&9 $ "! L$ C
.&6&9/ L !
ψ. $!/ <
& = & + ϕ
6
6
6 9
& = & + ϕ
9
6 6 9
# " I .& 6 & 9 / " ."
I.& 6 & 9 / !
<
' . /
= 6
4! & $ ! &
!& !!<
#
!&?<
=
−
= ! ⋅ ⋅
6
9
=
6
4.& 6& 9/ &; !)
! ϕ 6 ϕ 9 <
ϕ6.
6
9
/ = #.
/α
ϕ . / = #.
/α
9
6
9
9
= . α =
−
−
6
9
9
9 9
6
/ + .
9
/
!& ! )"8
$"%&! $.!!/ $
#! $5 $&$!"
$" & $&#.&/
!$" $ 5*!
$ & &
.5656/ !)"E
M "N " ! + MN
&5 #$ ! ! !$ *! !
& ! M! N "
M! N#$""!! +! !$
! ' " !
"*! $! & &
% ! !" #!$
6
9
66

5
*! " ! ! & " &
# $ H " ! HH " H
4*!$ $$ #$B
& "$! &
)
)-
)"8C& !)!
(. (/)/
-. (*0-
(
)
)-
(. (/1,
-. (,02
(
-
),
-
),
)+
)+
)*
(
( )* )+ ), )- )
(- ( )* )+ ), )- ) )-
)"E- #&
($)"!
O 5"$ %$5"
! )! $!5""
$ ( ! " & &
#!!& $ %$+$ &
!" ' !
$$ " $!$!"
& " ! O & "
!! "$
*
(;?(,-O @+ > (;?(,-O @+ > PO +1?P1O +4P P .98/ #
"6
(!4 8E587
;1??(,C.9/3 4 9 4-,+'!" 965E
)*
(
69

;1??(,C.9/ ;! 5'
)(QQ1?O >'13>,+'O >'(0=.677:/$ !
99 $ 0'$$O "34 :59
'1QQ?-,.9/ 9 4-,+'!" 965
E
'13>)(QQ1?O >(,,1101>)4.98/5!
4-,+"! 85E
,(+(@ F .99/ ,
? ,+!)
014'(1C R+> 31=R(?1C (; .96/ 6 7
'R3?-0(C%9668 +4
'$$ 3"5,$#
-0?R(=+0 Q> ;-QR(0@++ C=> =(,@?1Q+3P1 ?C> ,+'4'10@- 1)
.6729/" 8 .$@0"QO 0!
/F O $
1+),>F('(0;(@''1.98/5! 4-,+
"! 8E75827
P1Q(0=+1O +4P .677E/ 9
P1Q(0=+1O +4P.6778/ 7
, "$E 865E
PO +1?P1O +4PP.677/"
,$
6

!"#
!" !" #
# $
" % % " &"
'#"# &( )# "
" ( ( %
*% "#" ""
(##'# "
) " % + # "
" '##" ##" ##
" ," #" ##
" # # " ( # -# #
"## #&
# " ( # .)-) /00 *123 )34 ) #
# " '# %
"# +%( # % ""
" " # " '# " #
" % # # #
#'#"#5'5'55'
%# &# " '#&
# " " #"
$"%
'# " "" " ( #
#"" ##"#"
5'5'55'" #3 "###
""&" ( %6 ## #5'
5'55' "# " # #7
'##" ##( %$
o " ," "
o "" " "
o " " ( ###
o ( ##"
'# &# " #,"#" ( #
# # #8 # '# #
" " ##

'#(## # # "'#%
% " " # " (
# #
: ( " # "
#" ##"" 7 #
!"##$%'## "
""". 4'#(## # #" #
#: ## #
### " '#(
$#( ( # " '#
&" % # " (%
( # ."
7 4& . "7
42"##"#&" "
" #" 7
'%"# + " %
"#; '##" %
" # )3.)" 3 7
45'55'&'!())(%*!())+%
&
'(()
'(()&
'(()
; $#"
'(# $
• ""
• "" (#
• ##," "
• # " "
• #
• %( #" #&"
• #" #
• " ( ##
$"
'# ##"# . ( #%(7
4#"7
( ## '# #" ( ##" 7
9

) ( ## " # "##
" ; =$
7," "
7 " "
7" ( # ##
( ##"
*# # " $
-,.
,
-#,
.
*+,
/,
,&
*+,
*+,
,
; =$3 #
• 3 $ '# # " ," "" #
'#%"# #
% "# &"
#
• 0 $3% " 7
" # ( # #
• 1 $3% #" (# "#
&# (% "" " . 47
" . 4'# "7
"(## #&". 4
# '# # ( # #
>#
0"
'# # "% #
6 # # # ( ( ","
# )
,!"###%,!())+%3("##
""###(
# ( 7 " ""
'# # #
" % * -' ./ !"##$% * '

!())+())0% # # ""
(#
'# # ," # #
" "# @A .@ %" A " 4
6 % 3 %" A " .3A4 # @A
" # " 1 , !())(%
, !())(% 0 ( # 3A
&#
1" ( # # "
&# " # " '# " "#
" $
• &#
• (% "" " . 4
• " " . 4
&''!())$%# #"
"# &#
(#'## #"7
" #3A
1"
6 # . 4 " # # #
( +#" $
4
=4 " 8
4 ># "
."#" 48
4 " . #"""
4
94 &" ". 4#""
# "

2"
'#" # #7
*# ###( "$
• . ( # %(
4
• " ( ##
• ( ##"
: # #
%( '# ##%( $
• ","
• "
• (%"". 4
• " " ( ##
) # 1 " (% A)0
) " # " '# "
( "( ##"#'13"
'# # " # "" #( 1#= )
#" ( #BA ! "
'# # B " " '#
7 # "# " # # "
(" '# "" #DEA = .D( E"
" A " 4# '#
#3A-# " 7
4
4
x [Nm]
6
5
4
3
2
1
0
ψ A
= 15 [°]
V A
= 10,5 [kn]
ψ B
= 270 [°]
V B
= 10,5 [kn]
4
TCPA [s]
4
CPA [Nm]
1000
3
2
1
0
0 500 1000 1500 2000
t [s]
0
-1000
0 500 1000 1500 2000
t [s]
0 1 2 3 4 5 6 7
y [Nm]
H AB
[°]
200
0
0 500 1000 1500 2000
t [s]
; $ ' # 7 " " $ 4 # ># )
( ( # # " # # " 7 # " 8
.&4FFGH 841)84'1)84# !##I
; #( & " # " (# #
# # '# #
( " # 00 !"##0% 6 6 !"##$% '#
BA =FF=#$ "
= DEA I 1"=FF=#$ (((""%,
C

" (% 78296!"#:(% 3
# ""# ## "# ) # "
# " #)" (#I#)%
"0 ##"# "#
"
'#( ('# " ( 7
" '##) #I # " (
.#)4" "#)#
" " #" "&'!())+())0%3
#I #%#"# #)7
#I#
#)'# # "#)%( #)
#"> " ;
3"
'# # " # &" #
'# &" # #" # (% 3
" " " # " )3 " 5!;
" 2"# # #" 5!;#"
5!;.9
> 1:A-*/ .# 1:A-*/
#" 4
4"
'# " # "
"# #('# "
( ## $ : (
# '#
# " ( # # (% #
'##" ("
3 '.3'4" "
5
1:A-*/.J?=471&7 -3:
00.JJ4;
( +
&8281?

1)8/)A:-6 .JJ941
< # 3 '#1
'* . #4
3K*0/)- -D8 )AK)0D)- - .=FF=4 1
2 /. =FF=4A)
D:)1LL8:-/)M6 8-I)ND3B.=FF41@1
*"B0 =97 =FF
'# '09D( 997'
C # 3 1 R)*D'K I*L3*1L*N'6 ) 0)6 :20*/:3
:26 :20*/::-)LA:'S6 0)2:-L*T6/. 4
-*AB80:-53/.JJ941 , !
')'*1L0K )8 -I)ND3 B .JJ

!"#$%&' $
! "#$ #%
!"
##
$
%
#&"'!
()"(*)
( ()
+,
$ +,
()$+,
() *+
()( , *
&&'( %"
&' &% & %&
%%& %
& & &" % ) % )
&&%*+,#%&%
) *+,-.
• %/010%) &&
#&-)#(2 %
• %%
• %2&&(34&
&
• &,005/,51500607/5671&"
8#&"'& )
0 *&#&%&.
• )% &&&0&
• &
• %& %
• %% %#
&
* &4 & & 2%
&4#&&&%%/3)#41
()- .* ,
9) *: && *+, & % & 0) %
;*&%&%%&%&:8:8,%&&

& 8 % *+, & &
#).
• *+, & %
% :8 / #0
&%1 & %
-$.&/000'
• 0 %0) #
#0%)&&%%%&(
/1#
8&%%&,7
* %;&/,7*;1*+,:81&/000'
# % :8 %
:8%:8:8< !2&3445'
% # 2 *+,
% & %
16&3445'
; % ;= &
% 7< % & %
& 0 # & & )
* #0 & :8 % % -
%&*+,&&% & >&&
>,78&&7/871 87'%
# && % %% :8 && # *+, &&
)#& 0&
*%#,7*;#))#-
&& ##%#%,&;=&"
,7*; & *: 2%
# 7< % ,7*;
&% && # ) ,7*; -
-) /0123
? 0) *: &%
4>&*8/@>* 1%0
AA 35&

%#% %%%%
% % & / & >,7 &%
&" 9 &3445'1 # #) %&% &&
*+, )# %% &
& >%00D&%
− : % & &% C 9)#
%& #&#)#+,"#
%%&#
− 7

0>#'&%%#)
% & & %% &% %00%)
'E %& %
&& 5&&"
% %% &% ,& & #
%)0& 00
&"&&&&
% %% #
2% +2% %#)
& & / &
%1
+& 7 # #
7

• % %& & /1 C & # )
%& ,7*; & % & &
-%&&>7$&/00?'
>&%%&&
&&+&%&)
& %,7*;%&&
• & /1 C % & 2 '&
' (: %
, ,7*; # &0 #
% &&4 & 5 34
& / &&1 & % &
&,7*;&#8
&&%%%),7*; 5+,&
%& &
# & :8 % & && % %
#)&+,%%%&

#,7*;0%0%
%
,&&-&'&,7*;0)
#,7*;#&&*&)#
&%,7*;0)%&0)8*+, ,7*;
# %
&&!2&3445'>&&4,7*;
3%&%4C ##)
%#%#),7*;%
6)4 7
8*+,&%-/0%)
1 %% & ,7*; %&
).
•
&#0
>
& %& & & %

& # & % & %) &
%& & %#'&%'
8 &*+,
&%%%&*+,&"0#
%%&
• -&&
8 ,7*; %& &% -
&% &
#& # ;E &% & & &%
- % % & # ,7*; &
-,7*;%
• %0&&
8 &% & % &
%&&%&)&
)&&%-%)%4%
%#4%
6)6 85+.

8%# %(
%%&&'&%
%"2%&
6): &,9 ,
? ,7*; 2 - &
%&%,7*;#%"
*&%%%&&
&%&%,7*;
+,7*;0)
%&%7

• & %%&0%
# %%%%
&%&)#%&%% *#
%/1%&%&%%
• & 0% 0 %0 # &(
&&%
&%%
• 2%0 &&&%
%&% &
&
• % % 3%4 " & -. %& &
% ) F :%& /& %1 /&
%1%#"&8
& 2% %%&
8 & % - %&% &
% % & && 8 ) &
%&%%&8
0&%&&&
• %&#%"&&&F
8% #2%%
&%&%#& %%)&
%&%%
Product model
item
Function Document
Set Component
Spatial region
Socket
Connection
F.>%%"&5%&&5

:)- &!
+ %% - % % 0
- & %
% % % & &" , 3
&%&43#&%&43&%&40&&
% >#>&8%#
&%&%&+& % &%&#&
&%/3 %43%418
/N%1 /& %1 " & & /%&1
"&#"& %&"&/1
30&-04 F"&&&&
# & & # " & * -
%%&&%%
34#7% 3)4
"&8%-
& & % #
&(%3#4
#3&&4%%"& ,79 2
* %&% %&0
>,79%
:)4
5< %% % - & >,7
- 21 &/000'%%
0&%&#5% % & &
#)&&#) &)%5<
% *&%&) 8& %
&>,7872 &3444'%&%#
%&>,7%%#%)%
C &&%&%#
&0*: *+,&&
&
;) !,93 !9
7

• &&
• %&2&&
:% &7&
O:88:&%
;)( ,
* & ,7*; % 7< #
%% % % % 7< % % %
%% & % % %- :
)5"5/551&&&"
GAA %& 0
%&: 8&% %
%0%&%%%&%%
%%?>#%
& && % 8 #
&% & " %& #
7

" 7< & 9) 7<
%:-&&%&&,
&#8C&#+#8
00 , # " &
2#0& 80&&&
&3%4(&%&&%&0%#
& &"0# FG # : % %
%&&8+#&&%&
+ *+&83)4&&
%+ :"&%%
2% &"0#>%&"0#
&3&"4&&&:(34&
% % % % % 8 # % 7< %
&"%34##5"
)0)0 %&
)0&"0 5"&
& %0 # %( %4
%: #)#%% (#)#
&
Ship (part)
Ship (part)
Situation A
M
Rev
A
Situation B
(Propulsion
system + ship
have been
revised)
Rev
A
M
Rev
B
Propulsion (part)
Navigation (part)
Propulsion (part)
Navigation (part)
M
M
M
M
Rev
A
Rev
A
Rev
A
Rev
B
Rev
A
FG.%:&&%&
;)4 ,
:#&7

?&O:8%%&:&
#:%"&)
# : 7< % % :8
3)47 *&&&%#:87*
0 && E ) % 0 & %
&%0&2/&1&
: 7< % && ?> C & :
%# ?>%-
;): !7
&-:7 & % )# 2%( &
& && # & 5& && 2% :
- %& % ?> %0
#)&%&
;); 93 !
5) % :%
&&>)
&& && 30004 : &%
- * )# # # :4 % %
%- 87* # & F %:
,&7% % >%%7%% & ( % %
%& % 87*
* % >>8 79< %& & &
2%%( %
%&2%-

% % % %& 7< # &
&.
• #%%&&&>+&"
• %& %&&#0
• %% / #1 %0
( # % " 7< %
• & 0 %&
& ( %" %- 2 %&
&&#7

,;*6>8 > 5 ( F8P* , /MMM1 !-(
A * : :%& 8&&
>&/*::8>1:%
?*>:P,; + ( 68>>,9 + ( 98R5 7 ( E 55 ; ( E L

!
"
!!
" # ! $
! %&'"
!!!#!!
# $ ! #! "
"("#!)
" "!!
*# + $*
!" ) " * * !!!
#!,
,!"#!!-!
! ." (! (! (" '!!
/! $ # (! 0# !## # %12(&
) ) 2 ! #!
3! )
!
$3!#%4$& ##
!! !! ." ! ! "
#)"!#" #!
#! "!# " ) # !! "
! ! ! ! # ) ! "
!"")*0#5#
! *##,,, %-$(& ! # "# $ 4
##!#)"#
#! $%&'(()!
* ! + #
!+
!
+

4 # # ) !# ,) #
!###$")
3 !## # %12(& !
!! # "# #!3 $ # #!" !!
#! 3! 12( #!" !
!!!#"""#
#! $ / !)
!! #" # 0 7
" ! #! # , #
# !) 1 ) #!,!)
##!"
/#!3)/,
!" , ! !
" " # " $ "
#!#"
#!2#")
! 7# # !
# # #! # ,
! 5"!#!#
"$) 3#!!!
) )
$ 48$!292#(! ("#!#12(
,
,-,
1!
##!! !!)!
(
(
."' 2(:#!4;(#
1)5# 2 # )
0 /!"
4 5 5 # # # " ) !
'#
7(
(!

78$51!5
1!###!##
* * * ) * * ) * # "
# 7 .) # # # !" " # )
"!###! ))
" # # #= " # !
!= # # ,) # '
/ 3#! # # ) ) )/! #
!!$)/!) !"
###!0!#$ #
# ) #! # # ! 3
! ! #
$ 44!"
$ 448$

• !!2#
" #
4#"# !/)"!"
$"#?)!)#)
# !! ) ) ! !! $ ! -$(,
# # ) # !! ) "
$#!#*! #
#! 4 -$( *) !*
%(-1& ! # " ! " '
!# ) !/-$((-120""
0!"
D 42 EB+ 7 !## ,
#!!"##!,
''142EB+)*,*
!! !! # $ #
!!"##)#
*,* ' ! # # "# ?"
# # " !! # " #
0##" !
# !! '!
! 3 # !" #? 7
!!!42EB+# "#
$0#))"$1##
2(#%12(&2!")
)0#$0#" "!CCB*
7 0!# !" # #
!)8
• ()9!!
• () # # %! ! 3 )
!!!)&
• 7!
• @(
$%&&
$ ! !! ) ) #!
, )"

#!!!#
7# ) ! !!
!# 0# ! !!
#!)$)0!! 4(-42CBBB
$ " !!" ) # " #! )
0#
#'(
-#?#12(0#" !*2
("*#3%*2("*
!!!)"0!#&#
* #* # " ) !"
# " $
# 8
%& )!" ! ! # ! %
3!&
%& !"##)#"%
#) !)&
$" "#3)
$##"
" #D 12(#!,!*
" 12( ) 0 0# *
()#(#7>
* () # '# %('& ,! !
# # ) ! ! $
## ) "!
!)!$"#
4(-CBB4(-CBBB,4222+>C4# #
!"!#"!#
" ## # !"
)!$('#3#3 !")
0 $##!"#)
!#('!""!#
!"!#)!!"!!
$ ! !" 12( ) # "
! " # "" # #
#!#*!#!)
! 0#-!#!!"
#" ! #('!!"!###
) ## # )
#!!#!)##!#
#!!##
")#&*%
'"#*)/ !! 4
# ) 7 '! $ %7'$& # ! !
#!#7'$#/!"
!!*#

4)

##!)#!3#
5 # %! ) !&
"#"
7'$!!
) 0#
!
+,$*
- # ## 0
" ! ** ()
# ! ! !
0 ) D !#
) !!" "
! ) 0
###
$ # !## # " /
## $ # !
"#"#/!
'#!!)#

"&%.*%#
"! &&
$ ! " !" # ) " "
! "#!#!)!!
0# @)" ! "* ) "
12(,!!
)/##3#!# 74
"##! ##
78 (! # ! ! ## # %$
#!! )"#
##"#0
#!&
$ # !! " #
# !!"!$
0# !!" ! # ) 0" # # #!
'! #)/ "# )
" ! # #? #" ) #
*#* !!" #! !!"
"!
(!#!" " )/!
/""$#?!!"#12(
"!#! !$!)"!#
"" " !! 0# ! (!!* )
"!#!#!!
F

#
D # #!!#
0# 3 ) ) ! !" !
" 7 # #!3 # ) "!# , )
"!#-$(#!! #
0#! (!#""!
)*#!*!!!!"#!
! " # #
!!##!#!) ,#
4 ! ! #
#!!0#""#
" ! ! '" # #)/
# / 4 5#
- %45-& " # " ) !#
12(#!
5?!""!#12(
! ! # !)
!$##12()"
0# # 0 # "! / # $
!#### )/
! # 5 " #
@54!$0#"
"!!0#4#!!!
#! =4;(#"#"=
471)3#
$")!)#
!!!!)* 0#! "!
#!)0#
"/ #!#
# #""#!)!
# !! 7F $ #! ) #
#! )
!""#0!#()"#
"#!/)#!3)"
# 4 # # )
!" 0
7F8AKAK##))
( ! ! ,. '56(3 +
FF

(#!/##8
• 4" #! # "! # ) #
0# # " 3" 3!"
"!#0 !!
""0#!
• 4!!# ! #)
!/ )/3!")/
##" #
• D ! # "" #! #!# "
0 #!3 #
"!#
• $ # # !) ?
!! 0#
• $##!)#0#
! #
• $#! "#! ))#
""*01#%
$"!"# #!"#!
"3!)#! !#
4 " #? !" 3# " #
" ! 5 !! 0
0
D 4(-42CBBB*#!#*0
"!!*!/!#
$ 0# " !" !
"!# #!3 # # !
!!!#(!! 45-)
#!
"+ %2
5#)/! )"#
/#!-$((-1'#-$("
) D , 3 # 0 ) #
#!# 1#
) #!"# #!!"
/ ! # / "! # )
0#
+ #&
+0& #
$4'(%4'(&!!
0#12( ###0### )
!! 3#!3#4!
#"!30#)42
## %42& " !" " ) !! $ 4
5#%45-&!#12(
FE

0### "#!!
+#&&$*
$ 2! %2& '$-5-( !? %'" $ -!#
5# -! (& # #!# 2* ##
$!1#"!#
#!"# 0 ,# " " 0 ,
! ! #!" "
!! $ !? ! " # # #
*-"!###!?
) !! "!# # 12( #
!!,!$!!!"#
#/#512(# !"
#3$ 444)!!$)!!"
"! ,. '56(31 , 4 &
4+
$ 4448 : !! "!# !## #
#!!,.'56(3
7,
$12, # "/!34
"## ##$)
)12(!$) " )
!! 12(#
7 7,
&$12( #! /#!"#
>&4"12(#"
&$12(!")#
F&7 !!! )12(
E&$12( !
&$12(#!"#)
!!"#
6&12( !"
+&$12( ! !!"!!
C&$!12( !3!
!
B&$ )12(
&$12(!!!!#!#
7,
$! #12(0#!!
12($/0#!!)##!!!"
)
&' 12(" !##
>&$0" !!!"
&@#," #!
F&A"" #!
E&' !""""L5#(#
&230### /
6&( # !12(" !#"
+&1)"!" #!
!
C&$12(
F

$#'$-5-("!!!)##
"!#! 12(! $"!#
#" )# ,./&
'82661 , 1 , 7 ,. ')3051 9 & :
7 & ;'806 $ !! 0 / ""#
#)!!)#/#
#"#
$!!12(!) #0!#
3 # / ! ! "#
7##!)" !
!$!!012( )) )
/ " " 12( "!# #
## ,",.'56(3!
" # ## # # *3 *
# 12( ! 7E 3 * /
0!#%))#&!"#)
!*$#)/3/#
#!!)
7E8#!#,.'56(3
D ! 3 " / )
!12($)!!!"!# )
!"12() "! $"#0
4(- 6+CF #)/ ## ) 12( / $! 3#! /
##12()!!"##)
/12(#!##)/! !12(
!!!3""
$#)/)#!!##/
#!3##! #!)
!#!#))!!!!
!#'!!#!!!"
)
##"#""#!%
###/&12(,.'56(3
F6

-)
-& !
4 ! ) / # " 4(- 6+CF
!"#"#!312(!!$
) !" #)/ !
"!#4)0#)
# / !! !!
#)#
-&#0
D !! !! # ! ! )
/ #!!!3#!
)##!! ,
!! !! # / 0
!!!!#*!*!7F
!!!)( #""
"!#'*)"!
!

!
!
"# $%#
# $&'$($)
&' ) % $
&#'# # $ $) '
#&* !$+ & ) !##&' & &'
'$ $$$ && &
& , $$$'#)
&&'#&&''!
$$ &#&##&#
$$&
& +$# '
$-# '' #)
$ ' &(
$# & '#$$ $. $
# #&-$$$
## $ $ & $
' / #$ #$ $
& & 0 # # +
# $&'
& $ $ ' $ & # $
! "
0 $ 123$$&$ $'
! $' ' $ $ )
4*56 '$&
$ % $'' $&
'& .7 #
'$' '.4*5$&

) $ $ %$$9&:&
' &&+ #&
)
*$&&$ &$$
4*5 #$$ $) '
& & %$
# $
&$ ##&'#' $
. $ ) &&
& & $$
'&;'&'$
$ '$
$$&
%#'###

# && &
,&'$&# $)
$ $$9 #:#%
$& ' $&#
$$&;'&$
) & $# &#
, ' + !'$$
$7) $+#! &
# & "!$
$$ & + $
$$$$$ &% & '
$-$'$'
& $ $# #$
#9! !: &$+ 7$
#' ' $$$$# &
'! . & & $ & '!
) + $$ $$ &
'! %#$ $) &
$#>+
#"& ) & & '(
. $& ' $$# $
$#$ #$ &+&#-
$'$# $
$$%$$!'6'
$ #*$$$ &
$ $'$$
& "#$%&'()7 & #$
$#$$ $$$
#$7$$#
#$$& '#$ + $
## & & & & *
*$ $$ #$$
$ $$$) #!) #
$$&# $; $$$&
# $ $ $ $ $ =
$' & $) *$
&#$4*5$$$' $$'
# $ '') $
' ### $ $ $$
# $ ' ! $# # $ #
) $ $ $' $+
'> 4*5'
.&'$ #4'!'$4*5
& ) # #,5#
81

% #$ $) $$$$$
& ' '#$''
;'& $&#$$&#$$
$$ '' # $'&$
&%$& '$
$' $ # $$'
&5 $# $ '#
# 6 & $$ &
) $'&$ $
=$ $'#$$
#$'&#'$
$, $ #) #
$!) $$ . '
$) '& ;'&
&#$$ $$' &
$ $$$' #
$ &) #&$ ) $
$ )
#) $& $$ &*
& & +
) & '!$# ) #
' & $ && ' & $
$
+ ! ! & ! , %
%& $' & $) $
&## $.
& ' & $ ' &
) '$ $ $-#
& !$ $'!$$ $ $#
?
• % ##@' $
• % #$+$ )
• %$# '! 9+ $.7
:
.'& $ $'& '+
& ' $ .7 # & ! ,1 #
=$ !'&# # # !#$
! !$ ) #
#'A$B$$#$ $
,

,1?*;5!$5; ,
,

$$$# &'$ ') #
$$;&$ $ '&$
$+) $$ #+
! $'$' #
-"! &% '( & "
C &' '& ') ) #
$# '#'&
'' ?
/ 5 $ ? % # $$ $ )
.7 # 4*5#$ &$
$$'$$#- #$
$#
.5 $,+#?"+ $
' # '# $
#+$ . $&
# ) # &' # $
%## # $
$ # #&#'$+$$
$+#)
$#?0 & ) $ '
$+ ' ' $%$'
$' $# &&$$+#
# #' $$'!$'-# &
$# &$!$ 5 $ #'
$$) &$
'& $$$ 4 #
+#'-$ $$
($D
6 5) ?- #$$& @
$ $''$$0
! $$$'#!'
' ! $$# $$
-'=%?0 #' &AB
$#$$ %$# $
'+'# #
'$ #- +$
$ $ -"57E,' $ $& $5%"6
E/$'#
8

./0 * (! ! "! /
-+ $' &
$$ % # $
!#$;'&'
$& ' ) $
$) && $')
#$ '#$#$ >*#
$'!$' $$$'
'$$ $$
&$$$ $ $$'?
• $ #$$! '$$
$$ $
• /& $ ' $
• , $# $ $' +'
$ &
• % & ' # #$
#$$
. & & & &
- $!$ $'$
$#$ $$$ '
# $'!# #
&$' &$
#$ $%'
' ' & $ # # # $
$) #& &'
$ #
. &! &
#$ $#$
#$$'- )
#$ $ +$ $
! &# $$ ' ;& # $
& $
# &#$#'$ $
$ ' & # # 6 '
$'!$-& $
$$$## #5 ) #$$
&!' # '$$$
$
.# & 1 * ! &
% $$ $ !$)
$$'$;'&##
&#&$$ $!$$
88

$$$ ! $.$'!$$&#
$$& ''$$
$) ##$#$$*#
$ $ #$$ $) $
$'#(#$#&
$#$$ ' &!&
$$
2 & 3
%#'$# $ #
+$ &$' $$# & ) -
; * $+((+)'& $$ $
4*5$$ $'' -;
$ & $'?
2*(4
.& & $ $ %
&$$#$ &$'4*5$ #
%$ &% &'
$$$ $ $$ &
% $'! # & $ # 9
:
,?1 &)
$$G# #
,8?,#$$
$ $
2 %
* &' &
$# $ .$,F &''
# &'&
' &
8F

: $
: $
9! ! :
:
$
:
:
$+9$
#:
,F? -;
2# "& &! &
.$$ $
$'##$ $
# $,H.$ $
#$ $$##0
& $'!&! $"+ $$#
$$$ $& &'
&
%$ $ #$#' &
0 $+ $ ' $#
&#$#&+$$-
'&&$&&' $
& & =$
#&# #
& # '
# # & $ # $+ & $
&!
;# &$ $$$$'!
%$'!$$
'9& : &'' #(' &
$ $ #$'!&#$&
8H

& $*-$)
*&
Parallel Deck
LOA
Parallel Deck Aft (PDA)
Parallel Deck Fwd (PDF)
Displacement (DISP, CP, CB, LCB)
Parallel Middle Body Aft (PMBA)
Parallel Middle Body Fwd (PMBF)
Parallel Middle Body (PMB)
LBP
Breadth (BWL)
Depth (D)
Draught (T)
,H?% # $ $
2+1 & &
$$ #$$
6%918:$&$' $
$ &$# $! #$
'&$ #$$! # #$
$,2. $+#$$
$ $$%-;
$ $# #
#$'!
:-$#&
:$
#
$# &
:/&
$
,2?. $ #
:;
5) & &
%$'$) > $ $$
% $ + ' ' $ % #
! &, '$
# &,13% &' $$'$
$ #,11%&+9$$:
82

&& &,
$$$ &'%' &$
'# #+IJ>$' & $
% $$#
$ &. $ $# $
$$&$ #',# #$
# #$$) & #,1
,?5! &'
,13?$
) +
,11?. & #
!9: &
,1

$$ $&$$$
$) ##
'13K$*$3K
% + $ # $
'$ &' $$$ 7
$$ $'
,18?/'$
$+
-;
,1F?/56$* !
$5$
-;
6 "
6 & ( $'!
'' $$ #
%# ## '
#''' &#'
+ ! 96: $ ' $ -

:-; 5 $
:*5.5/%#
'
:%
: '
,1H?L $$$$6+
%-? $& && $
$#' '
Initial Design Change Beam Change LBP Change Parallel Change Cb
Change LCB
Middle Body
Change 27m -> 28m 161.9m -> 171.9 13.3m -> 18.3m 0.62 -> 0.64 77.1m -> 75.1m
Limiting KG - Even Keel (m) 8.81 9.10 8.97 8.78 8.68 8.63
Structural Weight (Tonnes) 3518 3607 3783 3534 3553 3505
Effective Power @ 18 kts (MW) 39.38 40.29 42.95 39.89 40.32 38.97
% + #'# &
$ &#$# $ $'6
$$& & "#57
9&# : , * *! # *#
) #@$$& $
$) 9 #:#
$ $) 9:5 ) # $'
6 $$$# $ $'-
F1

; & '$$ &,12
$ & * *!/# #
$#-; - #$
$&
,12? $ -; $%
!$ ) '
$ ' '
6 7 4
: . & '! $ #
# $ $
!* &
:5 $$9:
: 5 $ 5 $ ;
$ ' &
$ '
#
,1?5#$ #) & $-; )
0 -; $# +
%'!#&
& &'&#& #$$
$ $&$$$''
$# $!&!$$ $#$
#5 $$# $$ $$
) $$ #$ $$
, ) #&#$ & $ #$
#'$$
$$$,'$+ -; &'#+
# 4*5 ' #
'! !
%$$'#$ '$$
$'!$ & & #+4*5 &
F

0 ! & # $
&&& $) '$$ '!$ &
'&+#$$.
$$ + $ $#$
$ #,1
8 /4
5 & $$'& ' (
& &0 #
$#&& $ $ #
$$ %#&' $
& $ # $ ) & #
+# &&) '
$9 #:$ # &$''$$&
$ $$ .
'& $##''
$ ' #' $
#+$,#' # $
&'$$$$ + $ $
$$$$!
/&
*="/9

Modelling and Simulation of
Shipboard Environment and Operations
Jayanta Majumder, Dracos Vassalos, Univ. of Glasgow and Strathclyde, Glasgow/UK,
j.majumder@strath.ac.uk, d.vassalos@na-me.ac.uk
Luis Guarin, Guro C. Vassalos, Safety at Sea Ltd., Glasgow/UK,
l.guarin@safety-at-sea.co.uk, guro.c.vassalos@na-me.ac.uk
Abstract
This paper presents HELIOS, a software tool and framework that incorporates simulation models
of various aspects of shipboard operations and facilitates quick development of new models. The
core of HELIOS is a spatial database representing hull, subdivisions and general arrangement.
Numerical models and simulations of various aspects of shipboard operations are built around
the spatial database. These models are controlled interactively and visually as far as possible.
The numerical models integrated so far include crowd flow, vehicle loading, fire/smoke spread,
spatial coverage, and hydrostatics.
1. Introduction
Simulation-based ship design progresses rapidly. Initially, simulations were classical mechanical
models of hydrodynamics or structure analysis. More recently, computer based modelling and
simulation of people onboard the ship has opened up new opportunities. Most importantly,
it allows evaluation of a ship’s layout with respect to ease of evacuation and emergency mustering.
Crowd-flow modelling has been an active area of study for a long time, specially in
urban planning and design. Also, there have been some statutory guidelines about managing
civic crowd scenarios. More recently the concern has reached the maritime sector. A recent
statutory requirement that every new Ro-Ro passenger ship must be evaluated for evacuation
performance, has generated new waves of interest in crowd dynamics in the maritime sector. In
response to this regulation, several corporations and research organizations have come up with
their own method and software for modelling evacuation. Out own simulation tool HELIOS (Human
Environment Local Interactions onboard Ships) took some ideas from our well-established
evacuation simulation software EVI, http://www.shipevacuation.co.uk, and is meant to be an
extensible framework to accommodate modelling of various aspects of shipboard operations.
Modelling of shipboard occupants is not much different from modelling of crowds in buildings,
by and large it is a sound assumption that behavioral model of people onboard ships is no
different from that in a hotel building of similar size. However there are two aspects in which
the shipboard emergency differs from a civic building scenario.
– The ship motion and tilt can have additional effect on the people.
– The usual command to the occupants in case of a shipboard emergency is not as simple
as ’desert the compound’. It usually involves dynamically decided mustering based on the
location and nature of the emergency.
It may be tempting to equate crowd flow with fluid flow, but crowd dynamics is fundamentally
different fluid dynamics, since we deal with much smaller collections of people than would be
required to cancel all individuality effects and be amenable to continuum formulations. People
exercise significant free choice and do not follow conservation of momentum. This makes it
impossible to make a sound macroscopic model of crowd dynamics on the lines of fluid dynamics.
Microscopic simulation is a more reasonable model for crowd dynamics because it can capture
the complex behavior of a crowd as an emergent product of actions of its individual members.
364

As a result most of the models in the literature are microscopic. The many microscopic models
reported in the literature till date differ from each other in terms of the microscopic rules,
dynamics and algorithms. In this situation it is quite natural to expect different simulators to
differ in the details of crowd behavior. However, for a given scenario, the large-scale observations
in all the simulators should be the same, or else the situation calls for a concerted standardization
effort. There has not been any effort to harmonize the differences between different models
mainly due to the expensive and commercial nature of the implementations and non-disclosure
of the model details. One way forward in addressing this landscape of confusing multitude of
models is to put forward an open source implementation with fully published details, which can
come in totality under public scrutiny and can grow freely with contribution from students and
researchers worldwide. We have similar plans for HELIOS and a public licensed open version
may be released eventually, but before that we need to to draw up the long-term road-map, and
evaluate whether the project has the potential to be a sustainable open-source project.
2. Defining the Requirements of the Shipboard Environment Model
HELIOS was developed to help in the problems of shipboard operations planning and layout
design. The first problem was to define a faithful representation of the shipboard environment.
A 3D virtual reality model of the ship may be a good visual representation, but contains just
graphic primitives. For a simulation, a model must have some sort of meaning (semantic information)
associated with geometric entities. E.g., it should be possible to mark a region and give
it a name and later refer to it by that name, or to mark a point in the environment and enquire
about the occupancy or volume or material composition of the compartment that contains the
point. The entire environment is a large entity, and the occupants (people, cars etc.) are much
smaller. The locality of each occupant is a small part of the entire ship, yet these small parts
must be bound together by some topological relationship so that a plan to go from location of
the ship to another may be seen as a long sequence of small transitions from one small locality to
another. It should also be possible to distribute values over parts or whole of the environment,
e.g., the data from a fire/smoke transport simulation program (e.g. CO, CO 2 ,O 2 , and toxicity
distributions) should be possible to associate with the environment model in such a way that
the local and instantaneous value can be made to affect the occupants. Another aspect of the
requirements of an environment model comes from the fact that the existing data of shipboard
layout comes in the form of line drawings, i.e. general arrangement (GA) drawings. This does
convey the information in a human interpretable form, but it is not directly usable as a representation
of the topology of the ship. The line drawing is merely a set of lines, splines and arcs.
But we need in our computational representation the geometry, connectivity and the semantics
of sub-regions of the shipboard environment. One way to create our requisite representation is
to model it from scratch, but it would be all the more economical if it can be mechanically generated
from the line drawings. Semantic information may be included manually into the drawing
in the form of special graphical symbols, but the process of creation of the environment model
should be largely mechanized. The environment model should have a visual representation that
looks like the actual ship allowing display of simulation and user interaction. Thus, the ideal
solution appears to be a spatial database supporting object localization and local annotation.
3. Generation of the HELIOS Spatial Database
In HELIOS, the simulated objects are embedded in a spatial database. The spatial database
is a data structure representing the shipboard layout and supporting efficient computation of
queries like point localization, range searching etc. It is a two-manifold composed of triangular
faces. The GA drawing goes through a processing pipeline, Fig.1. The GA drawing
is a piece of 2D vector graphics consisting of line segments and algebraic curves like arcs,
circles and splines, Fig.2. HELIOS accepts such drawings in the widely used DXF format,
http://www.autodesk.com/techpubs/autocad/acad2000/dxf/. The first stage in the processing
pipeline involves replacing the algebraic curves by piecewise linear approximations to convert
365

the GA data to a set of line segments (we call this stage ’linearization’).
Drawing
Linearization
Cross−Snapping
&
Duplicates removal
Clustering into levels
Symbol recognition
Staircase/Ramp
generation
Triangulation
and Extrusion
Fixing degeneracies
Recognition by
shape analysis
Spatial
Database
Fig.1: Processing pipeline used to prepare the spatial data from GA drawings
Fig.2: General arrangement (GA) (left) and 3D spatial database generated from it(right)
The next stage is cross snapping and removal of coincident line segments. Cross snapping
involves merging of end-points that are close enough. This is done efficiently by successive
insertion of end points in a BSP tree, Berg et al. (2000). So far, there is no explicit information
on which groups of line segments belong to the same deck. This information is generated by
clustering the line segments with the following algorithm:
Data: A Set S of line segments
Result: A set of disjoint sets of line segments, each representing the cluster for a deck
Let D be the set (of sets) with elements {s} for each s ∈ S;
repeat
n ←− ||D||;
Create and initialize a 2D segment tree T ;
for each d ∈ D do
end
Create a slightly padded box b(d) bounding all segments in d;
Add b(d) to T
for each d ∈ D do
end
for each δ ∈ D with b(δ) overlapping b(d) (using T ) do
end
UNITE (d, δ)
D ← The new set of disjoint sets of segments, as resulting from the UNITE operation;
366

until n == ||D||;
Return with result D;
In this algorithm, the set of disjoint sets of segments is maintained using the UNION/FIND
algorithm with path compression (see Ch.22 of Cormen et al. (1990)), and the UNITE operation
is that of a standard disjoint set union. In practice the Repeat. . .Until very few times - twice
or so. After this processing is complete we get groups of line segments each belonging to one
deck. As regards ordering the decks, we use a convention. Usually the decks in the GA drawing
are laid out in ascending order of height from bottom to top. If this is not the case in a GA,
this has to be manually done.
The next stage is extraction of symbols. The symbols are added to the GA drawing to convey
information about the layout. Different symbols have different meanings, the location and pose
of the symbols are determined and appended to the data passing through the processing pipeline.
E.g., a ’reference point’ or ’origin of coordinate system’ for each deck tells that the decks are
to be so aligned that the reference points fall on the same vertical line in 3D. The symbols are
themselves simple drawing objects or entities available to the user as a library and meant to be
copied and pasted at appropriate locations in the drawing to convey the information. E.g., the
symbol for a reference point has the appearence of . The symbol can be inserted into the
drawing using any of the common drawing editors like autocad, qcad, intellicad etc.
The recognition of the symbols is done using the ’affine invariant’ matching, in which the symbol
is compared with with parts of the drawing in a way that is independent of scale, translation,
rotation and mirror flipping as follows:
Data: A symbol Σ as a set of line segments
The relevant part of the drawing given as a set of line segments, ∆
Result: Location of the symbol in the drawing;
l s ←longest segment in Σ with end points (x 0 , y 0 ) and (x 1 , y 1 );
Create a 2D segment tree T of the bounding boxes of each of the line segments in ∆;
startpt[0] = (x 0 , y 0 ); endpt[0] = (x 1 , y 1 );
startpt[1] = endpt[0]; endpt[1] = startpt[0];
( )
( )
1 0
1 0
flip[0] ← ; flip[1] ←
;
0 1
0 −1
Create an empty set of matched locations M;
for each δ ∈ ∆ do
for each i ∈ {0, 1} do;
for each j ∈ {0, 1} do;
p 0 = (X 0 , Y 0 ) and p 1 = (X 1 , Y 1 );
p 0 = (X 0 , Y 0 ) and p 1 = (X 1 , Y 1 );
Get an Euclidean operator E that transforms (flip[i] × startpt[j]) to p 0
and (flip[i] × endpt[j]) to p 1 ;
Transform a copy of the symbol and its bounding box first by flip[i] and then by E,
let the set of segments in the transformed symbol be Σ δ ;
Get all the line segments in ∆ that fall within bounding box of Σ δ call it ∆ δ ;
Boolean match ← TRUE;
for each σ ∈ Σ δ do
end
Look for a match of σ in ∆ δ , if not found set match ← FALSE
367

end
end
end
if match is TRUE then
end
Add the tuple (i, j, E) to the matched locations set M;
The step ’Get an ⎛ Euclidean operator ⎞ E . . .’ may be expanded into the following. The operator E
C −S T ( ) ( ) ( )
x
⎜
⎟
xa xb Xa
is of the form ⎝ S C T y ⎠, which transforms two points and to
y
0 0 1
a y b X a
( )
Xb
and respectively by rotation, isotropic scaling, and translation. This leads the equations
Y b
⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞
x a X a
x b X b
⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟
E × ⎝ y a ⎠ = ⎝ Y a ⎠ and E × ⎝ y b ⎠ = ⎝ Y b ⎠, to be solved to determine the elements
1 1
1 1
of E. The symbols are restricted to specially designated layers of the drawing to reduce the
computational cost.
The next stage in the processing pipeline reconstructs the geometry of staircases in the environment.
A general arrangement drawing or a building floor-plan is the plan view of the layout,
and the plan view does not contain the aspects of the geometry that would appear on a lateral
projection. Thus much of the description of a staircase or a ramp between two levels is absent in
a single planar projection. To reconstruct this information, instead of seeking what the geometry
actually is, we would find out what the best geometry should be, and hope that the designer
must have designed it reasonably close to the best geometry. We must formulate as to what
constitutes the quality of a staircase or ramp. A fairly reasonable and simple answer is that the
least steep is best. If we minimize an aggregated value of steepness of the staircase, it should lead
to a reasonable reconstruction. We optimize a steepness functional over the projected domain
of the staircase using the finite element method. If the vertical coordinate over the projected
domain of the staircase or ramp is given as a function z(x, y), we use the steepness functional
∫ ∫ (
∂z
∂x )2 + ( ∂z
∂y )2 dxdy. The integrand is the square of the greatest slope at a point (x, y), and
an area weighted sum of such local greatest slopes is what we minimize using the Ritz method,
Farlow (1993). We generate a mesh over the domain and describe the distribution of z over the
projected domain as a function of individual z values at the mesh nodes, and make a discretized
formulation of the steepness functional. For the value of the functional to be minimum, the
derivatives of discretized steepness with respect to z values at mesh nodes must vanish. Some
z values (where the stair-sheet meets the flat levels) provide additional equations, similar to
boundary conditions in physical problems. We reconstruct the staircase geometry by solving
these equations.
Fig.3: Generation of a spiral staircase
Fig.3 illustrates the generation of the geometry of a spiral staircase.
The center figure
368

shows a mesh with z function displayed by a color scale. Fig.4 shows two more examples
of reconstructions made using the variational method described. Minimizing our integral
∫ ∫ (
∂z
∂x )2 + ( ∂z
∂y )2 dx dy is equivalent to ensuring that the divergence of the gradient ( ∂z
∂x , ∂z
∂y )
is zero everywhere in the interior of the domain, i.e. there is no unnecessary internal source of
slope. Staircase steps can be generated by quantizing the surface at iso-z contours, but we have
left that for a later release of HELIOS.
Fig.4: Generation of staircases
The data at this stage of processing represents a building or ship with multiple horizontally laid
out levels, but the internals of each level consist merely of line segments (standing for walls and
boundaries of obstacles). The whole environment needs to be seen as a connected network of
subregions, primarily for the purpose of route planning and reasoning about the space. There
are several ways of getting a topological structure suitable for route planning from a set of
line segments and polygons, Fig.5 shows some Berg et al. (2000). The structured grid cell
partition - the last two in figure 5, although commonly used, is a big compromise since it entails
anisotropy (i.e. differences in speed along different directions) of motion. Of the remaining,
we chose constrained triangulation for HELIOS because it enables efficient solution to three
most important problems relevant to our model: route planning, point location, and visibility
predicate.
Fig.5: Network and partition schemes for location and navigation in the presence of three obstacles
shown as solid black polygons; from top left to bottom right: trapezoidal map, vertex
visibility graph, convex connectivity graph, constrained triangulation, Voronoi diagram, structured
grid-cell graph (squares and hexagonal version).
This stage of processing computes a ’Constrained Delaunay Triangulation’, Chew (1987), of the
line segments on each level. This essentially is a partition of each deck into triangular pieces
of floor space such that the original line segments only form some of the sides of the triangles
and not intrude the interior of any of them. The triangles on the floor area of Fig.7(B) show
an example of such a partition. The extrusion stage, which immediately follows triangulation,
369

merely assigns a height value to each of the walls. Constrained triangulation of an arbitrary
set of lines can lead to degenerate triangles that need to be excluded for the sake of robustness
and correctness of subsequent computations. Here degeneracies are overly skinny triangles that
topologically represent a connection but geometrically the connection is infeasible. Fig.6 (bold
lines are walls, dashed lines open sides), the triangle ABC illustrates a class of degeneracy
that appears in a constrained Delaunay triangulation. However all skinny triangles are not
topologically degenerate as they may as well represent a significant connection, e.g. the triangle
PQR in Fig.6. As degeneracies are excluded, new degeneracies become detectable requiring
iterations.
R
A
C
B A
C B
P Q
Fig.6: Illustrating degeneracy of triangles
(A)
Fig.7: (A) Comparing paths: based on adjacent cell sequence (zigzag), and based on furthest
visible way point (3 segments) (B) Simulated people finding their way on triangle mesh.
The environment model so generated is ready as a spatial database to support annotation and
simulation. However, a few more operations are supported for recognizing shapes of regions.
Regions have shapes and shapes have have certain signatures that helps grouping similar shaped
regions together. This is done by statistical clustering in the feature space of the shape/size
signatures. This is important in the context of ships to automatically identify cabins and public
spaces.
4. Modelling of Human Occupants
Modelling the mechanisms of human response to extreme stimuli like evacuation alarm onboard a
ship appears to be a formidable task, if at all possible in the framework of our present scientific
understanding. However, a behavioristic model may be built relatively easily. We take that
pragmatic approach. Rather than trying to address the complexities of human physiology and
psychology, we treat them as computational objects with some built-in behavior and capability
of being instructed and programmed to move around in the ship environment. These are heavily
attributed entities, with attribute values deciding their behavior. E.g., each one has age and
gender attributes. There is some data about dependence of walking speed on age incorporated
in HELIOS. Yet when the speed distributions are explicitly specified, this specification overrides
the values deduced using the built-in relationships. To model a shipboard emergency operation,
the modelled humans (’agents’) may be instructed or assigned a task of the following types:
(B)
– Going to an individually designated location.
– Given a set of locations, going to a convenient one of them.
370

A Wall
– Going to one or more locations successively following a convenient route.
– Follow an explicitly specified path.
– Staying at one point for a specified period of time.
– Carrying out a specified action within a specified time of an event.
– Carrying out a specified action on another agent when visible and nearby.
– Carrying out an action when in a particular location.
– Execute a compound agenda with several tasks of the above assigned with various priorities.
These task types give immense modelling power. The computational operations performed
by an agent may be seen as subdivided into perception, decision, and action. Perception
involves collecting local (in space and time) information as may be relevant, decision involves
figuring out the things to do (eg. finding out the direction to head for etc.), and action involves
making the changes as may be relevant (eg. stepping to the next position). This distinction
in HELIOS really aims at organizing the program structure and does not relate to modelling
inner mechanisms of human mind. The most noteworthy aspects of procedural implementation
of agent behavior is navigation. Tasks that are defined in terms of a destination location need
to be executed by finding the way to the destination and following a route that leads to the
destination. The computational procedure for this is named navigation. The navigation procedure
involves two main sub-procedures - topological planning and geometric plan-following.
Topological planning involves creation of a path based on connectivity of the triangular cells,
in a loose sense the path is a sequence of triangular cells of the triangulation that need to be
passed through to reach the destination. This path is computed by processing the connectivity
structure of the triangular cells. Let us consider the dual of the triangulation, which is a graph
in which there is a node for every cell. For every pair of adjacent cells that share a non-wall
side, there is an edge or arc between their nodes corresponding to the shared non-wall side.
Fig.8 shows an example of the dual graph of a triangulation in which only one connected
component of the graph is shown. The paths followed by agents are based on graph paths
on this navigational network. A path plan is more than just one path, it is a bunch of paths
clubbed together in such a way that for any cell it gives a path from the cell to the destination cell.
To FVW
007
Fig.8: Navigational Network
Fig.9: Free configuration space
It would be unrealistic model if the agents actually followed the zigzag paths in Fig.8. This is
addressed in the plan following sub-procedure. A basic premise in the plan following procedure
is that an agent always knows the cell that it is in. On a triangulation-based environment,
this information is much easier to maintain and recompute than in a convex segments based
environment like Vassalos et al. (2001). Knowing its current cell, the agent can immediately
retrieve a sequential path to the destination cell. Each element in the sequence of cells (path),
is a ’way-point’ leading to the destination. However, agents cannot go through walls or floors.
371

An agent will then head for the furthest way-point accessible by a straight line, i.e. the furthest
visible way-point (FVW). Fig.7(A) shows an example of a path going through successive furthest
visible way-points. As the agent moves on, new way points may become visible, and the direction
of approach might change. Observing human navigational behavior suggests that most people
don’t re-evaluate their direction of approach very frequently. This is incorporated in HELIOS
by some parameterized and randomized deferment of re-evaluation. The size of the navigational
network can have possibly millions of nodes. So it is important to use fast algorithms for
planning paths over them. The fact that the navigational graph is planar makes a hierarchical
single source shortest path algorithm computable in linear time, Klein et al. (1994). Also
since the inter-cell distance values may be reasonably quantized and scaled to range within a
small range of integers, the bucket based priority queue approach to Dijkstra algorithm, Thorup
(1999), makes the path computable in linear time. We have tried a recent implementation,
http://www.avglab.com/andrew/soft.html, of this idea and it measured adequate. We also
often use the BFS tree, Cormen et al. (1990), as a path plan, as it is easy to compute and
results in acceptable paths in most cases.
Plan following gives the agent a reasonably nice geometric path that leads to the destination,
respecting walls, but not yet the bodies of other agents. We call the procedural element that
ensures this ’dynamic avoidance’. In dynamic avoidance the agent tries out a number of directions
centered around the direction towards the FVW, and chooses the direction that makes
the most advance along the desired direction without violating the extents of any other fellow
agent. The dynamic avoidance primarily involves computing the maximum component of displacement
along a particular direction (which usually is the direction towards the FVW) that
can can be achieved by a displacement in any direction. The extent of the neighboring agents
is modelled by a rectangle - which is equivalent to four line segments. Walls and obstructions
too need to be avoided. When trying to compute dynamic avoidance for an agent (e.g. agent
007 in Fig. 9, where the agents are being shown as crossed squares), we consider the extents
of other agents or walls so offset from their actual geometry that the region outside such offset
regions is free for the center of 007 to move. This free region is the ’free configuration space’
for agent 007, shown as white in Fig. 9. The boundary of the free configuration space consists
of line segments and a circle. It can be shown that the optimal displacement is on one of the
intersection points of the configuration space boundary. The proof of this fact is similar to that
of the fundamental theorem of linear programming, with a minor addition due to the presence
of a circle. Using this observation, scanning through the intersection points on the boundary
of the free configuration space of an agent is used in finding the optimal displacement. This is
computed by transformation to a canonical position and orientation, for efficiency’s sake.
For the visual representation of the simulation to be convincing, it is important to animate
the motion realistically. To display the walking of agents, a skeletal animation
is used. Human gait data was extracted from the publicly available implementation in
http://www.mathworks.com/moler/chapters.html. In addition, we have recently incorporated
a technology used for game development, in which the animation can be designed using a class
of software tools called animation studios (e.g. 3D-studio MAX). This will enable us to include
more types of agent postures and movements in HELIOS than just standing, walking and running.
Quality of the graphic objects, which is directly related to the number of polygon faces used,
costs processing time. Naturally this leads to a limit to the best quality of agent graphic
that may be displayed given the contemporary computer performance. However, there is some
scope for tricks to stretch this limit. One example is avoiding drawing of agents that are
not visible, another is to draw the agents in low quality when they are far away from the
camera. The lalter method is called ’level of detail’ (LOD), Luebcke et al. (2002). There
are techniques for dynamic computation of LOD variations. To keep things simple, we have
372

used in HELIOS discrete LOD, in which the different LODs are fully pre-computed graphic
objects (in the form of OpenGL display lists), that are switched between as the camera
moves nearer or further. The apparent dimness near the top right corner of the screenshot
of Fig.10 (left) is actually due to switching to a lower level of detail for distant agents.
Fig.10: Some glimpses of evacuation/mustering simulation
5. Models of Other Shipboard Operations
The spatial database in HELIOS is a data structure supporting the queries and operations
required by applications that have objects requiring localization, local annotation, and geometry
based calculations. It serves as a support framework, and eases development of applications
around it. We have developed a few such applications and are in the process of developing more
of them. We describe a few of them in the following subsections.
One of the applications is an input model generator for a fire/smoke transport simulator called
Raeume, Shigunov (2004). The input model requires information on compartments, their
connectivity, material composition, ventilation details, fire location etc. It was quite easy add
some annotation functions into HELIOS, to enable the user to annotate the 3D geometry and
generate the input for Raeume. As a side effect, this ensured that fire/smoke simulation results
from Raeume could be easily imported into HELIOS. This, in conjunction with a model of effect
of heat and smoke on people, when incorporated into HELIOS agents, gave rise to the ability
of simulating complex scenarios of evacuation reacting to a fire/smoke spread. A study of this
capability has been described in Guarin (2005). Figs.10 and 11 illustrates the functionality of
simulating people in conjunction with fire and smoke.
Fig.11: Heat/smoke affecting people
Fig.12: Loading of cars into ferry
As an extension to this direction of development, we envision that with maturation of our fire
model, it would be possible to not just react to the fire simulation data but interact with it (e.g.
simulating our agents fire-fighting). Another model that would be easy to incorporate but add
373

great value is that of motion sickness. The motion sickness model itself is on the anvil in our
research center, and once completed, it may be integrated into HELIOS to achieve greater levels
of interactivity and ease of use. It was easy to incorporate mobile entities interacting with the
environment. We did an application on loading vehicles into ships. It is a simple extension in
which users can create vehicles at any location in the environment, then specify their paths and
watch them follow their paths. Fig.12 shows a screenshot of this feature. Frivolous as it may
seem, this application can be useful in designing facilities for loading and unloading of cars in
ferries. It has actually been used in an undergraduate thesis in our university to study design
alternatives for the Ardrossan car ferry terminal, Scotland.
An application on hydrostatics calculation has been developed that uses the geometric data subsumed
by HELIOS. It consists of a module that imports the hull and the subdivisions exported
by programs like NAPA. The essence of its working involves calculation of sectional properties
from the hull and computation of volumes of the compartments. The former is done by an added
functionality and the later was ordinarily supported by the geometric data structures in HELIOS.
A case based reasoning program has been plugged into this setup, that makes counter-flooding
suggestions when a flooding scenario is presented to it. This case based reasoning program was
developed as a deliverable to an European Union funded project titled COMAND. Fig.13 shows
some screenshots of the counter-flooding advice function developed using HELIOS. This feature
of HELIOS makes it useful as an onboard loading analysis program.
Fig.13: The hydrostatics functions of HELIOS
Visibility coverage as defined in the context of HELIOS, is the extent or part of the environment
that can be swept by a straight ray rotating about a point but is obstructed by an obstacle.
Intuitively, it is the area that can be guarded by a person standing at a point but free to look
around. One can define variants like distance (or angle) limited visibility, in which the region
beyond a specified distance (or angle) is considered invisible. We can also have both angle and
distance limited visibility coverage. Another interesting form of visibility coverage would be
locus visibility coverage, which is the region that would be under surveillance as a guard goes
along a specified path. All these forms of visibility coverage can be evaluated using HELIOS.
This can be useful in deciding positions and loci of of guards, crew and surveillance cameras. It
may also be useful in evaluating and grading positions of adverts in a pedestrian area. Fig.14
shows some screenshots of this module.
374

Fig.14: Visibility Coverage
Distributed ubiquitous monitoring with sensor networks is slowly but surely catching on as
a viable measure for ensuring safety and security. Too many accidents have been caused or
aggravated due to absence, incompleteness or inaccuracy of monitoring. With modern technology
of tiny and inexpensive processor-cum-transponder units (sometimes referred to as smart dust),
it is possible to set up a pervasive monitoring system that keeps track an indoor or outdoor
environment with a very fine granularity and high reliability. The overal setup of such system
requires a spatial database support for associating sensed data with spatial semantics. A spatial
database similar to HELIOS would be inevitably required in organizing the sensed data and
for automated reasoning about the sensed environment. Ranging from security to inventory
tracking, from structural to power monitoring, from fire safety to personal navigational aids,
from process automation to smart buildings - the potential applications are numerous and the
impact is going to be big. The geometry savvy spatial database of HELIOS already supports
several classes of queries that we envision as useful to such sensor fusion scenarios, more can be
developed as we investigate further along these lines.
6. Software constituents of HELIOS
HELIOS gratefully leverages great pieces of software without which it would have been too
much work to even contemplate - the usual and indispensable ’shoulder of giants’ phenomenon
of software development. In the development of HELIOS, we have deliberately not given in
to dependence on any proprietary or closed-source component. It is written in ansi C++,
compiled with gcc and Microsoft Visual Studio .NET. It uses OpenGL and GLUT for 3d graphics,
Tcl/Tk for graphics widgets and a scripting interface, swig for generating the scripting
interface from a C++ header file, libSDL for audio and for loading texture bitmaps, L A TEX,
fig2dev, and ImageMagick for automated report generation and numerical recipes textbook,
Press et al. (1993), code for linear algebra. The aforementioned jargon are household names
to developers and it is easy to find out about them by a google search, so omitting the references
to them. The geometry library CGAL (http://www.cgal.org) and the tool Triangle
(http://www-2.cs.cmu.edu/∼quake/triangle.html) have been used within separate programs in
the GA processing pipeline.
7. Conclusion and scope for future work
A well designed framework should significantly relieve the burden of work from the class of
activity it caters to. The HELIOS effort seems to be heading correctly in that direction.
We shall continue to add value to the framework and hopefully it will become an even more
efficacious tool in near future.
References
BERG, M. de; KREVELD, M. van; OVERMARS, M.; SCHWARZKOPF, O. (2000), Computational
Geometry, Springer
375

CHEW, P. (1987), Constrained Delaunay triangulations, Symp. Comp. Geometry, pp.215-222
CORMEN, T.H.; LEISERSON, C.E.; RIVEST, R.L. (1990), Introduction to algorithms, MIT
Press
FARLOW, S.J. (1993), Partial Differential Equations for Scientists and Engineers, Dover Publ.
GUARIN, L.; MAJUMDER, J.; SHIGUNOV, V.; et al. (2004), Fire and flooding risk assessment
in ship design for ease of evacuation, Int. Conf. Design for Safety, Osaka
KLEIN, P.; RAO, S.; RAUCH, M.; SUBRAMANIAN, S. (1994), Faster shortest-path algorithms
for planar graphs, 26 th ACM Symp. on Theory of Computing, pp.27-37
LUEBKE, D.; et al. (2002), Level of detail for 3D graphics, Morgan Kaufmann
SHIGUNOV, V. (2004), Fire development and smoke propagation in ship compartments, Ship
Technology Research 51(1), pp.9-20
THORUP, M. (1999), Undirected single-source shortest paths with positive IntegerWeights in
linear time, J. ACM 46, pp.362-394
VASSALOS, D.; KIM, H.; CHRISTIANSEN, G.; MAJUMDER, J. (2001), A mesoscopic model
for passenger evacuation in a virtual ship-sea environment and performance-based evaluation,
Pedestrian and Evacuation Dynamics, Duisburg
376

!"
#
! "
##$
"
$ % % "
&""%
" #
$%
!"""#
$##" #
%#$&
# ##'%"% "
" # $ #
("
# " "
#%
" #
Virtual Knowledge
Base
!
" # !
")*+" !,-.

&% '
!0 ##1"#
"
$ , % #
% (
#"")
(%#
'"" #&
"2%'"3
& "" #&
" " ! " #" # #
%%%
1"0##
%#% !
#" """"#"
" " " " & " '
% " " " 4#
#5 5 " "" " +"
!%"0#%%5 %"#"
"
"2* !'""
"* !#"
/

" "7#5 ("
, " % 8$ #
"7* !!0
! "
( 8 ! " %
## ""&'%"
(( " 0"
'()**+,
• 9%"#""# 5 "
• +" 8%
" " "
• "#
• """" "
!"""5#"
"#""#" &'%""
5" ' " '% ' "
&'()**+ :
" 884#;
"%'
"

'
:.?@3941?3A@1:.?+43341:B!3C:)666-"%./
. 0 0 -"/1 7
4""4 8"
D-B4@-@1:.?@3941:.?+43342>>
@8""D
D-B4@-@1:-@4E 1:.?@3942>>2#,
F .!,:4"::G'
2)6822
/>

Knowledge Modeling in Ship Design
using Semantic Web Techniques
Robert Bronsart, Michael Zimmermann, University of Rostock, Rostock/Germany,
{robert.bronsart,michael.zimmermann}@uni-rostock.de
Abstract
Within the research project KonSenS, the prospect of knowledge based engineering applied to
ship design is analyzed. An improved integration of knowledge, geometry and manufacturing
information can achieve an improvement in product quality and a reduction of design time as
well as manufacturing costs. Semantic web techniques are one means for knowledge modeling. A
consolidated information server is used to manage documentation and standards. An integration
into a CAD system is used to improve standards compliance. Decision support is given for
standardized tasks hereby easing the workload of the designer.
1. Introduction
The development process in the maritime industries is characterized by a complex interaction of
many partners working in parallel. From the initial concept up to the final design diverse and
often conflicting requirements need to be taken into account. This requires a constant exchange
of a significant amount of information.
Today, in the CAD/CAM environment there is no tight integration of the knowledge and information
needed to develop the final design with the geometry and manufacturing information
used for production. While the later is handled with sophisticated CAD/CAM solutions, for the
former a diverse range of applications and methods is used.
As a result, for the designer the information needed is available in different formats and from
different sources. Often, media breaks require that the information given in e.g. a document
is interpreted by the designer and applied in the appropriate context. With such procedures
there exists not only the increased probability of misinterpretation. Also knowledge reuse in the
design process as well as automatization is prevented.
Knowledge based systems are applications that capture the knowledge available for a problem
domain and represent this knowledge in a machine interpretable way. In ship design these
systems can be used to e.g. document best practice recommendations or for standardization
and automatization purposes. Also, knowledge can be extracted from key persons and made
available to other members of the team.
For the world wide web, the development of ’semantic web techniques’, Daconta et al. (2003),
is geared towards the definition of machine readable and more powerful relations between bits
of information. Such relations allow for a tight integration of all pieces of information needed
for ship design. Once accepted by the public this allows for a more precise search and retrieval
of information; automatic deductive reasoning is also supported.
In the collaborative research project KonSenS the University of Rostock is working on the problem
of modeling requirements and algorithms needed in ship structural design. With the help of
knowledge based methods the objective of this project is to achieve an enhanced automatization
and a higher quality of the final product.
In this paper the use of semantic web techniques for ship design is analyzed. Based on a
formal introduction to knowledge modeling a description of the techniques available and their
capabilities is given. The application of semantic web techniques in ship design is described.
381

2. Knowledge
As in all other engineering processes, in ship design one factor that determines the result is
knowledge. Today, with the focus placed on high quality, low costs and a short time to market,
a thorough and extensive understanding of all possible aspects is a key factor for success. A lack
of understanding may lead to cost intensive effects at a later design stage or in operation. But
what is knowledge?
Data, Information, and Knowledge
Knowledge is comprised of individual pieces of information called facts, Franken and Gadatsch
(2002). A fact is an atomic entity, i.e. an entity that is self supportive and not related to other
entities. Information is defined as a collection of facts with additional relationships and rules
between facts. This network of facts defines the information base.
Using deductive reasoning and experience the essence of the information is extracted from the
information base leading to knowledge. Here, experience represents knowledge the designer has
gained from e.g. previous reasonings, experiments or observations. Therefore, the extraction of
knowledge is always bound to the background of the person. Differing conclusions might be
drawn from an identical information base.
Types of Knowledge
From a theoretical standpoint different types of knowledge can be identified, Riempp (2004).
Structured knowledge is given in a predefined format, i.e. the semantic of the knowledge is
given as meta-information. Examples in ship design are parts libraries or class rules. For
unstructured knowledge no meta-information is given. Evaluation of this type of knowledge is
only possible if information about the context is available, i.e. additional constraints apply but
are not defined explicitly. In ship design the experience of the designer, some informal notation
or comments enables the engineer to abstract the required knowledge; for automatic evaluation
the determination of the context and constraints is difficult.
Explicit knowledge is knowledge that can be described using facts and relations. The transfer of
this kind of knowledge is possible with only little danger of misinterpretation. Implicit knowledge
is knowledge that is not defined explicitly but nevertheless available. Often, implicit knowledge
forms one foundation a team or society is based on. In ship design, experience and general
agreements are examples of implicit knowledge.
Finally, in most companies some knowledge is bound to certain persons as individual knowledge
and not available to all employees of the company. If such an employee leaves the company the
knowledge is no longer available. In contrast, social knowledge is shared by a team or society,
i.e. all members of the team are able to understand and apply this knowledge.
Knowledge Exchange and Management
In a collaborative environment the constant exchange of information and knowledge is mandatory.
As mentioned above knowledge is extracted from an information base. Hereby, the information
given is set in relation to already existing knowledge, the context and the problem
at hand. Therefore, for each person knowledge is represented as a different mental model. For
knowledge exchange to take place the mental model is transformed to a set of information that
is transferred to another person. Then, the other person uses its background to abstract the
knowledge from the information depicting a new mental model.
For knowledge exchange to take place the partners have to agree on a common language and
have to share a basic set of already existing common knowledge. Or from a more theoretical
standpoint, the transfer of knowledge can only take place if a common syntax and semantics is
agreed upon.
382

For an effective exchange of knowledge in a company precautions should be taken to optimize
a formalized representation of information required for operation. This enables the employees
to search for and acquire knowledge in a structured way. Structured knowledge with additional
meta-data gives a machine interpretable representation. Also, the extraction of implicit individual
knowledge from key persons and its preparation leads to a reduced dependency from these
persons.
In the marine business a formalized representation of knowledge used for ship design can also
be used to simplify the reuse of proven solutions and to document quality standards.
3. Semantic Web and Semantic Web Techniques
3.1. Standards
For a machine interpretable representation of knowledge not only is it necessary to store individual
facts electronically but also to add additional information about the relationships between
these facts. Here, relationships can either describe simple dependencies between facts but can
also impose more complex constraints defined by cardinality constraints or rules.
For an IT based evaluation of relationships and facts applications need to know about the
problem domain, i.e. some basic definition of the syntax, semantics and concepts used in a
problem domain needs to be available. For knowledge modeling the syntax and semantics is
mostly given by the modeling standards used. For each given problem domain the concepts and
the relationships between these concepts are defined in a taxonomy or ontology.
Taxonomies and conceptual models spawn a loosely coupled mesh of concepts and creates parentchild
relations between concepts The type of relationship between concepts is not identified. An
ontology takes the approach used for taxonomies to a higher level and adds e.g. support for
relationship types and constraints between concepts.
The semantic web working groups of the World Wide Web Consortium (W3C) were established
to work on standards for the domain and application independent modeling of knowledge. The
objective of the working groups is to create the means to structure individual facts and to put
them into context. Also, improved search capabilities, automatic deduction and reasoning based
on information available on the internet are addressed.
For this purpose the W3C published a series of XML-based standards, Fig.1. Based on XML and
XML Schema for the definition of content and syntax the semantics are described using the Rich
Description Framework (RDF) or Topic Maps (TM). For ontology support the Web Ontology
Language (OWL) standard is available. Upon these models inference engines or description logic
(DL) can operate to query the information model and to extract additional information using
deductive reasoning or first order description logic.
DL
OWL
RDF / TM
XML
Fig.1: Semantic web standards
383

3.2. Different Levels of Information Models
The standards developed for the semantic web cover different aspects of knowledge modeling and
representation. From the basic document in XML over relational modeling using topic maps
or RDF to full fledged description logic different levels of complexity needed for information
modeling are covered. In the following some aspects relevant for knowledge management are
explained.
Topic Maps and RDF The Topic Map and the Resource Description Framework, Powers
(2003), standard originate from two standards organizations, ISO and the W3C respectively.
Because these standards cover similar aspects and a conversion from TM to RDF or vice versa
can be achieved, Garshol (NN), in the following only topic maps are examined. Fig.2 shows an
example for a graphical representation of a topic map that can be used in ship design. With
this simple knowledge model the relations between stiffeners, cutouts and clips are defined.
Attributes with resource identifiers (URI) are used to link to objects not stored in the topic
map.
Cutout:
Type A
For Profile 140 mm
Clip
COA140
subtype of
requires
instance of
more info
Basic
Document
Feature
subtype of
Cutout
subtype of
Cutout A
instance of
subtype of
subtype of
Stiffener
is subtype of
Bulp
COA120
Text
Document
instance of
has
URI
120
is
Height
has
STB120
defined by
ISO Norm
Fig.2: A simple topic map model for the relations between stiffeners, clips and cutouts
Stemming from the work on electronic indexes topic maps are a subject-based classification
technique. As the name implies topic maps are organized around the notion of topics, which
usually represent primary concepts important for a specific problem domain, the ’subjects’.
Subjects are described using the basic constructs names, occurrences and associations. In a topic
map, every object itself is a topic with one or more given names. The name is used to create an
unambiguous identification and can be used for human interaction or machine interpretation.
For classification purposes topic types, which itself are also topics, can be assigned to topics.
This makes it possible to group certain topics relevant for a specific context.
Information objects like documents, class standards or parts of a CAD/CAM model are not
stored in the topic map but a topic may link to an information resource using the occurrence
construct. This enables a software designer to store information in the most suitable way for
a given task. CAD/CAM objects can be stored in the CAD/CAM system, documents in the
document management system.
With associations relationship between topics are defined. While associations only express that
some relation between two topics exist, association types are used to classify and group the
relationships according to their type.
384

One advantage of topic maps for software development is that it allows the development of
applications in which only an incomplete application data model is known at design time but is
configured or extended by the user.
Ontology Support
Topic Maps and RDF are tools for relational modeling. But similar to the mostly keyword or
full-text based search used in search engines on the internet, without a limited and predefined
vocabulary the quality of results is poor. Also, for knowledge based applications the meaning
of the relations and relation types need to be known.
With the OWL standard so called ontology based vocabularies are used. Applied to knowledge
modeling with semantic web techniques an ontology defines a basis of permissible relations and
types of relations. Roles can be restricted to apply e.g. only for certain relation types; cardinality
constraints can be given. Additional knowledge is encoded in the ontology model with basic
logical operators like AND, OR or IS NOT.
For ship design an ontology defined for a specific problem domain can be used to represent
knowledge about this domain as structured knowledge. For example, a basic ontology that
defines the knowledge about brackets, stiffeners and cutouts can be used to define a set of
permissible combinations. An extended ontology allows also to describe the context valid for a
certain part.
Reasoning
With RDF, topic maps and OWL a static yet extensible encoding of domain specific knowledge
can be achieved. On this basis the process of reasoning uses first order description logic to infer
additional knowledge from the knowledge base or to apply the knowledge base to a specific given
problem.
While first order description logic provides the means to validate a given knowledge model and
to compare a given set of information with this model it does not give a machine interpretable
representation of the meaning of constructs like relationship types, documents or other data
objects. Therefore, the meaning of the different concepts defined in a base ontology need to be
implemented as part of the application software applied. For a complex problem domain this
can be a significant task to complete.
4. Ship design and Semantic Web Techniques
Knowledge modeling and semantic web techniques offer the possibilities to apply the concept of
knowledge based engineering to the process of ship design, Krüger (2003). Within the research
project KonSenS, an application server is developed, Fig.3. The system offers an information
server that provides information about design procedures, standard and documentation. Using a
platform and system independent design the client-server solution offers a flexible and centralized
infrastructure. With the help of adapter interfaces to CAE-Systems or other applications present
in the heterogeneous environments found in many shipyards it is possible to consolidate and
centralize the management and configuration of different applications into the system KonSenS.
A stand-alone client can be used to access the application server directly.
Interoperability and Integration
With a diverse software landscape as present in today’s shipbuilding industry integration and
interoperability are important issues.
Here, interoperability guarantees that data can be exchanged with other applications. In most
cases a file based exchange using import and export functionality is chosen. While such a
solution is helpful to reuse data in other applications the issue of multiple data storage persists.
Merging issues and synchronization problems arise. Similar to STEP physical files the XML
385

ased standards offer the means for file based data exchange. The format of the exchange files
can be described with the help of so called schema’s. Checks for syntactical correctness are
possible.
Fig.3: Conceptual model of the application server and the client-server interaction
One objective of the project KonSenS is increased integration, i.e. the concurrent access of
diverse applications to one or multiple unified data repositories. This enables the user to work
with up-to-date data and removes the need for synchronization. For a seamless integration of
applications an ontology based information model can be applied. With such an ontology not
only the syntax but also the semantic and logic of the data can be defined.
Because of the network centric orientation of the committee developing the XML based standards
distributed storage and retrieval can easily be implemented. Platform independence, a large user
base and the availability of the appropriate tools ease the transition to these standards.
Flexibility
With STEP the information model for data storage and exchange is fixed upon system design.
This means that custom extensions to the capabilities of the data model can only be achieved
in cooperation with the software developers. Customization and extension of a data model at
runtime is not an option.
With semantic web techniques the knowledge encoded in topic maps or RDF structures an
increase in flexibility is given allowing for a yard specific configuration of applications. As
long as the underlying ontology is sufficient the information model can be extended without
loosing the power of automatic computer-based interpretation. Still, limits are present if the
base ontology does not offer sufficient means for the description of upcoming requirements.
Due to the integration capabilities offered by the network centric design the flexible combination
of different services available into one homogeneous information model is possible. Multiple
applications can be integrated.
5. Use Cases
For the maritime industry or, more specific, in ship design the application of semantic web
techniques can be used to ease the passage to knowledge based applications and to knowledge
based engineering. In this chapter possible use cases are shown.
386

5.1. Knowledge Modeling
For an organization operating in the maritime industry knowledge is an important asset for the
successful acquisition of and work on contracts. In the last years the importance of this role
has increased so that corporations actively seek to extend the benefits from all the knowledge
available. With the knowledge types defined above, the objective of corporations is to make
information available to the employee as needed, Nieuwenhuis and Nienhuis (2004). In ship
design explicit knowledge is available in the form of standards, that i.e. regulate the use of parts
etc., or as other documentation, mostly available as text.
Documentation
As part of the application server a documentation component offers the means to store documentation
that hereby is made available to all employees. These documents are linked to a topic
map or RDF representation founded on a base ontology of topics and topic types. This allows
for a consistent classification and reduces the ambiguity of freely defined keywords.
The search capabilities offered by semantic web techniques do not restrict information retrieval
to full text and keyword search, but also enables an application or user to search by context or
with even more complex logical operations. This leads to a reduced time needed for information
retrieval.
Also, for new employees or people not familiar with certain specifics a consistent knowledge
model provides these people with a tool that enables them to research and learn the procedures
common in a company. The problem of different work techniques or solution strategies can be
minimized.
Standards
In this paper, standards define predefined solutions or parts. A standards component is integrated
into the server. This component enables the administrator to store standard parts and
combinations of part. For constraints, context information and requirements a knowledge model
is used. While no internal shape representation is implemented, the relevant dimensions are
stored so that they can be exported to different CAD systems.
The standard catalog is linked into the base ontology for ship structural parts. While a paper
based catalog only provides a single, mostly shape-oriented view onto the standard parts, with
an ontology-supported relational representation of e.g. a parts catalog additional views can be
derived. These can be views with respect to areas of application, strength or manufacturing.
With these views additional support for a decision is given at the hand of the engineer.
Knowledge and the CAD Model
In the maritime industry the CAD model of e.g. a ship comprises the result of the application
of the engineers’ knowledge on the shipyard or network.
If life-cycle aspects, modifications or rebuilds of a design are taken into account the search for the
reason a certain solution was developed in a given way and which standards were used becomes
a serious obstacle. Media breaks play an important role in this issue. With an electronical
representation of knowledge the knowledge used for certain decision can be documented. This
allows an engineer to reproduce and validate the design if needed.
Also, the project KonSenS strives for a tight integration of electronically encoded knowledge -
this might be standards or other documentation - and the CAD model. With the help of ontology
modeling techniques, for a specific problem the corresponding documentation and standards can
be presented to the engineer within the CAD system where appropriate. With such an approach
the system provides decision support.
387

5.2. Context Sensitive Design
Standards like parts catalogs or listings of preferred solutions are stored in the application server.
Here, with relational modeling based on an ontology these parts can not only be linked with
documentation items but also can be put into relationship to other parts. A classification of
the type of relationship is possible; constraints can be imposed. This allows to define possible
solutions, e.g. a certain combination of parts. In the knowledge model such a solution can then
be linked to context information. This can be seen in Fig.2.
With qualified links from a solution to the context the definition of a permissible domain for this
solution can be achieved. I.e. it is possible to specify the requirements a design solution needs
to fulfill. Conversely, if the context is known the server can supply possible solutions. This eases
the workload of the designer.
As part of the CAD model additional meta data can be stored to add further information
about the context. This meta information is then used to constrain solutions or further quality
constraints. For example a bulkhead adjacent to a tank is marked as watertight. For subsequent
operations on this bulkhead this context information is used to e.g. deny the use of non-watertight
clips or of holes.
For the interaction of the system with the engineer or the CAD system the notion of tasks is
defined. A task represents an action performed frequently by the designers in ship structural
design. For each task the work-flow, i.e. the order of necessary action to reach a solution,
from the problem to a solution is defined; information needed as part of the solution process is
identified.
Similar to a design process based on conventional CAD system a knowledge enabled CAD system
offers the engineer an interface to select the action to perform. With an analysis of the context
additional information is derived from the geometric model present in the CAD system. With
this information the knowledge model stored in the knowledge base is queried and possible
solutions are presented to the end user. This leads to a significant reduction of the amount of
information that needs to be entered by the end user. Hence, a reduction of design time can be
achieved.
In the future an additional assessment of the solutions provided by the application with respect
to manufacturability, cost, strength and other factors is planned.
5.3. Standardization, Quality Control, and Automatization
The definition of an electronic standards catalog can guarantee that only correct and unequivocal
standards are published. For this purpose first order description logic can be used to validate
an information model and to warn about ambiguities or contradictions. As a result a concise
set of standards avoids differing interpretations of a standard that may lead to design errors.
With standards defined in such a way the engineers are not only supported in their decisions
but also the validity of existing solutions can be tested for. The validation of the CAD model
can detect errors at an early stage in the design process. This shows the ability to improve the
process of quality control and to guarantee that only applicable solutions are used. An improved
overall quality of the final product can be achieved.
In ship structural design series effects play an important role with respect to manufacturing
costs. The definition of standard solutions can help to reduce the diversity of parts used and to
increase the number of parts needed of certain types. This allows to explore cost saving series
effects.
With an extended version of the system the knowledge model available might help to improve
automatization and reduce the design time needed. As possible scenarios for application the fully
automatic creation of e.g. holes or of notches could be achieved if the context is fully defined.
388

Also, the definition of additional task groups can be applied to describe the definition of complex
parts like bulkheads or girder. Here, the design process is split into individual tasks; for a given
part the order these tasks are executed is defined. As an example, Fig.4 shows the tasks as they
might be applied to a girder.
5.4. Design Agents
Fig.4: Task based design process
In the maritime industry often design agents work as subcontractors on projects of one or multiple
shipyards. For each project the design agent’s CAD system needs to be configured according
to the shipyards requirements. Also, the engineers at the design agent need to familiarize themselves
with the appropriate standards and regulations.
Fig.5: CAD system configuration and knowledge base access
With the system, the access to documentation and standards can be granted, Fig.5. Furthermore
the advantages of the system can also be used by the design agent via network connection.
With the standards stored on the server in a platform independent way it is possible to create
instructions for automatic preconfiguration of a CAD environment.
389

Because standard catalogs are stored platform and system independently in the knowledge base
these standards can be used to configure the CAD system of the design agent according to the
specification provided by the system, i.e. to the requirements of the shipyard. For this purpose
the information server is able to export the configuration to a platform specific format that is
then used to configure the workspace. This enables the design agent to reproduce the settings
used on the shipyard with little effort.
Also, with the networked solutions chosen for the system access to documentation and standards
used on the shipyard can be given to the design agent. The decision support provided enables
the design agent to build according to the standards of the shipyard. The time needed to get
familiar with the specifics of a shipyard is reduced.
6. Summary and Conclusion
With semantic web techniques standards for the creation, management and use of machine
interpretable knowledge models are available. Such models are comprised of individual facts
linked by qualified relations; constraints can be used to capture additional information.
With knowledge modeling and semantic web techniques the integration of CAD data and other
information can be achieved. Knowledge and information can be made available to a team of
engineers. The definition of standard solutions and parts is possible. An ontology base allows
for an unequivocal classification of facts with respect to the problem domain.
With the software components described the knowledge base can be used for context sensitive
design. For a given problem only applicable solutions are presented to the user hereby reducing
the probability of design errors. Quality control can be achieved with validation of solutions
based on the knowledge available; series effects can be explored. Design agents can use the
knowledge model to understand the solutions preferred on a specific shipyard. The standards
available can be used for the configuration of the design agent’s CAD system.
An improved quality assessment of solutions presented with respect to multiple criteria would
help the engineer to choose correct solutions. The application of the knowledge model for
advanced automatization and for the definition of complex parts needs to be explored. Finally,
the development of a suitable base ontology that captures the relevant concepts for ship
structural design is a significant task not completed yet.
References
DACONTA, C.; OBERST, L.; SMITH, K. (2003), The Semantic Web, Wiley
FRANKEN, R.; GADATSCH, A. (2002), Integriertes Knowledge Managment, Vieweg Verlag
GARSHOL, L. (NN), Living with topic maps and RDF, www.ontopia.net
GARSHOL, L. (NN), Metadata? Thesauri? Taxonomies? Topic Maps!, www.ontopia.net
KRÜGER, S. (2003), The Role of IT in Shipbuilding, Compit’03, Hamburg, pp.525-533
NIEUWENHUIS, J.; NIENHUIS, U. (2004), Knowledge and Data Reuse in Ship System Design
and Engineering, Compit’04, Siquenza, pp.190-203
POWERS, S. (2003), Practical RDF, O’Reilly
RIEMPP, G. (2004), Integrierte Wissensmanagment-Systeme, Springer
390

! "#
!
!
"#
$
%
!
$
& $''
$ " # %& ' # ""
# "# ( ) "" "# ) *
# # "
* " "# "
+ , "# " #
"# # #* ##"## #-
## * " " "#
" # ."# # #
" / * # -/ " # #
#*"#
/ 0" '# #*" #
"0 # #" # #1
# # "" + ' *
) 2 #*"# ' #
/)"#%/&/) '* ##
# "# " # "" / / "# " #
#" # / " #)# #/
#"#) #" #1"
+/ # * #"#"#*" #
"# " # " #
* # # 3 % " 3 -#&
()**+ $" " " " #
4#')5# / ( * #6 #

3/ %3/&/" #*" /
) ''0 "" #13
/" '#*" "'" #""1
' * "# "
SimCoMar
FSG
NSWE
TUHH
TU-Delft
CMT
Maintenance of the
Simulation Toolkit
Tool
development
Simulation
application
Research
Simulation and
optimisation
Module
development
Influence on software
development
Support of
implementation
Distribution of
simulation
Know-how
exchange
Distributed
simulation
Simulation and
Virtual Reality
Simulation in
outfitting
. #)3
$## 8# 8 "
" "7-" ""# ""##
# # /" ##" ##1
#"# -"* "9
" # "# ))#'
Strategic planning Tactical planning Operative control
Definition of production flow
and milestones
Verification of plan
Adjustment of resources
Reaction on disturbances
or deviations
Production start Time
7./""# "
" # ') "
" "/" *#" "' #
## #"# / , #0
"
/*#* $88.* " # #
# ' "# #"# $*" #
# *# ,) " ## $ #*
"* " / " ' ')
" #" "# ' "$
" " #+ ##*## ##
"# # ') 1*#
/"*## *# "/0
7

" # $88 / )# # #
"# /" #"# "#"#
#" *#,)
Planning
Production
Design /
Engineering
Activities and
plan structure
Production
status
Assembly
tree
Part
geometry
Simulation
model
Verified
plan
.6'$88
/ #" " "##
- " " #" * #
## # / "1 # :63; ' # '
0"
# "$88 0"
* " **# / "" " * #*"#
" " " # '
< "* # "3)#'
'))+# ## #
0 /"# *#,) #
$88
'#" *"" $88* #*"#
# "# =/"" ##9# #" #
' * # # / "" # "
' #"*" # # 8
# """ / " *
**# *# ' #/"*#
# ) '# # # / #
" " # "
- " ## " # /' ""
" # " # "
# ')" / #* # "
' > ' #* "
9 ##'*9#
/##1, #* '
9#

Part fabrication
Machine planning
Pre-production
Program planning
Scheduling and
personnel planning
Profile fabrication
Machine planning
Section and
block assembly
Program planning
Scheduling and
personnel planning
Logistics
Simulation based transport
and storage planning
Hull erection
Scheduling and personnel planning
Painting
Simulation based
planning of painting
=.$88""
>. ".##*"
?.

*#99 # 9#?-"#'
') # "# " # # + 9 9 #
##'
$" ## #"# #
# 3$@ ( "# # 3$@
"""'"* #
""
/""# #"" # '$88""
7AA7" # # # ##-
" " , # # ## * /
*#1#') # "# /
')' ##, ##* *')/
#*" ""# "# 3#
'" #*##8 #" #
" "/"" ""# . #*
# " ' "#
' /*' " ##
9 * #1 "# #
- #) *# #" "/#
' " # ##
*# "# #"
B 2 ' #*"# # " # / ' 0
#" #- """
##*# #
C. # #) #"
$ " $88"" "" '"
) 2"# - " "
"# #
• *" #)2
• #*#", )
• #)
• * # # #
• '
>

D. #"
/ "# , ' "# "
#""" ## <
# # " /
#"*#"" "#"9
" #"* "#/'
' ) # ' " ### ) '
'"#
. " """
/ # ')# "'
#*" / ' " ##
"" $ " # *## ' $88 /
"" ' ')29
?

A. # "'
/ # ')
"# - # ' " )
5" " " # ) " ) #
$ # "*) # ) "## #
' "' / ##
" #",
') ( )**+ # "# #
"*# " " *
/ " # "
# # ") # #"'#
")# " # #*# 5" " # " )
#* ' " ##'
!" #
" # ' " $88
" #*#-# #
## ## *# #
"# # ## " ( $88 #
#"# E " $88""# *
" # ## AF )**, - "
" '"')#, 9#"#
/##*## $ "
"# ####$ '"" '"##
/" '" "# '*#
"+ )## *# ' # , /
*#"#"
C

$%
/ 0"$88'" #9*" #
- "# # " ' *# #
" 0 # @#
#*"#" ## #35# #@*
" # / $ , # # ' *
')# #'"##B632*
" #'"" " ## "# "
' " / ' "# " ' #
0 ' " # # " / "
"# " # / "* "
### + "9 #
*" /) #"9
' 1#*"
"#
/5-4$(5@ 6 %7AA& - ! ' .
7 #

The Potential of Free Software for Ship Design
Bastiaan N. Veelo, NTNU, Trondheim/Norway, Bastiaan.N.Veelo@ntnu.no
Abstract
This paper considers an unorthodox approach to software development and licensing, called Free Software,
Libre Software or Open Source Software (recently abbreviated as FLOSS), with a focus on its
potential in naval architecture. It is argued that this approach will increase productivity of programming
efforts related to ship design, and increase the use/development ratio of the resulting software. Advantages
and disadvantages of the approach are discussed, and an indication of how FLOSS for ship design
can be initiated is given.
1 Software for a Special Purpose
Maritime industries put special demands on computer applications, as the existence of this conference
illustrates. Advanced general purpose engineering design software (covered by the term “Product Lifecycle
Management”, PLM) is successful in many other branches of engineering. But, despite their level
of sophistication, they often fall short of our demands. Of course, computer applications exist that address
some of our special needs, but because the user-base, or market, is relatively small, these products usually
have one or more of the following disadvantages:
1. Limited functionality; especially functionality that is common in PLM applications may be lacking.
2. The user interface that we are presented with may not be as productive as the interfaces that most
of our colleagues in general engineering enjoy.
3. High licence fees for the user.
4. Low profitability for the producer.
Because of these disadvantages and the shortcomings of mainstream CAD systems, it happens that custom
software is developed in-house by an able naval architect, probably to address a small number of
issues initially. An important advantage of such an effort, besides now being able to address particular
issues, is access to the source code. Let us have a quick look at the advantages of source access.
1.1 Access to Source Code
Source code is of course the textual origin of software, that can be “understood” by both humans and
machines. It is what designers and implementors of software (the programmers) produce, and what machines
can compile into a binary format, which then can be run on computers to execute certain tasks.
The binary format is machine-readable only, so the internal workings of the software are hidden from
humans. Most software that you buy does not actually become your property, but you buy a license to use
the software in its binary form. Any attempt to “reverse engineer” its inner workings is often explicitly
prohibited. The knowledge that is represented by the source code of the program is a secret that is fiercely
protected by its licensor, and as a licensee you cannot extend or evolve the software.
Access to source code, on the other hand, means you have access to the inner workings of the program.
Besides the fact that this information is valuable in its own right, it also gives you various privileged
abilities, provided you have the required technical skills (which you are likely to have if you produced
the source):
To fix bugs. If you discover a bug in some software to which you only have access in binary format,
the only thing you can do is report the bug to the vendor, wait for the next version to be released
399

and pay an upgrade license. This new version may or may not fix the bug, and almost certainly
introduces new ones. With access to the source code you can track down the problem yourself and
most probably fix it yourself, here and now.
To inspect it. With access to the source code, you can assess the correctness of its algorithms, and with
it, the validity of the results that it produces.
To customise it. The software may have been written to assist in the solution of one specific problem.
At a later point in time, you may encounter a problem that has similarities with the earlier one.
With access to the source code, you can adapt the software to also assist in the solution of this new
problem.
To extend it. With access to the source code of a program, you have the possibility to extend it so that
it can perform more diverse tasks for you.
To evolve it. No non-trivial computer program is perfect. There is always room for improvement, e.g., in
the user interface, in the efficiency of its algorithms, in the accuracy of its output, to support new
hardware or to make use of performance features of new processors. Access to the source code
gives you the opportunity to make general improvements, or even experiment with alternative
approaches to the problem.
If you lack the technical skills to make use of these privileges, you can pay someone skilled, and still
profit from the privileges. These privileges are so valuable that they sometimes are the main motivator
for an in-house programming effort (Mutu, 2003).
1.2 Parallel Efforts
Raymond (1999) gives “empirical evidence that approximately 95% of [source] code is still written inhouse”,
and one may not be exaggerating much by saying that all ship design software available today
started out as an in-house or even personal project. However, few of these initiatives grow out to produce
a tool that others are willing to pay for. As software development usually does not belong to the core
activities of a design office, there are not enough resources to raise the software to production quality 1 ,
nor for support and maintenance that commercial distribution of the software would require.
Therefore, there is reason to believe that, on a global basis, there is a considerable programming effort
that is not exploited to its full potential. Now, if you are responsible for some of this effort, what can you
do to make it more worthwhile?
1.3 The Conventional View Reviewed
One way of seeing it, is that in-house developed software is an asset of very high value. Indeed, the
investment in programming effort may be colossal in relation to your selling business. But since you are
not licencing the software to others, it does not generate direct income. Obviously, the software is of
great value to you in the work that you do. You may then conclude that, because of the investment and
of its value to you, it is important to keep the software to yourself. In other words, you assume that the
secrecy of your software increases the competitive position of your selling business. However, chances
are that your competitors also use in-house developed software, and that the real advantage of mutual
secret efforts is relatively limited.
So what are the alternatives?
Give the software away in binary form. As you are not making any money on the software, and its
value for your competitive position is debatable, one option could be to give it away. You can try
1 “Production quality” in this context is a term to indicate a level of quality that makes software sell-able and involves
stability, efficiency, ease of use, user manuals etc. In-house developed software can be used for production in-house, even if it
is not of production quality.
400

to create a small revenue stream by making it “share-ware”, where people can pay a fee to make an
advertisement notice go away. But, as the state of the software is below production quality, it is not
likely to be of much use to anybody outside your department, not without the support that you are
not interested to provide, and few will think it is worth paying the share-ware fee. The benefits for
you are practically zero, unless you manage to turn it into a marketing stunt and attract attention to
your selling business, and for others the benefits are close to zero. Mind that you should disclaim
any warranty for the correctness of the software and the validity of its output, which you cannot
afford without the software creating revenue, so serious application of the software is not attractive
for third parties.
Publish the source code. This option includes the former one, because anyone will be able to compile
the software into binary form. It is important to note that source code is automatically protected
by international copyright law, as per the Berne Convention of 1886, meaning that no registration
is required, nor is the inclusion of a copyright notice. No-one is allowed to make copies of source
code or make changes without permission of its originator.
With the availability of the source code, third parties can now inspect it and assess the correctness
of the software, and theoretically decide to use it to solve real-world problems. However, source
code analysis requires a considerable effort, and copyright law prohibits third parties to make use
of any of the other advantages mentioned in section 1.1, meaning that they will have to accept a
low level of quality and lack of vendor support. The protected advantages may still be important
enough for others to engage in parallel programming efforts. There are no real benefits for you.
Put the source code into the public domain. To unlock all advantages of source code access to everybody,
you could explicitly give up on the copyright, and put your work in the public domain. This
has the potential of greatly increasing the use of your programming effort, and eliminates the motivation
for any parallel effort. Some people do this, simply because they like to see a wide adoption
of their contribution. There may be some secondary economic advantages (Raymond, 1999), but
the economic disadvantage can be far greater. Anybody or any corporation may legally take your
code and build a proprietary computer programme on it, or integrate parts of it into existing proprietary
software. By giving up on the copyright completely, you allow others to make direct profit
off your effort for no compensation, and you might not even know.
Release the source code under relaxed copyright. Most commercial software licenses impose further
restrictions, for which an agreement is necessary between licensee and licenser. But it is equally
possible to formulate a license that states additional freedoms, relaxing the protection of the copyright,
in exchange of specific obligations by the licensee. The license can state itself to be void in
case any of the obligations are breached, which effectively turns the act into a violation of copyright
law. For someone that does not accept the license and the obligations, the work is automatically
protected by ordinary copyright. For people who do accept the license, no signed agreement needs
to exist for the obligations to be binding.
This mechanism can be used to give others access to all advantages mentioned in section 1.1, and
at the same time to prohibit corporate “hijacking” of your code. This can be achieved by requiring
any derivative work or modification of your code to be released under the same license as you
did. Suddenly, for you as the copyright holder, this implies a great advantage: any improvement
that anybody makes to your work, you may incorporate. This opens an enormous resource that
has the potential to increase the quality of your software to production level and evolve it into a
more powerful tool almost for free. This is the mechanism that makes Free/Libre and Open Source
Software successful.
2 Definition of Terms
The English language has difficulties to put a name on software that is licenced under relaxed copyright.
The term “Free Software” has been used for many years now, and is often associated with a man called
401

Richard Stallman. In 1984, Stallman launched the GNU project (www.gnu.org) to develop a free operating
system. GNU is still an important part of the now widely distributed free operating system that is
informally called Linux 2 . In 1985, Stallman founded the Free Software Foundation (FSF, www.fsf.org),
to promote computer users’ rights to use, study, copy, modify, and redistribute computer programs. Both
Stallman and his projects still play an important role in the Free Software movement today.
However, there is an ambiguity in the word “free” because it has different meanings when used as in “free
beer” and as in “free speech”. In practice, both meanings often apply to Free Software, but the price of
Free Software is not really important. You may sell Free Software if you can. The latter meaning of the
word “free” is about freedom and liberty, which really is the essence of Free Software.
Unfortunately, most people think of economics when they think of something free, and you always need
to disambiguate the term when you speak of Free Software. It is possible that therefore “Free Software”
does not appeal to business people. This has been considered to be a problem, which has motivated an
other movement, the Open Source Initiative (www.opensource.org), in 1998. The Open Source Initiative
(OSI) is a marketing program for Free Software, and aims to advocate it on solid pragmatic grounds.
It has registered the term “Open Source” as a trade mark, and popularised it as a synonym for “Free
Software”. OSI certifies software as Open Source, and carries a list of approved licenses (amounting to
almost 60 licenses at the time of this writing).
Although the term “Open Source” is probably the most widely used term today, it is not without its
problems either. Some people feel that it does not cover the essence, i.e., freedom, well enough (Stallman,
2002). Indeed, sometimes software is claimed to be Open Source, whereas it really only is published
source code, without the copyright having been relaxed. As a matter of fact, OSI clarifies that “Open
Source doesn’t just mean access to the source code” and gives a detailed definition of the term, consisting
of ten criteria that software must comply with before it may be called Open Source. These criteria differ
slightly from the ones that the FSF practices; some of the license restrictions that the OSI accepts for
Open Source are too restrictive in the eyes of the FSF (FSF, 2001).
During a translation of the English text of the most important Free Software license, the GNU General
Public License (GPL), into Spanish, it appeared that Roman languages do not suffer the ambiguity
problem (González-Barahona, 2004). The word “free” with respect to price is translated into Spanish
as “gratis”, and “free” with respect to liberty is translated as “libre”. Because of the problems with the
terms “Free Software” and “Open Source”, some people have started to use the term “Libre Software”,
even though this is a mix of languages. This term is gaining popularity, notably in official circles in Europe.
For example, in 1999, the Information Society Directorate General of the European Commission
initiated the European Working Group on Libre Software (eu.conecta.it).
In 2002, the acronym FLOSS has been introduced, in a survey and study commissioned by the European
Commission (Ghosh and Glott, 2002), to cover all of Free/Libre and Open Source Software at once.
It is important to note that both Free Software and Open Source do not differentiate between the last two
options of section 1.3. That is, both Free Software and Open Source software recognise source code that
has been put in the public domain, because everyone is free to use such software in any way they like.
Software that is guaranteed to be FLOSS in all its derivative variants, by means of a clause that makes
derivative works inherit the licence of the original and the requirement that source code always must be
made available, is often identified with the term “Copyleft” (as opposed to “Copyright”). In general, the
advantages of FLOSS are considered to be highest under a Copyleft license.
2.1 FLOSS Licences
To give an exhaustive list of officially recognised Free/Libre and Open Source Software licenses is
far beyond the scope of this paper. For this the reader is referred to the sites of the FSF and OSI,
who maintain extensive lists of approved licenses (www.gnu.org/licenses/license-list.html and
2 To be precise, Linux is actually only the kernel in this operating system.
402

www.opensource.org/licenses/). However, the important question is not whether any particular license
is approved by either organisation. The important question is whether a piece of software that you
are interested in is licensed under terms that you can accept, and for this you should always consult
the actual license text that follows with the software. The other important question is which license to
choose or construct when you consider to write FLOSS or consider to release existing work as FLOSS.
To help answer the latter question, both organisations have put together guides and “HOWTOs”, see
(www.fsf.org/licensing) and (Raymond and Raymond, 2002).
For completeness however, we briefly explain the licenses that are used for relevant FLOSS as listed in
the appendix. Both the MIT and BSD licences allow almost everything, except removal of the license
statement and copyright notice. They also disclaim warranty and liability, and the BSD licence adds a
non-endorsement clause. The following licenses are all Copyleft. The most widely used license is the
GNU GPL license, or General Public Licence. Proprietary software can not include or even link with
GPLed code. The QPL, or Qt Public License, is rarely used, and is comparable but incompatible with
the GPL. The GNU LGPL, or Lesser General Public Licence, is similar to the GPL but allows LGPLed
libraries to be linked to by proprietary software. The wxWindows Library Licence is identical to the
LGPL, however with an exception that states additional freedoms for binary distribution.
3 The Case for FLOSS
Due to space limitations, this paper is not going to do enough justice to the case for Free/Libre and
Open Source Software. Many essays, articles and even books have been written on the subject by
far better analysts and FLOSS advocates. For example, “The Cathedral and the Bazaar” by Raymond
(1999) is very much worth a read, especially the online version that contains references to comments
and replies by others. The information on the OSI website is a very good place to start, because it
concisely discusses the case for FLOSS from the viewpoints of business management, users and of
developers individually (www.opensource.org/advocacy/). The phenomenon of FLOSS is actively
being studied, and MIT carries an impressive list of online articles from the FLOSS research community
(opensource.mit.edu/online_papers.php). Large scale surveys of the FLOSS developer community
have been performed by Gosh and Glott (2002) and David et al. (2003), in which respectively 2784
and 1588 developers participated.
Especially the OSI helps you weigh the advantages and disadvantages between an open development
model and a closed development model. Here it is often assumed that you are able to extract direct
revenue out of your proprietary software, or in Raymond’s (1999) words “collect rent from your secret
bits”. The OSI explains that even if this is the case, the pay-off of converting to FLOSS can be higher
than the pay-off of remaining in proprietary mode. However, that consideration is outside the scope of
this paper, and we will proceed with the simpler assumption that you are the only user of your in-house
developed software.
There are three main advantages of writing FLOSS as opposed to writing software in-house. Firstly, you
get valuable peer review. Secondly, you get to use free building blocks. And lastly, you work in an organisational
mode that is arguably the most effective for the management of complex systems (Raymond
1999).
3.1 Peer Review
The peer review helps improving the quality and feature-richness of your software. Because the software
is available freely, a community of “beta testers” (your users) will connect with you and help you find
bugs. And because they have access to the code and are allowed to play with it, they will send you bug
fixes if they can, in exchange for just gratification and recognition. For the same reasons, you may get
sent patches that add new features to your software.
403

3.2 Free Building Blocks
Because you are writing FLOSS, you are free to build on existing FLOSS. You can do that by linking
with one or more of the many excellent libraries that exist for different purposes, and thereby use the
peer reviewed work of others instead of reinventing the wheel yourself. Also, instead of writing a new
computer program from the ground up to help do your work, you may be able to find an existing project,
either fully functional or in early stages of development, that you can extend to make it satisfy your
requirements. In these ways you can have a flying start and reach your goal much sooner than when
doing it all alone.
The risk of depending on third party code that exists in a proprietary setting, namely that the software
may disappear because of a business situation with the vendor, is non-existent with FLOSS. If a piece
of FLOSS gets dropped by its originators, you are free to pick it up and maintain and evolve it yourself.
Therefore, a FLOSS project will thrive as long as there are people interested in it. The same advantage
applies to the accessibility of data files. The information in old data files, written in a proprietary format
with a proprietary program that is not available anymore, is inaccessible and effectively lost. But if you
have the source code of the application that wrote the data file, you can understand the format and extract
the information.
3.3 Your Competitive Position
If you are still reluctant to publish work from which your competitor may benefit, you may consider
the following. Although maritime industries increasingly play on a global market, most of your business
likely still relates to a certain geographic area. However, FLOSS development takes place on the Internet,
where location is irrelevant. Whilst you compete more or less locally, you will collaborate globally in
FLOSS development. Also, even when your nearest competitor starts using your software intensively, he
will make improvements and he will have to contribute them back to you and make your software better.
Therefore, it is important to be the first to embark in FLOSS mode, because it gives you more control of
the situation. You still own the software, and it is you who decides where to take it. Raymond (1999) also
says about this:
[T]here’s a serious opportunity risk in waiting too long: you could get scooped by a competitor
going open-source in the same market niche.
The reason this is a serious issue is that both the pool of users and the pool of talent available
to be recruited into open-source cooperation for any given product category is limited, and
recruitment tends to stick. If two producers are the first and second to open-source competing
code of roughly equal function, the first is likely to attract the most users and the most and
best-motivated co-developers; the second will have to take leavings.
So yes, your competitor may benefit from your actions, but you may benefit more.
3.4 Invitation to Take the Lead
If you are a scientist, commercial competition may not be so much of an issue, and with that the choice
for FLOSS should be easy. FLOSS poses great opportunities for learning, and universities are encouraged
to take the lead in developing FLOSS, also for maritime applications.
3.5 Play the Game Well
Before jumping on the FLOSS bandwagon in all enthusiasm, be sure to be prepared for the rules of the
game. FLOSS development is a voluntary community effort, and people skills are essential when leading
one. This is especially the case because the Internet is a poor medium for social communication. In order
to make FLOSS development work for you, you need to understand the process very well, or have a
natural feeling for it. Again, the writings of Raymond (1999) can be a source of insight.
404

4 Conclusion
This article has discussed how Free/Libre and Open Source Software can be an attractive alternative to
in-house developed software for ship design. The freedom to use existing FLOSS building blocks is an
important motivator to get involved in FLOSS development. Therefore, this article has an appendix with
references to selected FLOSS projects of various categories that are relevant to ship design. The use of
one or more of these building blocks makes a flying start possible in the initiation of FLOSS for ship
design. The appendix also shows that it is already possible to use FLOSS for some aspects of ship design
today, and that you will not have to pioneer the concept. If you decide to get actively involved, you will
not be alone.
References
DAVID, P.A.; WATERMAN, A.; ARORA, s. (2003), FLOSS-US — the free/libre/open source software
survey for 2003, Stanford Institute for Economic Policy Research. www.stanford.edu/group/
floss-us/
FSF (2001), Categories of Free and Non-Free Software, Free Software Foundation. www.gnu.org/
philosophy/categories.html
GHOSH, R.A.; GLOTT, R. (2002), Free/libre and open source software: survey and study, International
Institute of Infonomics, University of Maastricht, The Netherlands; and Berlecon Research GmbH,
Berlin, Germany. www.infonomics.nl/FLOSS/
GONZÁLEZ-BARAHONA, J.M. (2004), Quo vadis, libre software?, Universidad Rey Juan Carlos,
Spain. sinetgy.org/jgb/articulos/libre-software-origin/
MUTU, V.; IONAS, O.; GAVRILESCU, I. (2003), SURF — an in-house development for a ship hull
design software, 2 nd Int. Conf. Computer and IT Applic. Mar. Ind., COMPIT, Hamburg, pp.387–399
RAYMOND, E.S.; RAYMOND, C.O. (2002), Licensing HOWTO, draft Open Source Initiative working
paper. www.catb.org/˜esr/Licensing-HOWTO.html
RAYMOND, E.S. (1999), The Cathedral & the Bazaar, O’Reilly, ISBN 1-56592-724-9, www.catb.
org/esr/writings/cathedral-bazaar/
STALLMAN, R.M. (2002) Why “Free Software” is Better Than “Open Source”, in Free
Software, Free Society, GNU Press, ISBN 1-882114-98-1. www.gnu.org/philosophy/
free-software-for-freedom.html
APPENDIX
A
FLOSS Software
Examples of existing Free/Libre and Open Source Software are given in six categories: geometric modelling,
visualisation, numerics, finite element method, computational fluid dynamics and graphical user
interfaces. The information about each project also includes the latest version and release date at the time
of this writing, which is an indication of the degree of maturity and the developer activity respectively.
Note that the list is by no means exhaustive.
A.1 Geometric Modelling
A.1.1
Blender
Blender is a 3D graphics creation suite with a focus on the entertainment industry. Its modelling capabilities
include polygon meshes, NURBS surfaces, Bézier and B-spline curves, meta-balls, and “Smooth
405

proxy” style Catmull-Clark subdivision surfaces with optimal iso-lines display and sharpness editing. It
supports Python scripting for the creation of custom tools.
Homepage: www.blender.org
Latest version: 2.36, 22 Dec 2004
License: GPL 2
Language: C, C++, Python
Platforms: Windows, Mac OS X, Linux,
Solaris, Irix, FreeBSD
Fig.1: The Blender modeller
A.1.2
Wings 3D
Wings 3D is a polygon mesh modeller with a user interface that is easy to use for both beginners and
advanced users. Wings 3D uses subdivision surfaces rather than NURBS surfaces.
Fig.2: The Wings3D modeller
Homepage: www.wings3d.com
Latest version: 0.98.26b, 16 Dec 2004
License: BSD License
Language: Erlang
Platforms: Windows, Mac OS X, Linux and
other Unices.
(Image source:
www.naval-architecture.co.uk/phpbb/
viewtopic.php?t=12)
A.1.3
Coin3d
Coin3D is a set of libraries used for creating 3D graphics applications. Coin3D is fully compatible with
SGI Open Inventor 2.1, the de facto standard for 3D visualisation and visual simulation software in
the scientific and engineering community. Additional features in Coin3D include VRML97 support, 3D
sound, 3D textures, and parallel rendering on multiple processors. See Fig.4.
A.1.4
Open CASCADE
Open CASCADE is an industrial Open Source alternative to proprietary 3D modelling kernels, a library
that includes components for 3D surface and solid modelling, visualisation, data exchange and rapid
application development. Open CASCADE Technology can be best applied in development of numerical
simulation software including CAD/CAM/CAE, AEC and GIS, as well as PDM applications. The
Technology exists from the mid 1990-s and has already been used by numerous commercial clients. See
Fig.5.
406

A.1.5
FreeCAD
FreeCAD will be a general purpose 3D CAD system based on OpenCasCade. FreeCAD will aim directly
at mechanical engineering, product design and related features (like CatiaV4 and V5, and SolidWorks).
It will be a Feature-Based parametric modeller. Scripting is supported through Python.
Homepage:
Latest version:
License:
Language:
Platforms:
free-cad.sourceforge.
net
0.1 B107
GPL, LGPL
C++, Python
Linux, Windows
Fig.3: The FreeCAD system
Homepage: http://www.coin3d.
org/
Latest version: 2.3.0, 22 Jun 2004
License: GPL (commercial license
available)
Language:
Platforms:
C++
any UNIX / Linux / *BSD
platform, all Microsoft Windows
operating systems, and Mac OS X
Fig.4: The Coin3D graphics library
Homepage: www.opencascade.org
Latest version: 5.2, July 2004
License: LGPL-like with certain differences
Language: C++
Platforms: Linux Intel, Windows Intel and
Sun Sparc
(Image: RINA Finite-element pre- and post-processor
for ship certification)
Fig.5: The OpenCASCADE surface and solid modelling kernel
A.1.6
BRL-CAD
A powerful constructive solid geometry (CSG) solid modelling system that includes an interactive geometry
editor, ray tracing support for rendering and geometric analysis, network distributed frame-buffer
support, and image and signal-processing tools.
407

Homepage: brlcad.sourceforge.
net
Latest version: 7.0.2, 6 Jan 2005
License: BSD License, GPL, LGPL
Language: C, C++, Java, PHP, Tcl,
Unix Shell
Platforms: Windows and all BSD and POSIX
platforms, including Linux,
Mac OS X, Solaris, Irix etc.
Fig.6: The BRL-CAD solid modelling system
A.1.7
Varkon
VARKON can be used as a traditional CAD-system with drafting, modelling and visualisation if you
want to, but the real power of VARKON is in parametric modelling and CAD applications development.
VARKON includes interactive parametric modelling in 2D or 3D but also the unique MBS programming
language integrated in the graphical environment. VARKON is designed to be modified and extended
with knowledge and functionality specific to a certain product or problem. It is not a true solid modeller.
Homepage: www.tech.oru.se/cad/
varkon/
Latest version: 1.18A, 18 Oct 2004
License: LGPL 2
Language:
Platforms:
C
HP-UX, (Sun), AIX, Irix, VMS,
SCO/UNIX, FreeBSD,
GNU/Linux, Cray, (Windows at a
fee)
Fig.7: The Varkon CAD system
A.1.8
Sailcut CAD
Sailcut CAD is a sail design and plotting software. It allows you to design and visualise your own sail
and compute the accurate development of all panels in flat sheets.
Homepage: sailcut.sourceforge.
net
Latest version: 1.0, 20 Dec 2004
License: GPL
Language:
Platforms:
C++
GNU/Linux, Mac OS X and
Windows
Fig.8: The Sailcut CAD sail design and plotting software
408

A.1.9
SketchBoard
SketchBoard is a sketch oriented CAD software. It is a tool for designers to develop their design by
sketching and modelling in 3D. It has a system that helps converting the sketch into a polygon.
Homepage: sketchboard.
sourceforge.net
Latest version: 1.22, 22 Apr 2004
License: GPL
Language: C++
Platforms: Windows
Fig.9: The SketchBoard CAD software
A.2 Visualisation
A.2.1
ADMesh
Processor for repairing, transforming and merging triangulated solid meshes. Reads STL file format
(used for rapid prototyping applications) and writes STL, VRML, OFF, and DXF files.
(console application)
Homepage: www.varlog.com/
products/admesh/
Latest version: 0.95, 3 Sep 2003
License: GPL 2
Language: C
Platforms: Linux, SunOS 4.1.3, IRIX 5.2,
HP-UX, (Windows)
Fig.10: The ADMesh processor
A.2.2
Pixie
Pixie is a photo-realistic renderer that uses a RenderMan-like interface. Features include programmable
shading, motion blur, depth of field, ray-tracing, scan-line rendering, occlusion culling, global illumination,
caustics, etc.
Homepage: pixie.sourceforge.net
Latest version: 1.3.26, 29 Dec 2004
License: GPL
Language: C, C++
Platforms: Windows, All POSIX
(Linux/BSD/UNIX-like OSes)
Fig.11: The Pixie renderer
409

A.2.3
YafRay
YafRay is a powerful ray-tracer. It enables you to create fantastic images and animations of a photo
realistic quality. Thanks to its API (Application Programming Interface) and its modular structure, it is
possible to develop rendering plug-ins, making it possible to use YafRay from any program or 3D suite.
At the time of this writing, suites as Blender, Wing3D or Aztec take advantage of this feature.
Homepage: www.yafray.org
Latest version: 0.0.7, 5 Aug 2004
License: LGPL 2.1
Language: C++
Platforms: GNU/Linux, Windows 9x/XP/2K,
Mac OS X and Irix
Fig.12: The YafRay ray-tracer
A.2.4
GeomView
GeomView is an interactive 3D viewing program for Unix. It can be used as a stand-alone viewer for
static objects or as a display engine for other programs which produce dynamically changing geometry.
It can display objects described in a variety of file formats.
Homepage: www.geomview.org
Latest version: 1.8.1, 25 Mar 2001
License: LGPL 2.1
Language: C, C++
Platforms: Unix-like OSes including but not
limited to GNU/Linux, Solaris,
IRIX, and AIX
Fig.13: The GeomView viewer
A.2.5
MayaVi
MayaVi is a free, easy to use scientific data visualiser. See Fig.15.
A.3 Numerics
Beyond the software referenced below, there is a host of other powerful numerics libraries. Many of them
are listed at www.oonumerics.org/oon.
410

A.3.1
Octave
GNU Octave is a high-level language, primarily intended for numerical computations. It provides a
convenient command line interface for solving linear and nonlinear problems numerically, and for performing
other numerical experiments using a language that is mostly compatible with Matlab. It may
also be used as a batch-oriented language.
Octave has extensive tools for solving common numerical linear algebra problems, finding the roots of
nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary
differential and differential-algebraic equations. It is easily extensible and customisable via user-defined
functions written in Octave’s own language, or using dynamically loaded modules written in C++, C,
Fortran, or other languages.
Homepage: www.octave.org,
octave.sourceforge.
net
Latest version: 2.9.0, 15 Mar 2005
License: GPL 2
Language: C, C++, Fortran
Platforms: Linux, Mac OS X, Windows
Fig.14: The Octave language (mostly Matlab compatible)
Homepage: mayavi.sourceforge.
net
Latest version: 1.3, 18 Nov 2003
License: BSD license
Language:
Platforms:
Python
Linux, Mac OS X and other
Unices, Windows
Fig.15: The MayaVi data visualiser
A.3.2
FreeMat
FreeMat is a free environment for rapid engineering and scientific prototyping and data processing. It
is similar to proprietary systems such as MATLAB from Mathworks, and IDL from Research Systems.
FreeMat includes several novel features such as a code-less interface to external C/C++/FORTRAN
code, parallel/distributed algorithm development (via MPI), and plotting and visualisation capabilities.
See Fig.17.
A.3.3
Maxima
Maxima is a fairly complete computer algebra system written in lisp with an emphasis on symbolic
computation. Its abilities include symbolic integration, 3D plotting, and an ODE solver. See Fig.18.
A.3.4
ATLAS
The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing
on applying empirical techniques in order to provide portable performance. At present, it provides
411

C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from
LAPACK.
Homepage: math-atlas.
sourceforge.net
Latest version: 3.7.8, 23 Jul 2004
License: BSD License
Language: C, Fortran77
Platforms: Linux and other Unices, Windows
Fig.16: The Automatically Tuned Linear Algebra Software
Homepage: freemat.sourceforge.
net
Latest version: 1.09, 27 Oct 2004
License: MIT-type
Language: C, C++, FORTRAN
Platforms: Linux, Windows and Mac OS X
Fig.17: FreeMat, an other alternative to Matlab
Homepage: maxima.sourceforge.
net
Latest version: 5.9.1, 22 Sept 2004
License: GPL
Language:
Platforms:
C, Lisp
All POSIX
(Linux/BSD/UNIX-like OSes)
Fig.18: The Maxima computer algebra system
A.4 FEM
A.4.1
Gmsh (FEM Mesh Generator)
Gmsh is an automatic 3D finite element grid generator (primarily Delaunay) with a build-in CAD engine
and post-processor. Its design goal is to provide a simple meshing tool for academic problems with
parametric input and advanced visualisation capabilities.
412

Homepage: www.geuz.org/gmsh/
Latest version: 1.58, 1 Jan 2005
License: GPL 2
Language: C++
Platforms: Windows, Linux, Mac OS X
Fig.19: The Gmsh mesh generator
A.4.2
NETGEN — Automatic Mesh Generator
NETGEN is an automatic 3D tetrahedral mesh generator. It accepts input from constructive solid geometry
(CSG) or boundary representation (BRep) from STL file format. The connection to a geometry
kernel allows the handling of IGES and STEP files. NETGEN contains modules for mesh optimisation
and hierarchical mesh refinement. Works together with NGSolve (see Section A.4.3).
Homepage: www.hpfem.jku.at/
netgen/
Latest version: 4.4, 17 Nov 2004
License: LGPL 2.1
Language: C++
Platforms: FreeBSD, Linux
Fig.20: The NETGEN mesh generator
A.4.3
NGSolve
NGSolve is a general purpose 3D finite element solver, supporting boundary value problems, initialboundary
value problems and Eigenvalue problems for the available types of equations, namely scalar
(heat flow), elasticity, and magnetic field. NGSolve performs adaptive mesh refinement, the matrix equations
are solved by optimal order multi-grid methods. Works together with NETGEN (see Section A.4.2).
See also Fig.22.
A.4.4
CalculiX
A Three-Dimensional Structural Finite Element Program designed to solve field problems. With CalculiX
Finite Element Models can be build, calculated and post-processed. The pre- and post-processor is
an interactive 3D-tool using the OpenGL API. The solver is able to do linear and non-linear calculations.
Static, dynamic and thermal solutions are available. Both programs can be used independently. Because
the solver makes use of the Abaqus input format, it is possible to use proprietary pre-processors as well.
413

In turn, the pre-processor is able to write mesh related data for Nastran, Abaqus and Ansys and for the
free cfd code duns. A VDA CAD interface is available.
Homepage: www.calculix.de
Latest version: 1.2, 25 Jul 2004
License: GPL 2
Language: Fortran77, C
Platforms: Unix, including Linux and Irix
Fig.21: The CalculiX solver
Homepage: www.hpfem.jku.at/
ngsolve/index.html
Latest version: 4.4, 17 Nov 2004
License: LGPL 2.1
Language: C++
Platforms: FreeBSD, Linux
Fig.22: The NGSolve solver
A.4.5
SLFFEA
SLFFEA stands for San Le’s Free Finite Element Analysis. It is a package of scientific software and
graphical user interfaces for use in (non-linear) finite element analysis.
Homepage: slffea.sourceforge.
net
Latest version: 1.3, 14 Nov 2003
License: LGPL 2
Language: C
Platforms: Linux, (Windows)
Fig.23: San Le’s Free Finite Element Analysis
A.4.6
TOCHNOG
TOCHNOG is a feature-rich finite element program. Among the FE models supported are: differential
equations (materials), convection-diffusion equations, Stokes and Navier-Stokes (fluids), elasticity
(isotropy and transverse isotropy), plasticity (Von-Mises, Mohr-Coulomb, etc.; plastic surfaces can be
414

arbitrarily combined). Residues in equations and error estimates for all data can be printed or plotted
using gnuplot/plotmtv, CalculiX or gmsh.
Homepage: tochnog.sourceforge.
net
Latest version: 26 Nov 2001
License: GPL 2
Language:
Platforms:
C++
POSIX (such as Linux, BSD,
UNIX-like OSes) and Windows
Fig.24: The TOCHNOG finite element programme
A.4.7
OFELI
OFELI (Object Finite Element LIbrary) is a library of finite element C++ classes for multipurpose development
of finite element software. It is intended for teaching, research and industrial developments as
well.
Homepage: www.ofeli.net
Latest version: 1.3.0-3, 5 Dec 2004
License: GPL
Language: C++
Platforms: Windows, All POSIX
(Linux/BSD/UNIX-like OSes)
Fig.25: The Object Finite Element LIbrary
A.5 CFD
A.5.1
FEATFLOW
FEATFLOW is both a user oriented as well as a general purpose subroutine system for the numerical
solution of the incompressible Navier-Stokes equations in two and three space dimensions. It supports
stationary and non-stationary problems.
Homepage: www.featflow.de
Latest version: 1.2d, 12 Apr 2000
License: “Open Source”
Language: Fortran77, C
Platforms: Unix and Linux, Windows and
DOS
Fig.26: The FEATFLOW Navier-Stokes solver program and library
415

A.5.2
DUNS
The DUNS (Diagonalised Upwind Navier-Stokes) code is a 2D/3D, structured, multi-block, multispecies,
reacting, steady/unsteady, Navier Stokes fluid dynamics code with q-omega turbulence model.
Homepage: duns.sourceforge.net
Latest version: 2.7.1, 25 Sept 2003
License: GPL 2
Language: C, Fortran77
Platforms: Linux and other POSIX
compliant platforms
Fig.27: The DUNS code
A.5.3
OpenFlower
OpenFlower is an open source CFD software (FLOW solvER, literally) written in C++. It is mainly
devoted to the resolution of the turbulent unsteady incompressible Navier-Stokes equations with a LES
approach. It can deal with arbitrary complex 3D geometries with its finite volume approach.
Homepage: openflower.
sourceforge.net
Latest version: 0.3, 11 Oct 2004
License: GPL
Language: C++
Platforms: POSIX, including Linux
Fig.28: The OpenFlower CFD software
A.5.4
Gerris Flow Solver
Gerris is a tool for generic numerical simulations of flows, possibly in geometrically complex geometries
and including adaptive, multi phase and interfacial flows capabilities.
Homepage: gfs.sourceforge.net
Latest version: 0.6-patch-1, 21 Oct 2004
License: GPL
Language: C
Platforms: All POSIX
(Linux/BSD/UNIX-like OSes)
Fig.29: The Gerris Flow Solver
416

A.6 GUI
A.6.1
Qt
One of the key design goals behind Qt is to make cross-platform application programming intuitive, easy
and fun. Qt achieves this goal by abstracting low-level infrastructure functionality in the underlying window
and operating systems, providing a coherent and logical interface that makes sense to programmers.
The Qt API and tools are consistent across all supported platforms, enabling platform independent application
development and deployment. Qt applications run natively, compiled from the same source code,
on all supported platforms. Qt is the basis of the “K” Desktop Environment for Linux (KDE).
Homepage: www.trolltech.com/
Latest version: 3.3.3, 11 Aug 2004
License: dual GPL and QPL, and
commercial (including support
for Windows)
Language: C++
Platforms: Linux, Solaris, HP-UX, IRIX,
AIX, many other Unix variants,
Mac OS X, embedded Linux
Fig.30: The Qt application framework
A.6.2
GTK+
GTK+ is a multi-platform toolkit for creating graphical user interfaces. Offering a complete set of widgets,
GTK+ is suitable for projects ranging from small one-off projects to complete application suites.
GTK+ has been designed from the ground up to support a range of languages, not only C/C++. Using
GTK+ from languages such as Perl and Python (especially in combination with the Glade GUI builder)
provides an effective method of rapid application development. GTK+ is the basis of the “Gnome” desktop
environment on Linux.
Homepage: www.gtk.org
Latest version: 2.6.1, 8 Jan 2005
License: LGPL
Language: C++
Platforms: GNU/Linux, BSD, Solaris, IRIX,
HP-UX, AIX. There is a
Windows port.
Fig.31: The GTK+ GUI library
A.6.3
wxWidgets
wxWidgets gives you a single, easy-to-use API for writing GUI applications on multiple platforms, with
native look and feel. On top of great GUI functionality, wxWidgets gives you: online help, network
programming, streams, clipboard and drag and drop, multi-threading, image loading and saving in a
variety of popular formats, database support, HTML viewing and printing etc.
417

Homepage: www.wxwidgets.org
Latest version: 2.5.3, 10 Oct 2004
License: wxWindows Licence
(OSI certified)
Language: C++
Platforms: Windows, Unix, Mac OS X, MGL,
OS/2
Fig.32: The wxWidgets GUI library
A.6.4
Leonardo
The Leonardo Library (LL) is a cross-platform, open-source C toolkit for program development. The
library is light, well-documented, easy to learn, and covers a large number of functionalities, including
graphic user interface, thread, I/O and memory management. Differently from other programming
toolkits, the LL also includes components with fundamental algorithms and data structures. Graphic user
interface components defined by the library preserve the look and feel of the target platform.
Homepage: www.leonardo-vm.org
Latest version: Qt-1.0.0b, 30 Nov 2003;
Win32-1.1.0b, 13 Feb 2004
License: LGPL 2.1
Language: C
Platforms: Linux, Windows
Fig.33: The Leonardo Library
A.6.5
FOX Toolkit
FOX is a C++ toolkit for easy and effective development of Graphical User Interfaces. It offers a wide
collection of controls, and provides state of the art facilities such as drag and drop, selection, as well
as OpenGL widgets for 3D graphical manipulation. FOX also implements icons, images, and userconvenience
features such as status line help, and tool-tips. Tool-tips may even be used for 3D objects.
Homepage: www.fox-toolkit.org
Latest version: 1.3.22, 26 Dec 2004
License: Relaxed LGPL 2.1
Language: C++
Platforms: Linux, FreeBSD, SGI IRIX, HP-UX,
IBM AIX, SUN Solaris,
DEC/Compaq Tru64 UNIX,
Windows
(Image CFD Research Corporation)
Fig.34: The FOX GUI toolkit
418

Optimization of Surface Utilization Using Heuristic Approaches
Yves Langer, Maud Bay, Yves Crama, Frédéric Bair, Jean-David Caprace,
Philippe Rigo, University of Liège, Liege/Belgium
{Yves.Langer,Maud.Bay,Y.Crama,F.Bair,JD.Caprace,Ph.Rigo}@ulg.ac.be
Abstract
A scheduling problem arising in factories producing large building blocks is modelled applying
optimization techniques. The application is a shipyard workshop producing prefabricated keel
elements. The objective is to maximize the number of building blocks produced in the factory
during a certain time window. The solution combines a Guided Local Search heuristic with Fast
Local Search techniques. A final discussion explains the additional real-life issues arising in the
industrial application and how firm-specific constraints can be conveniently considered by the
model.
1. Introduction
This paper presents a new method to solve a scheduling problem that arises in factories producing
large building blocks (in our case, a shipyard workshop producing prefabricated keel elements).
The factory is divided in equal size areas. The blocks produced in the factory are very large.
Once a building block is placed into the factory, it cannot be moved until all processes on the
building block are finished. The blocks cannot overlap. The objective is to maximize the number
of building blocks produced in the factory during a certain time window.
More precisely, we are given a set of n rectangular-shaped blocks. Each block is characterized by
its geometric dimensions (width w j , length l j and height h j ) but also by processing information
such as its processing time t j , its ready time r j and its due date d j (j ∈ {1, ..., n}). We are also
given a number A of identical two-dimensional areas, having width W and length L. Time is
considered as a third dimension. The areas are fully dedicated to the production of the blocks.
The problem consists of orthogonally ordering the blocks into the areas, while respecting the
time constraints, and with the objective to produce the largest number of building blocks. In
practical terms, we have to assign six variables for each block j:
• p j = {0, 1} indicating whether the block j is produced or not
• the name a j = {1, . . . , A} of the area where block j is to be produced
• x j and y j coordinates, representing the position of the upper left corner of the block j in
the area
• an orientation o j = {0, 1} (either horizontally or vertically) for block j
• a starting date s j
A solution will be considered as feasible if the individual and the collective constraints are met.
We call individual constraints those which focus on one block only, regardless of the other blocks.
Major individual constraints are:
• blocks must fit within the width of an area (x j ≥ 0 and x j + [o j w j + (1 − o j )l j ] ≤ W )
• blocks must fit within the length of an area (y j ≥ 0 and y j + [o j l j + (1 − w j )l j ] ≤ L)
• blocks must fit in their time windows (s j ≥ r j and s j + t j ≤ d j )
419

Collective constraints focus on the interaction between the positions of different blocks. In a
first step, the only collective constraint considered is that we need to prevent the blocks from
overlapping.
We assume initially that there exists at least one feasible solution for the set of blocks initially
given. I.e. all the constraints can be satisfied when p j = 1 for all j ∈ {1, ..., n}.
2. Analogy to the 3D-BPP
In the three-dimensional bin packing problem (3D-BPP), we are given a set of n rectangularshaped
items, each characterized by width w j , height h j , and depth d j (j ∈ {1, . . . , n}) and
an unlimited number of identical three-dimensional containers (bins) having width W, height
H, and depth D. The 3D-BPP consists of orthogonally packing all the items into the minimum
number of bins.
The major difference between 3D-BPP and our initial problem is that, in the former,
items/blocks must fit into the container height (z j ≥ 0 and z j + h j ≤ H), whereas they must
fit into their time window in the latter (s j ≥ r j and s j + t j ≤ d j ). (One can compare a bin
in the 3D-BPP to a timeline of the two-dimensional representation of an area, which gives us
a three-dimensional representation of the problem.) The differences between minimizing the
number of bins and maximizing the number of blocks will not complicate the formulation, since
we will assume (initially) that there exists at least one feasible solution for a fixed number of
block and of areas/bins.
The 3D-BPP is strongly NP-hard. (See Garey and Johnson (1979) for more information about
the complexity of combinatorial optimization problems. Indeed, it is a generalization of the
one-dimensional bin packing problem (1D-BPP), in which a set of n positive values w j has to be
partitioned into the minimum number of subsets so that the total value in each subset does not
exceed a given bin capacity W. 1D-BPP is the special case of 3D-BPP for h j = H and d j = D
for all j ∈ {1, ..., n} and it has been proven that the 1D-BPP is NP-Hard, Coffman et al. (1997).
For such difficult problems, one way to contain combinatorial explosion is to allow algorithms
to reach fairly good solutions, without guaranteeing that the best possible solution is reached.
Local search heuristics use this strategy.
Faroe et al. (2003) proposed a new heuristic for 3D-BPP. Their method is very flexible allowing
to adapt it to various additional constraints. Therefore it fits perfectly to our problem, as to
many other real-life problems.
3. Finding feasible solutions
3.1. General approach
The local search heuristic proposed to find a feasible schedule strictly enforces the individual
constraints only. Then, penalties linked to the collective constraints are summed up in an
objective function that is minimized. With no additional real-life collective constraints, the
objective function value of a given solution is the total pairwise overlap between the blocks.
Therefore, with a randomly generated unfeasible solution where blocks can overlap, searching
for a feasible solution is equivalent to minimizing the objective function, since an objective value
of zero indicates that also the collective constraints are met. For any solution X, let overlap ij (X)
be the overlap (in square meters days) between blocks i and j. The objective function can now
be formulated as
f(X) = ∑ overlap ij (X) (1)
i

of a block around one of its four corners.’ A neighbor of X is therefore constructed by assigning
a new value to one of the variables x j , y j , s j , a j , o j . This definition of a solution space includes
all feasible schedules and that there is a path of moves between every pair of solution.
A typical local search procedure proceeds by moving from the current solution X p to a neighboring
solution X p+1 ∈ ν(X p ) whenever this move improves the value of the objective function.
This may lead to two types of difficulties. First, the solution may settle in a local minimum.
Several standard methods, such as the Simulated Annealing, Aarts and Korst (1989) or the Tabu
Search, Glover (1990), exist to avoid this shortcoming of local search procedures. Secondly, the
neighborhood of any given solution may be quite large (even if continuous, variables like x j , y j
or s j can be discretized for practical purposes). Therefore, exploring the neighborhood to find
an improving move can be very costly in computing time. To deal with these issues, we present
in this paper an application of the Guided Local Search (GLS) heuristic, and its accompanying
neighborhood reduction scheme called Fast Local Search (FLS).
3.2. Guided local search
The Guided Local Search Heuristic (GLS) has its root in a Neural Network architecture named
GENET, Wang and Tsang (1991), which is applicable to a class of problems known as Constraint
Satisfaction Problems. The actual GLS version with its accompanying FLS has been first shown
by Voudouris (1997), Voudouris and Tsang (1997,1999), and applied to the 3D-BPP by Faroe
et al. (2003).
Basically, GLS augments the objective function of a problem to include a set of penalty terms
and considers this function, instead of the original one, for minimization by the local search
procedure. Local search is confined by the penalty terms and focuses attention on promising
regions of the search space, Voudouris and Tsang (1999). Iterative calls are made to a local
search procedure, denoted as LocalOpt(X). Each time LocalOpt(X) gets caught in a local
minimum, the penalties are modified and local search is called again to minimize the modified
objective function. In a certain measure, the heuristic may be classified as a tabu search heuristic;
it uses memory to control the search in a manner similar to Tabu Search.
GLS is based on the concept of ’features’, a set of attributes that characterizes a solution to the
problem in a natural way. In our adaptation of the model, features are the overlaps between
the blocks, and the indicator I ij (X) = {0, 1} denotes whether blocks i and j overlap or not. In
a particular solution, a feature with a high overlap is not attractive and may be penalized. As
a result, the value of overlap ij (X) can measure the impact of a feature on a solution X (’cost
function’ in Faroe et al. (2003)).
p ij denotes the number of times a feature has been penalized. p ij is initially zero. We want to
penalize the features with the maximum overlap, that have not been penalized too often in the
past. The source of information that determines which features will be penalized should thus
be the overlap and the amount of previous penalties assigned to the features. For this purpose,
we define a utility function µ(X) = overlap ij (X)/(1 + p ij ). After each LocalOpt(X) iteration,
the procedure adds one to the penalty of the pairs with maximum utility.
After incrementing the penalties of the selected features, they are incorporated in the search
with an augmented objective function
h(X) = f(X) + λ ∑ i,j
p ij · I ij (X) = ∑ overlap ij (X) + λ ∑
i

3.3. Fast local search
The ’fast local search’ (FLS) procedure, Voudouris and Tsang (1997), Faroe et al. (2003) is used
to transform a current solution X cur into a local minimum X ∗ = LocalOpt(X cur ). It allows to
reduce the size of the neighborhood with a selection of the moves that are likely to reduce the
maximum utility overlaps.
We define the sets ν m (X) as subsets of the neighborhood ν(X) where all solutions in ν m (X)
only differ from X by the value of the variable m (m = {x j , y j , t j , a j , o j } with j ∈ 1...n). (In the
case of m = {o 1 , ..., o n }, ν m also includes the particular change in x j and in y j that considers a
rotation around the four corners of a block. To simplify the explanation, this technical issue is not
detailed.) The neighborhood ν(X) is thus divided into a number of smaller sub-neighborhoods
that can be either ’active’ or ’inactive’. Initially, only some sub-neighborhoods are active.
FLS now continuously visits the active sub-neighborhoods in a random order. If there exists
a solution X m within the sub-neighborhood ν m (X cur ) such that f(X m ) < f(X cur ), then X cur
becomes X m ; otherwise we suppose that the selected sub-neighborhood will provide no more
significant improvements at this step, and thus it becomes inactive. When there is no active subneighborhoods
left, the FLS procedure is stopped and X cur , the best solution found, is returned
to GLS. From a less formal point of view, FLS selects at random a variable m within a list of
active variables, as long as this list is not empty. Then, it searches within the domain of m any
improvement of the objective function. If it does not exist the variable m becomes inactive and
is removed from the list. By doing so, we focus specially on variables open for improvement.
The size of the sub-neighborhoods related to the a j and the o j variables is relatively small:
A in the first case, 5 in the second (initial + four corners). Therefore FLS is set to test all
the neighbors of these sets. But, on the other hand, using an enumerative method for the
translations along the x, y and t axis would become very expensive in terms of computing time,
if areas and/or time windows are large. However, only certain coordinates of such neighborhoods
need to be investigated. If m represents x j , changes in the overlap function only depend on x j
(h(X) = h(x j )). Most of the terms of this function are constant, thus, since we want to compare
values, only the few terms dependent on x j should be computed. Furthermore, an overlap is
the product of four partial overlaps (three for the overlaps on each of the x, y and z axis, and
the fourth equals one if a i = a j ; zero otherwise). Since we know that only the partial overlaps
for the x axis depend on x j , computing efforts can be reduce to their smallest size. Also,
overlap ij (X) = overlap ji (X), so that the computing time of one solution is linear (n) instead
of quadratic (n 2 ). Additionally, all functions overlap ij (x j ) are piecewise linear functions, and
therefore the functions will attain their minimum in one of their breakpoints (or at the limits
of their domains). As a result, FLS only needs to compute the values of f(x j ) with x j at
breakpoints or at extreme values. In fact, there are at most four breakpoints for each function,
and only the first and the last one are evaluated. Indeed, in regard to the analogy with the
3D-BPP, a good packing intuitively supposes that the boxes touch each other.
FLS represents a relatively fast procedure that leads to a local minimum if the amount of active
sub-neighborhoods is relatively small. Remember that LocalOpt(X) is called iteratively by GLS,
and that penalties are changed with an objective of escaping local minima. Activation of subneighborhoods
should therefore allow moves on penalized features. The following reactivation
scheme is used, Faroe et al. (2003): (1) moves on the two blocks i and j, corresponding to the
penalized features, are reactivated. (2) We reactivate the moves on all blocks that overlap with
blocks i and j. The latter reactivation is added to allow FLS to pay attention not only to the
two overlapping blocks but also to the whole area around the penalized feature.
4. Selecting the blocks
In the previous chapter, we described a method that minimizes the collective constraints under
restriction of the individual constraints and we supposed that there exists at least one feasible
422

solution for the set of blocks initially given. Let us denote this procedure by GlobalOpt(X).
If GlobalOpt(X) is efficient, it should find a solution with an objective function of zero after
a certain time and this solution would be one of the feasible solutions. However, in the initial
formulation of the problem, we do not know whether a set of blocks is feasible or not. The
combination of GLS and FLS can be used anyway if we rely on the following heuristic assumption:
there exists no feasible solution if none is found within a certain amount of computing time T .
Consequently, the search heuristic GlobalOpt(X, T ) is utilized as a test of feasibility and gives
the correspondant schedules if a feasible solution is identified within T .
Several methods have been tested using this concept. The objective was to remain as close as
possible to the working methods and habits used in the factory under study. From this point
of view, an efficient approach for the industrial application is to start GLS with a randomly
generated solution X 0 that includes the entire set of blocks (p j = 1 for all j = {1, ..., n}). After
a search of T seconds, the algorithm is stopped and returns X 1 = GlobalOpt(X 0 , T ), the best
solution found (in terms of overlap). One of the blocks with the highest overlap is removed from
the set (X 1 → X 1 ′ ) and the heuristic GlobalOpt(X 1 ′ , T ) is restarted. The entire procedure ends
if a solution X n with zero overlap is found.
A variant procedure is to start with an empty set X 0 (p j = 0 for all j = {1, ..., n}). At
each iteration, if the solution X n+1 = GlobalOpt(X n , T ) is feasible, then an additional block
is inserted in the set; otherwise an overlapping block is removed. This procedure is stopped
after a certain computing time, or by any more sophisticated stopping criterion, and returns
the solution with the largest collection of blocks. Fig.1 shows the iterative processus of this
procedure.
Fig.1: Test instance (T = 1 s, Time limit = 600 s)
Both approaches suffers from one major default: they are likely to have aversion for the largest
blocks. Indeed, we do not have an appropriate weighting scheme to evaluate the preferences
between blocks, and, since small blocks generally provide smaller overlaps, they are preferred
to larger ones. In the real-life situation, when the entire set of block cannot be produced, the
person in charge of scheduling can either subcontract specific blocks in other factories, or change
some temporal parameters (e.g. intensify the workforce to reduce processing times or postpone
due dates). No formal information can describe all the aspects of these choices. For this reason,
the operator should be able to change manually the collection of blocks to be produced. Starting
from our ”fairly good“ feasible solution X n , iterative X n+1 = GlobalOpt(X ′ n) calls are ordered
423

manually after deliberate changes (X n → X n ′ ) in the assignment. In addition, a last procedure
provides a list with each block that is not assigned even though a feasible solution that includes
the block can be found.
By not regenerating solutions on a random basis, some of the information from previous solutions
is preserved. A drawback to this approach is that the structure of a previous solution can
confine GLS to an area of the solution space that can be difficult to escape. (Faroe et al. (2003)
suggest a similar problem in their approach for 3D-BPP.) We may therefore not reach the very
best solution. However, the modus operandi described in this section is developed for a daily
industrial use. In that setting, the above drawback may actually be viewed as an advantage.
Indeed, it may be very costly for the company to mix up the schedules over and over again.
Traditionally, methods for problems of similar classes utilize a construction algorithm during
the search. A slight improvement may disturb the whole solution; with GLS, non-problematic
regions are not perturbed. Murata et al. (1996) developed a tricky construction technique based
on partial-orders coding scheme for the 2D-BPP. Imahori et al. (2005) adapted this approach
for a problem very close to our’s.
5. Additional real-life issues
Additional constraints may occur in any firm-specific situation. The tool proposed here is easily
customizable to most of them. For example, we may need to restrict or force the position of a
block (e.g. a tool is only available in one area or the block is already in process). Intgrating those
constraints is trivial: restricted positions are not generated and unfeasible neighbors simply do
not exist. As a result, the end-user may fix the value of any variable (including p j ) or reduce its
domain.
Specific collective constraints may also appear in the wording of a problem. In our case, the
areas of the factory have one single door, and the crane bridge can only carry blocks up to a
certain height. As a result, a large block may obstruct a door, and some blocks might not be
deliverable in time because there is no route to transport them out. We dealt with this issue in
the same way as for overlaps. For each generated solution X, we add to the objective function
h(X) a new term accounting for exit difficulties:
g(X) = h(X) + ExitP roblems(X) = ∑ overlap ij (X) + λ · ∑
p ij · I ij (X) + ExitP roblems(X)
i

References
AARTS, E.; KORST, J. (1989), Simulated Annealing and Boltzmann Machines – A stochastic
approach to combinatorial optimisation and neural computing, Wiley
COFFMAN, E.G.; GAREY, M.R.; JOHNSON, D.S. (1997), Approximation algorithms for bin
packing: A survey, D.S. Hochbaum (Ed.), Approximation Algorithms for NP-Hard Problems,
PWS Publ. Company
FAROE, O.; PISINGER, D.; ZACHARIASEN, M. (2003), Guided Local Search for the threedimensional
bin-packing problem, INFORMS J. Computing 15/3, pp.267-283
GAREY, M.R.; JOHNSON, D.S. (1979), Computers and Intractability: A Guide to the Theory
of NP-Completeness, W.H. Freeman
GLOVER, F. (1990), Tabu Search: A Tutorial, Interfaces 20/44, pp.74-94
IMAHORI, S.; YAGIURA, M.; IBARAKI, T. (2005), Improved local search algorithms for the
rectangle packing problem with general spatial costs, European J. Operational Research 167,
pp.48-67
MARTELLO, S.; PISINGER, D.; VIGO, D. (2000), The three dimensional bin packing problem,
INFORMS Operations Research 48/2, pp.256-267
MURATA, H.; FUJIYOSHI, K.; NAKATAKE, S.; KAJITANI, Y. (1996), VLSI module placement
based on rectangle-packing by the sequence-pair, IEEE Trans. Computer-Aided Design of
Integrated Circuits and Systems 15/12, pp.1518-1524
SCHOLL, A.; KLEIN, R.; JÜRGENS, C. (1997), BISON: A fast hybrid procedure for exactly
solving the one-dimensional bin packing problem, Computers & Operations Research 24, pp.627-
645
VOUDOURIS, C. (1997), Guided local search for combinatorial optimization problems, Ph.D.
Thesis, Dept. Computer Science, Univ. of Essex, Colchester/UK
VOUDOURIS, C.; TSANG, E. (1997), Fast local search and guided local search and their application
to British Telecom’s workforce scheduling problem, Operations Research Letters 20,
pp.119-127
VOUDOURIS, C.; TSANG, E. (1999), Guided local search and its application to the traveling
salesman problem, European J. Operational Research 113, pp.469-499
WANG, C.J.; TSANG, E. (1991), Solving constraint satisfaction problems using neural-networks,
IEE 2 nd Int. Conf. Artificial Neural Network, pp.295-299
425

!
"
!"#
!
"!# "" $
"! %
& !
& ' !
!!! !
!
!(!! )! ! !!
$ !*!
" !
+& !
&
# & #,-./0
. ,1./00 !2 3/ 4+,#
&
# & / 2 5 6 7 8
2 #$%&&'(
!
!
&
9 &
& :&

$"
&<
/! :
& &! )$*++,(-
" = >
"=& >
"= !
7 ! )$*++,(-?2$
&'
@
%"
! &
# $ ! !
9 &
! & &=
" >
" !>
" >
"
"
< &
'& & !
& = & &
&"'
!#$%&&'(!9
#
!9=

6 &
/
2
7<
7<
6 &
/
<
9
4 &
8' C
:
7<
7<
7<
7<
7<
7<
7<
&=%" 7"
,= (&)>
E , E= @ @ $ (
& $ '=
@ ! $ @)> F
@>
, = @!! @ !
>F @>
1 , 1= @ @
()! (3:G3: )>
F@>
,= @!!@ "!
"!(H3:GH 3: )&
@62: @62:
)"'
# * !
2 !
I
! !
! !
# &#$%&&.%&&/%&&'(-
.
&
&
! J. 2
! & 9
'
E
&!
6 2 : (62:) # 62:
&= *
$ & = *
/! ! &
! &
! &
D

*"
# * !
# $%&&'( 2 !
I
! !
< & ! =
(62:) !01 $*++2%&&%( 6 2 : # =
*
: & ! & &
&!
' & !"#$%&&'(-
" "& ! ! >
" "!! !!"! " !
!
6 & =
" ! !&
" & !
& =!" "& "
& ! & !
& "
! * &
! # =
" >
" >
" >
" &
& #$%&&'(-
" $ >
" >
" !#>
" >
" = * *
( !)>
" (!! !!* )>
" >
" ( )>
" "! >
" >
" >
" >
"
6.
-

2
3: /
27!#
/+ /
< % 3$
% /L/
2L8 %
% :
33
% <
,
3/
3!
% 2
8
M
5*9 L
5*:
2 9
5
% :
3:
6.=A
#$%&&.%&&/%&&'(
B
8 !
& 6
! & $ ! ! &
:A:3 (: A& : 3 ! !) 6", $
! ' !01 $*++2%&&%(
$ &
$ 9

!!"! : !
$ !" "& ! 3
$%&&&( 9 "& !
&
"! * $
& & !
$ ! & !
!
3 $%&&&( # $%&&'( ! !
& *
*
*
$ !$ !
!"
# &#$%&&'(-
" @ @ >
" ? @ & >
" >
" >
" !
! !! ! ! *
9

" @!!77 "&@>
" @!!/* // @& 9

. * >
! >
E & =
" >
"
1"./
: !!
& ?: 2 ! 9' :@
& =
:≥3 (.)
&= :" ! ' :O >
G!! >
"!! >
3"$ ! '
+ !9

! ' $ ! '
6 &$ ! :
5:3%83 8
& & ? @ ! !
& !01
$%&&%%&&/(5 $*++'(5 $*++'(64$%&&*(#$%&&'(-
" (.)>
" ()>
" (E)>
" ()
% ! '!99 &
> &> ! > & >
> !! !
!!& =
O . Q Q E Q (E)
& "!! >
. E " !!&
!99=: ''
2. 2 2E 2
& R R R R
& R R R R
! R R
/& R R R
R R
"&! R R
!2"./ 3 4/56
6 & ! 6 &
!
!
: 2 ! 9':
9' :
! ! !
!!"./
&
& !
& 5 $*++7(-
∆: # O( )( ) ()
∆: # & !
∆: # !$ ' !
61&∆: #
?+.@ 6
E

% @+.@=
wskaznik A
1
0,8
0,6
0,4
0,2
0
1 2 3 4 5
iteracje
w ersja B1
% @+@=
wskaznik A
1
0,8
0,6
0,4
0,2
0
1 2 3 4 5
iteracje
% @+E@=
w ersja B2
wskaznik A
1
0,8
0,6
0,4
0,2
0
1 2 3 4 5
iteracje
w ersja B3
6=9 "
Local safety indices
Local safety indices
1st iteration
2nd iteration
deltaA values
1
0,5
0
0,8363 0,914
0,4953
0,3522 0,4311
0,608
0,3521
1 2 3 4 5 6 7
deltaA values
1
0,5
0
0,8363
0,49530,3539
0,62390,5478 0,627 0,9286
1 2 3 4 5 6 7
1st iteration 0,8363 0,4953 0,3522 0,4311 0,3521 0,608 0,914
compartments
2nd iteration 0,836 0,495 0,354 0,624 0,548 0,627 0,929
compartments
Local safety indices
Local safety indices
3rd iteration
4th iteration
deltaA values
1
0,5
0
0,89790,8137 0,6104
0,74570,67240,6453 0,9286
1 2 3 4 5 6 7
deltaA values
1
0,5
0
0,89790,9096 0,6228 0,74150,67260,6453 0,9286
1 2 3 4 5 6 7
3rd iteration 0,898 0,814 0,61 0,746 0,672 0,645 0,929
4th iteration 0,898 0,91 0,623 0,742 0,673 0,645 0,929
compartments
compartments
61=7 ∆: # @:@ 6
E1

: ! !!
& 9 &
$
!$"./
!&
(52/) $ && !!"!
! 7 !& &
"!
2 !
& : ' ! !! *
! !
! !&
!!* ! !! &=
/9 O.G 29 (1)
/% O.G 2% ()
&= /9 29 "!!* ! ! >
/% 2% "!!* !!
!!!! ! !
$*++2(#$%&&.%&&/(-
29 O(((5: 9 SO . 3:
3:
: (')"!! :
! ( ) !
! ! +&
E

!! &&&
!!!
: " G ' '
U' !
RU ' '
&=
K 3J O(R . R V R ) (..)
W KOXY O. Y #O. (ZZR )(ZZR # )(R R # )[ (.)
&= K 3J G K>
W K G K
! ! '=
39OK 3J W K (.E)
&39( )K
9K ! !!* / &=
/ O.G\(39) (.)
&\ !
' !!& K
! 6 " ! !
!! '
: ' ! ! &
]O.1000 -0Q^6 !
&
!999=!!: . :
3 ! < X [ / %!
: . D0D0 0. ,
: .-;.0 0. ,
!9J=* !! !
<
3
% ! *
6" " 39O.E0.;0; / O00-10
: " 39O.E0.;0; / O00-10
( )
!%"
% 8
! # &!
# & &= !
E;

(! ) ' (& & )
' 5:3%83
!8 & 27A:2/99".:+ +".
& & ! !01$%&&%(
& ! !9
" & >
" 9
!&"
:
9!
" "! "
!! "!
!!
2/ 6 2:
& *
!
& && !
9 ! 9 <
7 (9

7
::4>:MM++:3/: 3KM+7B 249 (00.)
8 # .
2 2?22@
8394 < (00E)
D 9/ 2!2 7 J2:+U00E<
8394 < (00E!)
<

Optimisation of Vessel Resistance using Genetic Algorithms
and Artificial Neural Networks
Andrew Mason, Patrick Couser, Formation Design Systems, Fremantle/Australia,
AndyM@formsys.com
Garth Mason, Cameron R. Smith, Brian R. von Konsky, Curtin University of Technology
Abstract
It has been found that an artificial neural network is able to produce results of sufficient accuracy to
be useful for preliminary prediction of vessel resistance, with the major benefits of: being relatively
simple to set up; being easily retrained with new data; and that Froude number may be easily
included as an independent variable. In this work the Neural Network is fitted directly to the original
tank test data, rather than to a set of smoothed curves varying in the Froude number axis. In addition,
different network architectures have been investigated, with networks containing two hidden layers
being seen to perform well. A procedure for the optimisation of design parameters using a Genetic
Algorithm has also been evaluated. The Genetic Algorithm uses the approximation provided by the
Neural Network response surfaces for its objective function. This has been found to be effective and of
acceptable performance.
Nomenclature
B
C F
C R
C T
C W
F n
g
L
L/∇ 1/3
R e
S
T
υ
WSA
∇
ν
ρ
Demi-hull maximum beam of waterline
Coefficient of frictional resistance [ITTC-57 Correlation line]
Coefficient of residuary resistance
Coefficient of total resistance
Coefficient of wave resistance
Froude number [υ/ √(gL)]
Acceleration due to gravity
Vessel length between perpendiculars
Slenderness ratio
Reynolds number [υL/ν]
Catamaran demihull centerline separation
Demi-hull draft
Vessel velocity
Wetted surface area
Demi-hull volume of displacement
Fluid kinematic viscosity
Fluid density
1. Introduction
Artificial Neural Networks (ANNs) have been used for classification and prediction across many
disciplines including medicine, engineering, and computer science, primarily because of their ability
to model non-linear functions quickly and accurately.
In the field of naval architecture, interpolation and prediction of hull resistance from model
experiments and tank testing have traditionally been made using statistical regression equations.
However, this is a problem that is also well suited to neural networks. Specifically a neural network
may be a more favourable option than statistical methods since they have been shown to provide
greater flexibility and can more quickly create accurate models of complex systems, Jain et al.
(1996).
440

This paper describes an investigation into the accuracy of ANNs as prediction tools for hull resistance
and follows on from the work presented in Couser et al. (2004). The goal of the original investigation
was to determine a predictive model for residuary resistance (C R ), based on input values of Froude
number (F n ), Separation-Length ratio (S/L), Breadth-Draught ratio (B/T) and Slenderness ratio
(L/∇ 1/3 ). The data used for the investigation originated from a series of tank tests described in
Molland et al. (1994,1995), Insel and Molland (1992).
In the previous work, the authors had the choice of using the raw tank test data, or using a larger
dataset derived from a least squares fit to the F n axis of the raw data. At that time it was felt that the
larger dataset would give superior results, however in retrospect it was felt that the additional fitting
step may have introduced errors. As a result it was decided to attempt fitting of the original
experimental data directly, despite the data being highly non-linear in the F n axis, there being a
relatively small number of points and the presence of significant noise in the data.
The non-linearities in the solution surface fitted to the resistance data by the neural network raise an
additional problem when it comes to using the output of the trained ANN within an optimisation
procedure. Because the five-dimensional solution surface is multimodal, it is not feasible to use a
gradient-based optimisation method to reliably find the optimum set of parameters.
To address this problem the authors have implemented a simple Genetic Algorithm (GA) based
optimisation framework to investigate the application of GAs to catamaran design optimisation. The
framework was designed to be as flexible as possible in order to experiment with the GA parameters
to determine the best combination of these settings.
2. Neural Networks
According to Sarle (1994)
Neural Networks are general purpose, flexible, non-linear models that, given enough hidden
neurons and enough data, can approximate virtually any function to any desired degree of
accuracy. In other words, Neural Networks are universal approximators. Neural Networks can be
used when there is little knowledge about the form of the relationship between the independent
and dependent variables.
Most ANNs have some sort of training rule whereby the weights of connections are adjusted on the
basis of training data. In other words, ANNs learn by example and exhibit some capability for
generalization beyond the training data. There are many different types and topologies of ANNs. The
form that has found widest application is the feed-forward multi-layer perceptron or MLP.
Fig.1: MLP topology
441

MLPs have an input layer with a series of inputs, one or more hidden layers and an output layer. The
number of input elements is equal to the number of variables in the input dataset and the number of
outputs equal to the number of result values required. The number of hidden layers and the number of
elements in them can vary, and there are several techniques used to determine the optimum structure.
There is considerable overlap between the fields of ANNs and statistics. In ANN terminology,
statistical inference means learning to generalize from noisy data. Most ANNs that can learn to
generalize effectively from noisy data are analogous to statistical methods. For example:
• MLPs are a subset of the class of non-linear regression models.
• MLPs with no hidden layer are basically generalized linear models.
• MLPs with one hidden layer are closely related to projection pursuit regression.
• MLPs with multiple inputs, multiple outputs and one or more hidden layers are analogous to
multivariate, multiple non-linear regression.
Despite the similarities between ANNs and statistical methods, ANNs have some specific advantages-
• Power. ANNs are capable of modelling extremely complex functions. In particular, ANNs are
non-linear. For many years linear modelling has been the commonly used technique in most
modelling domains, since linear models had well-known optimisation strategies. Where the
linear approximation was not valid (which was frequently the case) the models suffered
accordingly. ANNs also keep in check the “curse of dimensionality” problem, which bedevils
attempts to model non-linear functions with large numbers of variables.
• Ease of use. ANNs learn by example. The ANN user gathers representative data, and then
invokes training algorithms which enable the ANN to learn the structure of the data. Although
the user requires some knowledge of how to select and prepare the data, the level of user
knowledge needed to successfully apply ANNs is much lower than that required for more
traditional statistical methods.
2.3. Training and Testing Overview
The ANNs discussed in this paper were developed and tested using software called NeuroIntelligence,
Alyuda (2005). NeuroIntelligence is a commercial ANN program, which specialises in the training of
multi-layer perceptrons. NeuroIntelligence contains a variety of training algorithms, including back
propagation, conjugate gradient descent, quasi-Newton and Levenberg-Marquardt methods.
2.4. Training and Testing Data
The data set used to train and test the ANN is a series of geometrically similar catamaran models
based on the hull shape shown together with the parameters described in Table I.
Model B/T L/∇ 1/3 Demihull
WSA m 3
3b 2.0 6.27 0.434
4a 1.5 7.40 0.348
4b 2.0 7.41 0.338
4c 2.5 7.39 0.34
5a 1.5 8.51 0.282
5b 2.0 8.50 0.276
5c 2.5 8.49 0.277
6a 1.5 9.50 0.24
6b 2.0 9.50 0.233
6c 2.5 9.50 0.234
Table I
442

Both C T and C W data from a series of tank test experiments on scale models were available from
Molland (1994), in four catamaran configurations (S/L=0.2, 0.3, 0.4 and 0.5) for each model. In this
work the ANN was fitted directly to the C T data, rather than deriving C W for each model. Over the
past decade there has been considerable discussion over the breakdown of C T into its F n and R e
dependent components for these types of catamaran vessels. The decision to fit the model C T data was
made as it allows the reader to select their own scaling method.
It is essential when training an ANN that an unbiased estimate of the generalisation error be available.
In order to achieve this, it is necessary to partition the data into mutually exclusive training and
validation sets. Data from the validation set are held out from the training process and are used to
estimate the error between the fitted neural network and the original function. The network
architecture and early stopping of the training process can be determined using the validation set
error. However this can contain some bias toward the chosen network architecture and as such a
separate, independent test set should also be kept aside for a truly unbiased estimate of the network
error.
The resistance data available for neural network training was randomly partitioned into mutually
exclusive training (85%), validation (13%) and test (2%) sets. Because of the small number of data
points in the dataset it was not possible to allocate a large number of points to the validation and test
sets, and these were set to reasonable minimum values based on recommendations from Guyon (1997)
2.5. ANN Architecture
The initial test network architectures were constrained to three layers, one for input, hidden and output
layers respectively. This architecture was chosen as previous research indicated that multiple hidden
layers are rarely effective in terms of both accuracy and training speed, Neocleous and Schizas (1995).
A search was performed using the architecture search function in NeuroIntelligence. This allowed
multiple networks to be trained with different numbers of hidden layer neurons and the results
collated to display the optimum network. Training runs used the Quasi-Newton method for 50,000
iterations, and 10 retrains were performed for each network topology to minimise error. The range of
architectures searched was from 4-4-1 (i.e. 4 inputs, 4 hidden layer neurons and 1 output), to 4-17-1
(i.e. 4 inputs, 17 hidden layer neurons and 1 output).
Fig.2 displays the results of the search process with both the Average Absolute Error (AAE) and the
standard deviation of the results reducing as the number of hidden layer neurons increased.
Improvement in error values tended to level off at about 10 hidden layer neurons, with improvements
from that point onward being small.
Average Absolute Error
0.33
0.31
0.29
0.27
0.25
0.23
0.21
Validation error
Mean Validation Error
0.19
0.17
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Hidden Layer Neurons
Fig.2: Validation set error for 10 retrains of each network architecture
443

It is important that both training and test set error be in broad agreement with the validation set error,
and it can be seen from Fig.3 that the three sets of values correlate well as the number of hidden layer
neurons increases.
Min. Average Absolute Error
0.28
0.26
0.24
0.22
0.2
0.18
0.16
0.14
0.12
Training Set
Validation Set
Test Set
0.1
4 5 6 7 8 9 10 11 12 13 14 15 16 17
Hidden Layer Neurons
Fig.3: Minimum error values
Neural networks trained with large numbers of hidden layer neurons tend to suffer from overfitting.
This overfitting cannot always be determined from the minimum validation set error if the dataset is
small. One way of minimising the risk of overfitting is to select the network architecture based on a
criterion that balances minimum error against network complexity. One such measure is Akaike’s
Information Criterion, Akaike (1974), which has been widely used for model selection for both
conventional statistical models and neural networks.
-7050
-7100
-7150
-7200
AIC
-7250
-7300
-7350
-7400
-7450
-7500
4 5 6 7 8 9 10 11 12 13 14 15 16 17
Hidden Layer Neurons
Fig.4: Akaike’s Information Criterion
A graph of Akaike’s criterion for the trained networks, Fig.4, shows a minimum value at 14 hidden
layer neurons and it can be concluded that this network architecture is a reasonable compromise
between error values and network complexity. An additional consideration is that the standard
deviation of the Average Absolute Error values for the validation set is at a minimum at 14 hidden
layer neurons, which gives some confidence that these results will be repeatable in subsequent
training.
444

Couser et al. (2004) found that a hidden layer containing approximately 15 neurons was optimal for
this dataset, and it is encouraging that despite the different treatment of the data, the new analysis is in
broad agreement with this conclusion. In this work architectures containing two hidden layers were
investigated but were not found to be advantageous, except for an indication that architectures with
two hidden layers may be effective if the number of neurons in the first hidden layer was small.
As a result, an investigation was performed to determine whether network architectures with the same
or less total number of degrees of freedom could be found that would outperform the single layer
architecture. It was felt that if these degrees of freedom could be redistributed into two hidden layers
the ability of the ANN to model a highly non-linear dataset might improve.
As the total number of two layer architectures was high it was not feasible to search all possible
configurations. Instead architectures were investigated that had either the same total number of hidden
layer nodes as the previously determined optimum (i.e. 14), one less total hidden layer nodes than the
optimum (i.e. 13), two less total hidden layer nodes than the optimum (i.e. 12) or three less total
hidden layer nodes than the optimum (i.e. 11). For each of these total numbers of hidden layer
neurons different architectures were evaluated containing between 1 and 8 neurons in the second
hidden layer.
0.2
Min. Average Absolute Error
0.195
0.19
0.185
0.18
0.175
Total 11 HL neurons
Total 12 HL neurons
Total 13 HL neurons
Total 14 HL neurons
0.17
0.165
0 1 2 3 4 5 6 7 8
Neurons in 2nd Hidden Layer
Fig.5: Minimum error values for two hidden layers
Fig.5 clearly shows a trend towards lower validation set errors when more than one neuron is placed
on a second hidden layer. The networks containing a total of 11 and 12 hidden layer neurons have
minima at 4 and 5 second layer neurons respectively, while the networks with a total of 13 and 14
hidden layer neurons continued to improve up to the point where there were 8 neurons in the second
hidden layer, the maximum tested.
On the basis of this testing, the network selected used a 4-7-5-1 architecture. This network had
training and validation set errors only slightly higher than the 4-14-1 architecture, but scored
significantly better on Akaike’s criterion due to it having two fewer nodes in the hidden layers.
Appendix 1 displays sample C T curves derived from this ANN architecture for models 4b, 6a and 6b.
These models have been selected for illustration as they have proven to be the configurations most
difficult to fit in previous work, due to the combination of significant noise and nonlinearities in the
F n axis.
445

3. Optimisation using Genetic Algorithms
An ANN derived from the catamaran resistance data permits C T to be estimated when a set of specific
input parameters is defined. However it is often desirable to fix the value of one or more parameters
and then determine the optimum values of the remaining parameters.
To achieve this, a search or optimisation method is required. This process is complicated in the case
of catamaran resistance due to the interaction of wave patterns between the two demi-hulls, which
may cause significant non-linearities in the vessel’s resistance and an associated likelihood of a multimodal
solution space, Molland et al. (1994). In this case it is necessary to use a method capable of
global optimisation to find the minimum resistance.
One such method is the Genetic Algorithm (GA). GAs are a search and optimisation method based on
the process of biological evolution. GAs differ from traditional optimisation techniques in that they
involve a search from a population of solutions, not from a single point.
Each iteration of a GA involves a competitive selection that penalises poor solutions. The solutions
with high fitness are recombined with others to produce members of the next generation, which
inherit properties from their parents. Solutions are also mutated by making small, random changes to
one or more free parameters. Recombination and mutation are used to generate new solutions, which
are biased towards regions of the space for which good solutions have already been seen.
The steps involved in a genetic algorithm are as follows:
Initialise the population
Evaluate initial population
REPEAT
Perform competitive selection
Apply genetic operators to generate new solutions
Evaluate solutions in the population
UNTIL some convergence criteria is satisfied
One of the strengths of GAs is that they perform well on noisy solution spaces where there may be
multiple local optima. GAs tend not to get stuck on a local minima and can often find the global
optimum.
GAs have been used by several researchers to optimise catamaran designs, Doctors and Day (2000),
Tuck and Lazauskas (1996), Hearn and Wright (1998). However these have calculated resistance
directly using first principles analysis. One weakness of GAs is that they are slow due to the high
number of evaluations of the objective function required. This means that the performance penalty
implicit in first principle analysis of resistance is a significant impediment to effective optimisation
using GAs.
The use of an ANN based objective function allows the fitness to be evaluated in a small fraction of
the time taken to perform first principles analysis and permits the GA optimisation to complete in a
reasonably small amount of time. It also allows a researcher to use existing experimental data that
may have been derived from tank testing which cannot be reproduced easily.
4. GA parameter settings
4.1. Exploration versus exploitation
A GA based search can be viewed as a trade off between the maintenance of sufficient diversity in the
population to permit the coverage of the entire solution space (exploration), and the need to converge
on the optimum solution within an acceptable time (exploitation), Eiben and Schippers (1998).
446

There are several variables or algorithms that can be applied to manipulate the degree of exploration
or exploitation that the GA exhibits, Goldberg (1989). These include:
• Selection method
• Elitism
• Population niching - fitness sharing
4.2. Selection
Much research has been done into different selection methods with two of the most widely used
methods being roulette wheel selection and tournament selection. Roulette wheel selection works by
choosing two individuals from the population and comparing their fitness scores. The individual with
the highest fitness score is selected to be a parent for an individual in the subsequent generations.
Roulette wheel selection assigns a likelihood of representation in the following generation
proportional to the magnitude of an individual’s fitness score. The difficulty inherent in the use of
roulette wheel selection is that the likelihood of representation in the following generation is
dependent on the scaling factor used to scale the results of the objective function to create fitness
scores. Changing this scaling factor can dramatically change the results of the selection process, and it
is difficult to determine the correct scaling factor ahead of time.
On the other hand, tournament selection is a simple comparison of fitness values and is independent
of their scaling. As a result, tournament selection is both easier to implement and more robust in use
than roulette wheel selection.
4.3. Elitism
Elitism ensures that the next generation’s best individual will be at least as good as any from the
previous generation by automatically including the best individual from the previous population,
Andris and Frollo (2002).
4.4 Fitness sharing
Fitness sharing works by scaling the fitness of individuals based on how similar they are to all other
individuals in the population. Individuals that are very similar to others in the population are given a
slight penalty, while individuals that show novel features are rewarded by increasing their fitness
relative to the population. This is intended to ensure that the population maintains sufficient diversity
to avoid premature convergence on false optima, Goldberg (1987).
5. GA based optimiser prototype
A prototype GA based optimisation framework, HullGA, has been developed by the authors in order
to evaluate the feasibility of using an ANN model for the objective function of an optimisation
process. The GA code used for the prototype developed by the authors was developed and tested in
MATLAB 5.3 (The MathWorks 2003). The objective function used is the predicted total resistance
coefficient (C T ) for the catamaran configuration at a selected F n .
A design was adopted that allowed some experimentation with different parameters which may affect
the evolution process. Parameters which can be adjusted via the user interface are –
• Population size
• Limit on number of generations evaluated
• Selection method – roulette wheel or tournament selection
• Mutation rate
• Elitism - on or off
• Fitness sharing - on or off
447

The prototype also codifies specific exploration and exploitation phases, each of which used their own
settings for the above parameters.
A preliminary evaluation of the effects of the interplay of the different evolution parameters has been
conducted, but no comprehensive study has been done due to the large amount of time required.
Initial conclusions are as follows –
5.1. Population size
The goal of testing population size is to ensure that the population is large enough to maintain
sufficient diversity to avoid premature convergence.
Tests were run for population sizes ranging between 10 and 150. Negligible differences in rate of
convergence or the fitness level of the best solution were observed for populations greater than 20
individuals. From these results, it appears that there is no advantage to be gained from a population
size greater than 20 for this particular dataset.
5.2. Selection method
Much research has been done into different selection methods and there is support in the literature for
both roulette wheel selection and tournament selection.
In the case of the HullGA prototype it was found that tournament selection gave the best results,
primarily due to the difficulty of choosing suitable fitness scaling parameters to avoid premature
convergence when using roulette wheel selection.
5.3. Elitism
The use of elitism during the exploration phase may lead to premature convergence in a multi-modal
solution space. Initial experimentation with the HullGA optimiser indicated that it may be best to use
elitism only during the exploitation phase of the optimisation process.
5.4. Fitness sharing
Fitness sharing has been shown to be effective in maintaining population diversity during the
exploration phase, which helps to prevent premature convergence on local rather than global optima.
During the exploitation phase, however, this diversity may inhibit convergence to an optimum
solution and thus fitness sharing may not be useful during this phase.
Although roulette wheel selection appears to benefit from fitness sharing, previous research has found
that fitness sharing can display chaotic interactions with tournament selection, with unexpected
results, Oei et al. (1991). This interaction between evolution parameters is an area for future
investigation.
6. Example catamaran optimisation
Based on the test results, a GA with tournament selection and fitness sharing in the exploration phase,
and tournament selection and elitism in the exploitation phase, was used to optimise catamaran hull
forms for minimum resistance The exploration and exploitation phase were evenly divided over the
total number of generations.
Fig.6 demonstrates an example at Fn 0.3. In this case resistance was optimised based on range
constraints for S/L Ratio (0.15 to 0.5), B/T ratio (1.5 to 2.5), and L/∇ 1/3 ratio (6.27 to 9.51) as
described in Molland et al. (1994).
448

Fig.6: The HullGA user interface
Due to the multi-dimensional solution space, in this case four free parameters, it is not feasible to
visualise the complete surface. The 3D surface plot in Fig.6 captures C T values (vertical axis) against
B/T ratio and L/∇ 1/3 ratio, at a fixed S/L ratio, equal to the average S/L ratio of the population.
The graph in the lower left corner of Fig.6 illustrates the best, worst and average fitness values over
the generations evaluated. The highest fitness values in the population are indicated by the dashed
line (upper), the average fitness values by the solid line (middle), and the lowest fitness values by the
dash-dot line (lower).
The initial oscillations in the fitness graph illustrate the exploration of the solution space using fitness
sharing. As the three fitness plots meet it can be seen that the GA is converging to an optimal part of
the solution space.
7. Future work
The work described here has used a GA to find the optimal solution in a problem space with four free
parameters. More useful results could be achieved if additional catamaran hull parameters were
included for optimisation, such as longitudinal centre of buoyancy position (LCB), prismatic or block
coefficients (C P or C B ), or midship area coefficient (C M )
Another natural extension to the work described here is to extend the GA to perform multi-objective
optimisation. Example objectives might be the simultaneous optimisation of both catamaran
resistance and seakeeping qualities.
449

8. Conclusions
The work detailed in this paper has demonstrated that a sparse dataset with a relatively high degree of
noise can be fitted effectively with a feed-forward neural network. In addition we have demonstrated
that there may be benefits resulting from the investigation of networks with two hidden layers rather
than one. In particular it may be possible to find network architectures that have fewer degrees of
freedom combined with lower error levels.
The work detailed in this paper has also demonstrated that a combination of GAs and ANNs can be
successfully used as an optimisation tool for catamaran design parameters. In this problem domain it
appears that using tournament selection alone during the exploration phase, and tournament selection
with elitism in the exploitation phase gives the best results.
This research has also shown that the success of a GA is closely related to the selection methods and
other parameters used. However, a particular combination of parameters may not produce a
successful optimiser in a different problem domain. In particular, if the solution space becomes more
multi-modal in nature, the importance of selecting the correct GA parameters increases.
References
AKAIKE, H. (1974), A New Look At The Statistical Model Identification. IEEE Trans. Auto. Control.,
19, 723
ALYUDA (2005), Neurointelligence Manual, http://www.alyuda.com
ANDRIS, P.; FROLLO, I. (2002), Optimisation of NMR Coils by Genetic Algorithm, Measurement
Science Review 2/2
COUSER, P.R.; MASON, A.P.; MASON, G.; SMITH, C.R.; VON KONSKY, B.R. (2004), Artificial
Neural Networks for Hull Resistance Prediction, 3 rd COMPIT, Siguenza
DARPA (1998), Neural Network Study, AFCEA International Press
DOCTORS, L.J.; DAY, A.H. (2000), The Survival of the Fittest – Evolutionary Tools for
Hydrodynamic Design of Ship Hull Form, Royal Inst. Naval Arch.
EIBEN, A.E.; SCHIPPERS, C.A. (1998), On evolutionary exploration and exploitation, Fundamenta
Informaticae 35
GOLDBERG, D.E. (1989), Genetic Algorithms in Search, Optimisation and Machine Learning,
Addison-Wesley Inc.
GOLDBERG, D.E.; RICHARDSON, J. (1987), Genetic algorithms with sharing for multimodal
function optimization, 2 nd Int. Conf. Genetic Algorithm
GUYON, I. (1997), A scaling law for the validation_set training_set size ratio, Bell Laboratories
HEARN, G.E.; WRIGHT, P.N.H. (1998), Michell wave resistance characteristics resulting from the
optimisation of a catamaran hullform via genetic algorithms, EMAC’98
INSEL, M.; MOLLAND, A. (1992), An investigation into the resistance components of high speed
displacement catamarans, Trans. RINA 134(A)
450

JAIN, A.K.; MAO, J.C.; MOHIUDDIN, K.M. (1996), Artificial neural networks: A tutorial,
Computer 29(3), pp.31-44
KOUSHAN, K. (2003), Artificial neural networks for prediction of ship resistance and wetted surface
area, Marintek
MATLAB version 5.3: The MathWorks [Online] http://www.themathworks.com.
MOLLAND, A.F.; WELLICOME, J.F.; COUSER, P.R. (1994), Resistance experiments on a
systematic series of high speed displacement catamaran forms: variation of length-displacement ratio
and breadth-draught ratio, Ship Science Report 71, Dept. Ship Science, Univ. of Southampton
NEOCLEOUS, C.; SCHIZAS, C. (1995), Artificial neural networks in marine propeller design,
ICNN’95, Int. Conf. on Neural Networks, Vol. 2, pp.1098-1102, New York, IEEE Computer Society
Press
OEI, C.K.; GOLDBERG, D.E.; CHANG, S.-J. (1991), Tournament selection, niching, and the
preservation of diversity. IlliGAL Techn. Report 91011, Univ. of Illinois at Urbana-Champaign
SARLE, W.S. (1994), Neural networks and statistical models, 19 th Annual SAS Users Group Int.
Conf.
SCHIZAS, C.N., NEOCLEOUS, C.C. (1995), Artificial Neural Networks in marine propeller design,
Int. Conf. Neural Networks
TUCK, E.O.; LAZAUSKAS, L. (1996), Unconstrained ships of minimum drag, Dept. Applied
Mathematics Techn. Report, The University of Adelaide
451

Appendix 1
4b - S/L = 0.2
4b - S/L = 0.3
10
10
9.5
Experiment
ANN
9.5
Experiment
ANN
9
9
8.5
8.5
8
8
CT (x 1000)
7.5
7
CT (x 1000)
7.5
7
6.5
6.5
6
6
5.5
5.5
5
5
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Fn
Fn
4b - S/L = 0.4
4b - S/L = 0.5
9
9
Experiment
Experiment
8.5
ANN
8.5
ANN
8
8
7.5
7.5
CT (x 1000)
7
6.5
CT (x 1000)
7
6.5
6
6
5.5
5.5
5
5
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fn
Fn
Fig.7: C T curves for model 4b
452

6a - S/L = 0.2
6a - S/L = 0.3
8
8
Experiment
Experiment
7.5
ANN
7.5
ANN
7
7
CT (x 1000)
6.5
6
CT (x 1000)
6.5
6
5.5
5.5
5
5
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fn
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fn
6a - S/L = 0.4
6a - S/L = 0.5
8
8
Experiment
Experiment
7.5
ANN
7.5
ANN
7
7
CT (x 1000)
6.5
6
CT (x 1000)
6.5
6
5.5
5.5
5
5
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fn
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fn
Fig.8: C T curves for model 6a
453

6b - S/L = 0.2
6b - S/L = 0.3
8
8
Experiment
Experiment
7.5
ANN
7.5
ANN
7
7
CT (x 1000)
6.5
6
CT (x 1000)
6.5
6
5.5
5.5
5
5
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fn
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fn
6b - S/L = 0.4
6b - S/L = 0.5
8
Experiment
8
Experiment
7.5
ANN
7.5
ANN
7
7
CT (x 1000)
6.5
6
CT (x 1000)
6.5
6
5.5
5.5
5
5
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fn
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fn
Fig.9: C T curves for model 6b
454

!
"! #
$ #%
#%
&#
! "
! ! !
!" !#$
!! %
&' !"! (" (
)! !
# (( ( *!
! !
+#( "(! !
, ' !! ! ! * !
! $! "
! !"$&" ! !
(
" (" ( ( !
# " ! "
" ! ( ( "
( # - !
! !.
!! " !
!!
!! ( / & *
" ( * 0- 1
/&*"
!! (
#! $%
2 3'())*
" " "(
# *"# "(
(" ("!("3
3 , !("
( !' ! (" !

' ! !( (" !# ("3
# * (!
(" + ,-())(#
. !' ! +
' 5 ! "
!
! !! " (
67* !
1 " !
!* ("
" ' ! ( /"
!!!
! (
( # !( ( /&*
! 8
!!( %
• /
• !'#((" !
(" !!(
• ("3(" !3
• ("#"
• * ("
• & (
! # !
/&*# * # " (!
!
&!
,9(!/& *
: !
(" " ! !"
(!
• ; 3
• +
• 8
• . < !
• *"
"! ! !# (
'
/&* ((!3 =
! !
, ! ! (
" (
( ! $ '
/ ! (1
(!("!6
7 ( "( ! 0 3
!!" ! " $
4

,? !/&*+&+/
! 1 ?/&* ( ,?
!(
(%(
+
/
@
8
&
.
)
*+
%
*+
. "
*"
,9%, !/&* ,?%@ !/&*
&#())*
&!! %
! ' ! !! 3
! !! (" !
!!(" 3 (";
!("# A;0
) +(" "1! !'
! " !(" !!(
!! 3 8*5)
! .! /00(1!((!
! !!"
" 1/00/#' !(!
'!A;!! ( '!" !
(" ("
/&*
&!#! '
/&* !! !
)# ("" ! !
" +! ! !
+
!!!! ! !
&!&!
!" !8/ /&*"
! !$!
! " !" !$#1
! !! 0 "
@ !" 6( ()*37 (!"
! (
>

&!,! )
!! !(" !
• ( ! ("
/&* ("!
• -"6( (7 !"
• ! " !
!! /&* !
"( (
&!-! .
: ! ! (
! (" " " 3
: " ! !
! ! !! ! :
/&* !#&+/ !
"
!!! ! 3
"" ,A,( #!3
C1!6C17
,A% + (
6"7 ! 6(7
3"
,%;(( ! (
3
,! $"
@ ( (
?DD? ?DDA.&())2#"( /&*
!88 # 8 # "
!/&* ! !
! ! /&* ( ! @3 4ADD
)C88 # 2/ 5(E 3 ! !
: ?DD? @3 BDD )C 8 # 25( E )#3 ( !
'(/&* !/?DDA
B

,%G/ 5(E G
,4%G5(E )#G
1%8
+3 ! +3 !-4
" ADABA ?FD?
( ?F?DD ?BAAD
067 DDD A??D
;67 ??D ?9BD
; !67 9?DD 9?DD
/ !67 9DD 9A
/! 49B AB
; ! 9D>>4? B4F4B
/" ?4 ?
/&* !( %+. "#
!5()))!( 3= &
* 3:!(!
+ ;/8:/( +@ H
,>%& !#( !!' D
$+3 !"
" ( ' ( '(
! " ( :
# " ! ! !
!! 8*5).! /00(#
!3 (
: ( !
F

!! !#( " :
!! ( ("/
! 1 ,>
!!!" " (" # 3
,! #?D!'
""3 !"
,!! /
"("
"(" ! ' '! ,
" ("
!( ! $ ! "!(
! ! *( ! !
# (! " $
! ! ! !!! !
,!#! 0/ $
"/&* "! ( (
" (
!
!/&* !! " (
(!
8 # ,B
,B%/ 25(E )#3
! ! "
" ( (" ! !
( !( !
(
! ! FDD
$/ ( !
( " ( !
# " " ( 9 !
!
" /" ! "
!! ( # "#" ":
" ""(
31 "
"(!
4D

-! 1 %
" ! /&* 3 !
!3"! !"
( .&())2#)#!
! " # " !
+#" !A> " (
I4J#" %
,46
% ?
= ? ⋅
D
? π D
( !( D " ?
"!2/ 5(E 3!!"!!
06?DD?99?FK?DD?9?D?7( ,
"!25(E )#3!! /!
(?? ( "
-!! (
" ( ""
/&* ' ! * 2/ 5(
E 3"6 L?F?7( (" ADD
9A ,F(("((,9D(
(" (" (
!(" ! ("". "#
("!,99( ("
,9? 9 ( " ! 88 # " ( # "
!" / ,949F!8 #"
" ( ,9? 9B
! " " !#""
!( "0" /&*
(". ("! ("
,9?
! (" 6/07 68/7
( ,9A 9!2/ 5(E 3 94 9>!25(E )#3
@ ! !
! !" $ %
, , 8
σ = 68
− 8D7
± 6
− D7
7
7
! 7 7 88 ! !
#8 ) ) ( !"3# ,)1$
/&* ! "!"!
2 "! 5"
!( !(
"!!2/ 5(E 3
( (" (( !+ ("
(
' "
88
49

2/ 5(E 3
Hs (m)
6.0
5.0
4.0
3.0
2.0
1.0
Significant wave height
Hs (WAVEX)
Forecast 2002-11-29
Forecast 2002-11-30
Forecast 2002-12-01
0.0
2002-11-29 00:00 2002-11-30 00:00 2002-12-01 00:00 2002-12-02 00:00 2002-12-03 00:00
,F%& ! ("
Zero-upcrossing wave period
14.0
12.0
WAVEX
10.0
8.0
6.0
4.0
2.0
0.0
2002-11-29 00:00 2002-11-30 00:00 2002-12-01 00:00 2002-12-02 00:00 2002-12-03 00:00
Tz (s)
,9D%&$
Relative wave peak direction
250
WAVEX
200
150
100
50
0
2002-11-29 00:00 2002-11-30 00:00 2002-12-01 00:00 2002-12-02 00:00 2002-12-03 00:00
Dir (deg)
Acceleration (m/s2)
1.0
0.8
0.6
0.4
0.2
Vertical acceleration at bow
(SDEV)
Measurements
Octopus using WAVEX
Octopus using forecast
,99%& !("
"6DM!("7
Stress (N/mm2)
14.0
12.0
10.0
8.0
6.0
4.0
2.0
Stress SB
(SDEV)
Measurements
Octopus using WAVEX
Octopus using forecast
0.0
2002-11-29 2002-11-30 2002-12-01 2002-12-02 2002-12-03
0.0
2002-11-29 2002-11-30 2002-12-01 2002-12-02 2002-12-03
,9?% + /&* "
(6 " 7
,9A% + /&* ,9% + /&*
6

70
2.5
Stress [N/mm²]
60
50
40
30
20
10
Measurement
Octopus
ACCv [m/s²]
2
1.5
1
0.5
Measurement
Octopus
0
04-02-15
00:00
04-02-15
06:00
04-02-15
12:00
04-02-15
18:00
04-02-16
00:00
04-02-16
06:00
04-02-16
12:00
0
04-02-15
00:00
04-02-15
06:00
04-02-15
12:00
04-02-15
18:00
04-02-16
00:00
04-02-16
06:00
04-02-16
12:00
,9B% + /&* #
" (
,9>%+ /&*#
,25(E )#3 ( /&*
!!( " ! !1
! "!(" 1
" (" !( (" ,9
(" ! "
2! 34
! !!"
( " "(" #/009#
! #!
!!" !!! !!#
! !! ( " ' !
25
20
Measurement
Octopus
Roll [°]
15
10
5
0
04-02-15
00:00
04-02-15
06:00
04-02-15
12:00
04-02-15
18:00
04-02-16
00:00
04-02-16
06:00
04-02-16
12:00
,9F%+ /&*# 5(E )#
,9F( ! !+3 !-4
! !! !"(
!! !
: !" #
. " !!
!(( !-
" ( ,?D,
! !!" !
5 !!(" ! ",
( ! /0::'/000
( ' (
4A

! !
!! 5 !! !
"!& /00;&#()))#
3000
2500
2000
Vertical bending moment [MNm]
1500
1000
500
0
-500
-1000
Hogging(linear)
Hogging
Still-water
(Hogging+Sagging)/2
-1500
Sagging(linear)
-2000
Sagging
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
Wave amplitude [m]
,?D% @" (" " ! ?DD )C
("&#()))
, !(! "
/&* (" !! (
&#()))#)" (" ( (
*!/&* "
""(" ( "
"(+""(" !
(( "
,?D
5! 01
1'"! ! !!! /&*
" ( !
!( " !/&* $( !!
0 "" " ! !
!! ! (
# " 23 *!
! ( / " !
!! " ! !!
4

1! ( !
# 1/&*"(
" ( (!
! !#" 2*
1! (
"
,# ( "
!!' ("!!( "'#
6! $%$
/&*"! "3 "
$ "!
# ( "(
!!/&* 2/ 5(E 3 25(E
)#3!( $ !!
!! !
!!
! ! (#
" ! 1" C1
( : /&*
" " ! "
(/&*( !!
* /&*( !
" !
1 (! ( !!
0 ((! ( "
! "
N ! "$ !!!!
( (
! !!" !. " #
! # ( !
/&*" ! 6 8/("
7 ( !"!#!
!"! , !/&*"
" ! 3"
1( !!
7!
( ( (
! !" ( (
" "" !
4

(" (!!!("(
1 "( " (/& *
/&*! !!
#
0 !("( =
!! ! " /&*(" (
8 #("88 # (
" '( 3
"! !" ( ! ! !
"!#",
("(" "
!( ! !/&*
! 3! (
!(!2/ 5(E 3 25(E )#3 !,
!(" ( !!
! /&*
( ! (" "
. "#(" '=
"(" ! (
(* (" =
!( ("! !
(" / "
"
) ! (!(( (
!/&*"
8(%
" !#/&*( !!"!
" ! * 0- + */ @ / !
(!2/ 5(E 3 25(E )#
3!" "
!/&*
01&*5*6?DDA7 0(O
0C+) 8 69FFF7 ,
&/ABFF/-*
*5)/P*& &< &Q51) Q 6?DDD7
@
*@+*55 ; 69FF97 < " / & AB
9999A?
44

15. +

! " ! "#$%&'("#
#$% ! "#$%&')#*!+
& ! "#$%&',
'
!"!
#
$#
%
$!&%$!'
( #
#
###
#
## #
##
)"
()*
#'*-**-.###-#''-#
&#'*''# #%*'# #--#'**'#
/ * '-# '& - & - #'
' +& * '' &#' ' - &+
#-#&
0--'--*''#'-#'#
** ' # &+ -' * ' ' - --#
--#1'2*'#3124#'-#'* '
*12'#-#'***&-'-#'
''* - &+- *
12**&#'-#'*#--*
-.
0*-#'-# #+-'-.
#--#*#'##-#-
# - ' - -- * & * -' /#
'*#''#'

+) ,- & %
+)(
&+*#'##*-*-'
-*&#'#'&#*#
-#'#+'+#'#'# #+'#'-'
# ' &+ # --# **' -' #' #+
#+ +'&-##''#**'
#*#--#*#' -&'#
-.#*'#'2/*-#*
%# '# -' #+ - '# # * '#
''-'--%*''*%#'#-
6#''#.-7&'-# '''#
''-' #+
89:2*'*!#66#6
+)+ , - .
#-'-#- '-#-
-'-.#&''& /#'-' ''
% #' ;# - ' # # *#*#
#'

8?:6#6' **#--#*%#6#'#-'
*&'-'#
/) ,0
/)( , - .
'#'-&# *#--# +**
'# ' - --# ;'' '
%#6#'#'--#--*#'127
# + #' -*' '# ' &+ ' & -- ''
'''--' --*'**'-#-*&*
'# @' -' & * &+ & '' ' &
*'-
8A:6#6' **#--#*%#6&'#'
'-''&1'2*'#
=>

)+0
%# &*12'*&+*#'2
&'-#&+&*## . '#'##
.&'*''#-'#'*
'##*&-' #+#&#
--#''#

)2-
%* &;-*"#+%'-*%# &'
1' & #' '*#*'&&''#
& '** *'&--**'*
1' &
, # -# &+ & ; '# '#
%# ' 1' & - '# '#
%# '# - '# '7 & 6# '# #
'#'**-'-#''*"#+%
12 ' - --# -# * '#
&&-* '#
*# -# 3 '+4 %# '# & "#+ %
# '* -' -' -# ' # & #
* #+ -# + ' ** # ' &#
'#"#+% &&# '*''#-'
-#&-'-#21' &-'-#
# #*-'#'-'#''7#+#**
'''#-#+ -#'#
'*# '
# ' ** * *# '+ -# &#
# -''#'&*-'-*'+2*
'#''' * ##-'-#&#&-
#-'*#'+ #'
)-'&*&+&##&*:
• *'#'-*#--#
•

- # 3 C%04 &# --' *#
8D:-'#'C*%*'*-#
#'&'*#*##+'+'
. #+'
8:8#*#'#
%**12'*#''#
**#''''-&&+1' &
;---*'#1' & --#*
*"#+6 ' ''**"#+%
''# *# -# -* # * ''# C%0 #+ # 2
#' '"#+%##' '''''#'#
'-*--*1' & '#
*#-' #+
=A

0
1 0
8=:1-*1' & '*"#+%2'
C*%*'*"#+%
*--*12*1' & &%# &
'1' & #'''#&# #
B%# &#+''#'+&# --#+
1' &*#"#+#
0
1 0
8:2-*"#+%%#'1' &*'#
B#*"#+%*##*-'
-'-#1' &
0
1 0
85:1' &*"#+%'#
1'1#
=

)-''#-*'1' &-#''*''#'#
''**-'#'*%1' &#
'#' * # ' * %# & # -
*##
1 0
0
89>:%##'''1' &
-- * &+ -' '' -- # *
'-' '-# *# -# '

899:*-'-#
0 & 12 --# ' ' --' * ' %# ' 1'
&'&+-'&# ''
-
'' -# * 1' 2* '# ' - ' --#
- #*&'-#-*&*'#-''#
'#''#
-##&*&+*#'''#
' - * /# '-' & - *
-#
--' &+ ' # ' '' * # '# * ' ' &#
* # - &# -# * ' #' -'
#/#*1'2*'#
=

Global Optimization for Safety and Comfort
Daniele Peri, Emilio Campana, INSEAN, Rome/Italy, {e.campana,d.peri}@insean.it
Abstract
Design engineers community seems to be still Lipschitzian on the usefulness of numerical
optimization. Criticisms are often focused on the simplicity of the optimization problem solved
(e.g. resistance minimization) when compared to the complexity of a real-life design problem,
involving tens of different criteria. Indeed, much more challenging requirements are on the
desk of the design team and solutions tend to become more complex by the hour, particularly
when new features, missions, or capabilities are to be considered for the final design. In order
to address complex requirements, the design team typically explores different solutions by means
of systematic variations of the hull form, while in a second phase the results are analyzed in
order to reach the objectives. A much more efficient way is to adopt numerical optimization
techniques. The main features requested to the new design (objectives and constraints) are
translated in a mathematical form and then passed to a numerical optimization framework, able
to manage all the tools necessary for the solution of the problem. Hence, new problems can
be easily faced, discovering the right direction for the design development. In this paper some
original Global Optimization (GO) algorithms are illustrated: a Multistart Gradient Method
(MsGM), an evolutionary algorithm (Particle Swarm Optimization, PSO) and a Lipschitzian
method (Diagonal Rectangular Algorithm for Global Optimization, DRAGO) are introduced and
applied to the shape optimization of a cruise ship for improving safety and comfort, comparing
the numerical results.
1. Introduction
Efficiency, economy and great environmental compatibility of shipping with respect to land and
air transport seems to support the growth of the fleets, as witnessed by the fact that about 90%
of the world trade is being transported by ship, Payer (2004). In this scenario, the need for
new designs with increased safety, efficiency, flexibility of use, speed and comfort, is becoming
evident.
Far from being the only factor of innovation, safety is however a major element of public concern,
especially when pollution of the environment is involved, and the quest for designs capable of
reducing the risks of shipping is challenging design engineers. Progress in ship design is also
fundamental to improve the comfort of both crew and passengers.
The quest for new design might give impulse for more numerical optimization in ship design.
The increasing attention on this topic is partially due to the appealing opportunities given by
these techniques. In fact, the (naive) dream of each shipowner would be a computer program
able to design the perfect ship for a given task. On the other hand, the design community is
suspicious about the real ability of an optimization framework to manage all the aspects of the
design activity with a sufficient degree of reliability.
For this reason, the researchers and code developers have to move mainly along three directions:
(1) Increase problem complexity: include as much as possible different disciplines in the
optimization problem, enlarging the number of different issues the optimizer is able to treat simultaneously;
(2) Gain reliability by applying high-fidelity solvers, with a solid ground of physics
inside, and increasing the grid density of the adopted meshes. Examples are Duvigneau et al.
(2003), Jacquin et al. (2004), Tahara et al. (2005); (3) Explore the algorithmic side, looking
for techniques able to increase the chance to find the maximum improvement within affordable
overall time.
This last point is the focus of this paper. Algorithms underlying different optimization philos-
477

ophy are described and applied to solve an optimization problem of the redesign of a cruising
ship, eventually comparing the numerical results.
2. The quest for a global minimum
The easiest (and maybe naive) way to perform optimization is to start from an assigned design,
evaluate its performances, explore the performances in a neighborhood of the initial design: once
a direction of improvement is identified in the design space, move toward this direction until
an improvement of the design is still possible and keep iterating for a few steps. The identified
minimum is clearly a local one, which may be enough for our purposes.
If more improvements are necessary or appealing, global optimization might be the proper
choice. Once a local minimum is found indeed, we are not sure about the existence of better
local minima, located in different attraction basins, with better performances than the present
one.
The minimum value among all the local minima is the global minimum, defined as the point
such that:
F : X → R , X ⊆ R N
x, x ′ ∈ X
x = argmin{F(x ′ )} ⇐⇒ F(x) ≤ F(x ′ ) ∀ x ′ ∈ X
where X is the subset of R N where the objective function is defined and x, x’ are design vectors.
A few comments on certifying the global minimizer. Following the definition of global minimum,
we can state that the global minimum has been found only if sufficient information about all the
existent local minima are available. This represents an hint about the complexity of the problem
we want to solve, since a detailed search on the Feasible Solution Set (FSS) becomes necessary,
enhancing the price of the solution due to the larger number of objective function evaluations
requested. Furthermore, defining stopping criteria for this algorithm is also more complex, since
the usual condition of null gradient for the objective function is poor. As a consequence, the
extension of the search in the design space is sometime adopted as an indirect indication of the
detection of a global minimizer.
Beside information about the objective function and on the FSS, to guarantee the completeness of
the FSS investigation the algorithms too have to possess some special features. Non-deterministic
algorithms, like Genetic Algorithms, are not suited to this particular aim. They are able to
improve substantially the objective function, but the randomness of the search guarantees their
completeness only if the number of attempts is huge and dealing with real-life problems (those
for which the price of the computation of the objective function is not negligible), this feature
makes the GA less attractive than deterministic algorithms.
3. GO Algorithms
In this section, some GO algorithms are defined. All of them are substantially deterministic algorithms.
Since no assumption is possible about the objective function (continuity, boundedness
etc.), no mention is given about the theoretical properties of the here described algorithms.
3.1. Multistart Gradient Method (MsGM)
The simplest way to investigate more than a single basin of attraction is to perform different
local optimizations starting from different points in the FSS. The here adopted MsGM is based
on the Conjugate-Gradient algorithm described in Peri et al. (2004). Two different choices
are possible: local searches can be performed sequentially or in parallel. Here we adopt the
second choice, and hence, at each step, M gradients of the objective function must be computed,
being M the number of different starting points. If NDV is the number of design variables,
each gradient evaluation requires 2*NDV evaluations of the objective function when a centered
difference scheme is adopted. Moreover, at least one more evaluation for each moving point
478

is requested after the descent direction for that point has been defined. Summarizing, the
price of the algorithm is M*(2*NDV+1) solutions for each iteration. In order to reduce the
computational costs, the algorithm has been modified as follows:
1. Distribute M points over the FSS.
2. Evaluate the M points in their actual position.
3. Build up a meta-model of the objective function adopting all the available known points.
4. Evaluate the objective function gradient in all the M points by using the meta-model (no
further evaluation of the objective function).
5. Compute the M descent directions.
6. Move the M points along the descent directions.
7. go to 2
In this way, the price of each iteration becomes M instead of M*(2*NDV+1). More explicitly,
if we have 6 design variables and 6 different starting point, the price of each iteration passes
from 78 to 6. In the algorithm description, the concept of meta-model has been introduced.
A meta-model is an approximation of the objective function obtained from sampled values.
Details are reported in Peri and Campana (2005). A last comment related to the strategy for
the starting point selection is necessary. In fact, the uniformity of the distribution of these
points is of paramount importance, since the probability to fall inside as many attraction basins
as possible is connected with the sparsity of the initial distribution. For this reason, an LP τ
sequence, Statnikov and Matusov (1995) is adopted in this phase: its easiness in being generated
and uniformity of the distribution are two key features of this kind of sequence.
3.2. Diagonal Rectangular Algorithm for Global Optimization (DRAGO)
Another algorithm is inspired by the family of the interval search algorithms Schubert (1972),
Jones et al. (1993). Here some bound values for the design variables are assumed, and the so
defined hyper-rectangle is considered as a single interval. This original interval will be subdivided
into smaller intervals across the promising value of the objective function. The estimate of the
value of the objective function y i inside a potential new interval i is made by assuming the
Lipschitz constant value, and then computing the expected objective function value y i as
y i = (f u i + f l i )/2. − K ∗ (u ij − l ij ) (1)
where i denotes the interval index, j the design variable, u i and l i the upper corner of the i th
hyper-rectangle, f l and f u the objective function value in l i and u i , K the Lipschitz constant and
y i the estimated infimum of the objective function inside the i th hyper-rectangle. This estimate
is based on the assunption that if we fix the rate of improvement as the Lipschitz constant, the
objective function inside the i th interval cannot be improved more than y i . It is clear that the
original Schubert (1972) algorithm has been modified, and each hyper-rectangle is characterized
by two points only, that is, the extreme corners.
The initialization is made by computing the objective function in these two vertex of the original
hyper-rectangle only, regardless the dimension of the problem. At each iteration, the hyperrectangle
to be divided is detected, and it is partitioned sequentially along all the directions.
For each subdivision, two new hyper-rectangles are obtained, and only two new values of the
objective function are needed, Fig.1. The Lipschitz constant is estimated as the maximum value
of the ratio of change of the objective function along each interval augmented by a certain factor.
479

This algorithm is characterized by the coexistence of two different souls, global and local. In
fact, large unexplored intervals become promising due to the term −K ∗ (u ij − l ij ), in which the
dimensions of the interval dominates, while the absolute value of the objective function at the
extremes plays in the term (fi
u + fi l )/2. A global phase is active when some huge intervals are
still unexplored, and a local phase occurs when the objective function values at the boundaries
of an interval are extremely low.
3
ξ2
1
f
1
ξ2 f
1 2
f
2
1
3
ξ1
ξ1
ξ1
ξ1
ξ2
1 2
f
1
2
ξ2 f
1 2
3 4
ξ1
ξ2
ξ1
Fig.1: Course of the DRAGO algorithm. Sequence of partitions of the design variable space
(ξ 1 , ξ 2 ), obtained using informations coming from the objective function space (ξ 1 , f and ξ 2 .f)
Asymptotically, this algorithms guarantees the exploration of the whole FSS. In order to avoid
an extensive but unessential exploration of the FSS, some weights on the local and global phase
are necessary.
3.3. Particle Swarm Optimization (PSO)
In its first implementation, Kennedy and Eberhart (1995), Particle Swarm Optimization (PSO)
was a pure stochastic method. The swarm simulates the social behavior of some individuals,
sharing information among them while exploring the design variables space. Each particle has
its own (individual) memory to remember the places visited during the exploration, while the
swarm has its own (collective) memory, to memorize the best locations visited by the particles.
The particles have an adaptable velocity and investigate the design space analyzing their own
flying experience, and the one of all the particles of the swarm. Each particle is a potential
solution of the optimization problem under consideration, as happen in the classical Evolutionary
Computation (EC) techniques. However, PSO method has not a direct “recombination operator”
and it does not use the “survival of the fittest” concept.
The basic PSO formulation defines each particle as a potential solution of a problem in
a N-dimensional space, where the i th particle of the swarm can be represented by a N-
dimensional vector, X i = (x i1 , x i2 , ..., x iN ) T . The velocity of this particle is given by the vector
V i = (v i1 , v i2 , ..., v iN ) T . The best previously visited position of the i th particle is denoted as
P i = (p i1 , p i2 , ..., p iN ) T . Defining b as the index of the best visited location by the whole swarm,
and letting the superscript denote the iteration number, the swarm is moving according to the
following two equations given in Shi and Eberhart (1998,2001).
{ v
n+1
id
= c 1 r1 n (pn id(
− xn id ) + c 2r
) 2 n (pn bd − xn id )
x n+1
id
= x n id + χ vid
n+1 + ωvid
n (2)
where d = 1, 2, ..., N; i = 1, 2, ..., n sw , and n sw is the size of the swarm; ω is called inertia
weight; c 1 , c 2 are two positive constant, called cognitive and social parameter respectively; χ is a
constriction function, which is used to limit the velocity; r 1 , r 2 are random numbers, uniformly
distributed in [0,1]; and n=1,2.., determines the iteration number.
The role of the inertia weight ω, in equation (2), is considered critical for the PSO’s convergence
behavior. The inertia weight is employed to control the impact of the previous history of
480

velocities on the current one. Accordingly, the parameter ω regulates the trade-off between the
global (wide-ranging) and local (nearby) exploration abilities of the swarm. A large inertia weight
facilitates global exploration (searching for new areas), while a small one tends to facilitate local
exploration, i.e. fine-tuning of the current search area. A suitable value for the inertia weight ω
usually provides balance between global and local exploration abilities and consequently results
in a reduction of the number of iterations required to locate the optimum solution. Experimental
results indicated that it is better to initially set the inertia to a large value, in order to promote
global exploration of the search space, and gradually decrease it to get more refined solutions,
Shi and Eberhart (1998,2001). An initial value for ω was set and the gradual decrease was
calculated as follows:
(
ω = ω 0 1 − n − 1 )
n max
The parameters c 1 and c 2 , are not critical for the PSO’s convergence. However, proper finetuning
may result in faster convergence and alleviation of local minima. Random parameters
have been excluded from this implementation, eliminating every non-deterministic behavior of
the algorithm, Campana et al. (2005).
3.4. Genetic Algorithm
As a further reference point, a Genetic Algorithm (GA) code provided by the author and described
in Yang et al. (1998) has been applied. The algorithm has been simply applied with the
default settings.
4. Hull form parameterizations
In the past years, a number of different parameterizations styles have been proposed in literature,
following three main guidelines:
• CAD-based: a commercial CAD system is included into the optimization cycle. The ship
hull is modified using the features of the selected CAD. This option requires the license for a
specific CAD system, that could be expensive, and new releases of the product may require
modifications in the interface with the optimizer. Moreover, the meshing operation, that
is, the production of a computational mesh on the modified design must to be performed
each time the hull is modified, that is time-consuming and also insecure, because the
mesh quality could be not ensured if strong modifications are applied. Moreover, in some
parametric CAD system is uneasy to obtain an existing design produced with a different
product, and the modification of some details of an existing hull cold require a strong effort
in producing the original design, without ensuring the precision of the original geometry.
• CAD-emulation mode: some features of a CAD system are emulated and the new hull
is obtained in a similar way, but without the use of a specific product. An example is
reported in Tahara et al. (2005): the IGES file of the modifying geometry contains all the
informations about the control net of the hull surfaces, and the control points of the net are
moved as into the CAD system. An alternative approach is to produce a net around the
hull surface, than controlling the net points. An approach of this family, called Free-Form
Deformation (FFD) is described and applied in this paper. The computational grid is also
deformed, and it is not required to be generated at each step, maintaining the quality of
the original one.
• Perturbation approach: an analytical patch is applied to the computational mesh, in an
additive or multiplicative manner. These approach have been explored in Peri et al.
(2001), Peri and Mandolesi (2005). The easy way in which the new geometry is produced
has, as a single drawback, the difficulty to maintain everytime the fairness of the original
surface, while flexibility is one of the major features of this approach.
(3)
481

In this paper, we are adopting the FFD approach Sederberg and Parry (1986). The portion of
the hull to be modified is embedded into a rectangular control region. The control region is
partitioned with regular subdivisions along all the three coordinate directions, and the intersections
between the subdivisions represent the control points of the domain. Once the control
points are shifted, an set of hexaedrical shapes is obtained, and the included volume is modified
via Bernstein polynomials defined by the position of the control points. Different control region
could be sequentially applied to the same hull portion. In order to reduce the number of design
variable at the price of limiting the variety of obtainable shapes, a subset of the control points
can be moved together. If necessary, the displacement of one control point can be connected
with the displacement of a different point, in the same direction or not, with the same or a
different (prescribed) law. This few examples may give an idea about the flexibility of the tool.
The global movement of the embedded volume makes the modification of the hull shape very
smooth, preventing unfaired regions.
5. Problem description: minimizing the whipping of a cruising ship
Comfort and safety of a cruise ship are of paramount importance, since the achievement of these
tasks is the core of the success of a ship of this class. In fact, customer satisfaction is the primary
goal of a cruise company. During the years, more and more comfortable ships, with improved
seagoing features have been produced, increasing the active control features as well as the passive
security systems. In this framework, one of the most interesting problems to be solved for a
cruise ship is the whipping problem. With this word we are indicating the resonance effect on
the structures induced by small but continuous impacts of the stern of the ship on the sea water,
particularly when the ship is at rest, just outside the harbor, for example during the waiting
time for the free dock availability. In this situation, the ship is nearly in open seas at rest and
the active control systems are inefficient and only the hull shape might help. By moving up the
stern of the ship the waterline is reduced and this might reduce the performances of the ship,
while by lowering the stern location, the transom is also moved toward the propellers, probably
increasing the induced vibrations. Finally, the occurrence of whipping is also connected with
the slope of the stern and of the characteristics of the incoming wave. Clearly, there is not a
simple solution to this problem.
Bearing in mind the focus of the paper, that is to compare different GO algorithms in the redesign
problem of an existing ship, a case study for minimizing the number of expected stern
slamming events and their probability has been set up.
During a preliminary analysis of the behavior of the original hull with incoming waves of 3.5
meters of amplitude, it was found that the worst condition occurs for incoming waves of a period
of 9 seconds and for a direction of 75 degrees. These conditions have been adopted for the test.
The objective function F is
f = 0.5 S o
S i
+ 0.5 P o
P i
(4)
where S is the number of slamming events per hour, P is the probability of the slamming event,
and the underscores are o for optimized and i for initial.
The adopted constraints involve the displacement of the ship, that cannot be varied more than
1% of the original value, and the beam, that is fixed. As to the geometry manipulation, three
different boxes for the FFD approach have been used in order to modify bulb, stern and bow
regions, Fig.2. Ten design variables have been used to move the hull shape and these are the
variables of the optimization problem too.
482

X
Z
Y
Z
X
Y
Z
Z
Y
X
X
Y
Fig.2: Details on the parameterization scheme for the cruise ship: three FFD blocks. Black
dots indicate the moving vertexes.
6. Numerical solution: Native form algorithms
In this section, all the original algorithms have been applied in their native formulation, while
in the next section improved versions of the algorithms will be presented.
The same initial distribution of points has been applied for PSO and MsGM. For GA, a random
population is enforced. The number of initial points is equal for all the algorithms that requires
an initial population, and it has been set to 25. DRAGO is the only one that do not require
an initial population. A limit on the number of objective function evaluations has been set
(100*NDV = 1000).
All the previously described algorithms have been applied, and different results have been produced
by each algorithm. Results are reported in Table I.
Table I: Optimal values of the objective function (OF) given by the different algorithms. The
iteration number (It.#) at which the minimum value is found are also reported, together with
the absolute value, the percentage gain (Gain%) and the unit cost (Cost) of the percentage
improvement (It.#/Gain%).
Algorithm It.# OF Gain% Cost
GA 306 0.6548 34.52 8.86
PSO 546 0.6905 30.95 17.64
DRAGO 665 0.6905 30.95 21.48
MsGM 24 0.8095 19.05 1.26
GA gives the best performances, obtaining the lowest value of the objective function in the
smaller number of iterations. One the other hand, MsGM algorithm do not improve at all
the objective function, since the best value is obtained during the evaluation of the starting
population. PSO seems to perform better than DRAGO, reaching the same level of the objective
function in a smaller number of iterations. These results are partly in disagreement with previous
483

esults obtained on a different test case, as reported in Campana et al. (2005) and in Table II for
completeness. Here the objective function was the peak of the heave’s RAO for a fast monohull.
The only strong difference between these two applications is related to some features of the
objective function. Here the objective function is nearly discrete, since the number of slamming
per hour S is an integer number. Consequently, the objective function (4) is a compound of the
step function S and a smooth function (the probability of the slam event) P , and the combination
results in a function with many plateau. On the other hand, the peak of the RAO’s heave used
in the other application is a continuous function. As a consequence, as well explained by the
result of MsGM, the gradient of the objective function is nearly zero on a large portion of the
FSS, and the multistart gradient method meets strong difficulties in finding a descent direction.
The same feature seems to influence also DRAGO method, since efficiency of the method is
related to the estimation of the Lipschitz constant, whose value is connected with the values at
the bounds of each interval. For the PSO algorithm, a reason of the discussed results is still
under analysis.
Table II: Optimal values of the objective function (OF) given by the different algorithms for the
test case depicted in Campana et al. (2005). The iteration number (It.#) at which the minimum
value is found are also reported, together with the absolute value, the percentage gain (Gain%)
and the unit cost (Cost) of the percentage improvement (It.#/Gain%).
Algorithm It.# OF Gain% Cost
PSO 286 0.9872 1.34 213.43
DRAGO 277 0.9884 1.23 225.20
GA 309 0.9904 1.02 302.94
Simplex 130 0.9999 0.08 1625.00
7. Numerical solution: Improved algorithms
Different variants of PSO exists in literature and they have been tested recently, Campana et al.
(2005). The main difference between the native form and the improved one is the total absence
of random selection, in the initial swarm distribution and in the evolution coefficient. The initial
swarm has been selected by using an LP τ sequence, Statnikov and Matusov (1995), of feasible
solutions. Moreover, the computation of the velocity of the particle, once a non admissible region
has been reached, follows the indications of Venter and Sobieszcanski-Sobieski (2004), and the
selection of the coefficients has been carried out in order to stabilize the search, as performed in
Clerk and Kennedy (2002).
For the MsGM algorithm, different metamodels have been applied during the course of the
optimization. In fact, the use of a single metamodel might be not be the best solution, because
at the beginning of the search very few points are known, and a highly precise metamodel could
trap the local search too close to the initial point. On the contrary, a simple polynomial fit
do not locate precisely the global optimum, but is able to give smooth tendencies about the
region the global optimum is located in. As a consequence, simple metamodels (polynomials
and polynomials plus ANOVA, Giunta et al. (1997)) are adopted in the early stage of the
search, while much more flexible metamodels, like Kriging or neural networks, are adopted once
a sufficient number of solutions are available. Moreover, a limit on the descent step has been
imposed, in order to maintain diversity among the searching elements.
For the DRAGO algorithm, the local Lipschitz constant has been estimated basing on the
informations given by a metamodel analysis. Furthermore, at each iteration, two intervals are
partitioned, one selected among the smaller ones and the second one from the bigger ones. In
order to establish the dimension of an interval, the mean value of the size of the actual intervals
and the variance of the dimensions are adopted.
The results from these new implementations of the different algorithms are reported in Table I.
484

Here the GA results are the same as in Table I. The improvements obtained for the modified
algorithms are evident. All the original algorithms have an higher efficiency than the GA.
DRAGO algorithm still find a value better than the GA: the improvements are comparable but
the number of iterations needed is strongly reduced.
Table III: Optimal values of the objective function (OF) given by the improved algorithms. The
iteration number (It.#) at which the minimum value is found are also reported, together with
the absolute value, the percentage gain (Gain%) and the unit cost (Cost) of the percentage
improvement (It.#/Gain%).
8. Conclusions
Algorithm It.# OF Gain% Cost
MsGM 182 0.3810 61.90 2.94
PSO 189 0.3810 61.90 3.05
GA 306 0.6548 34.52 8.86
DRAGO 152 0.6905 30.95 4.91
Four different optimization algorithms have been applied to the design of a cruise ship for the
optimization of the comfort qualities. Usefulness of the application of global optimization algorithms
has been clearly shown, in terms of efficiency and obtained improvements. Indications
about the future directions for the development of more efficient global optimization algorithms
can be traced by this paper.
Acknowledgments
This work has been partially supported by Ministero delle Infrastrutture e dei Trasporti in the
framework of the research plan “Programma di Ricerca sulla Sicurezza”, Decreto 17/04/2003
G.U. n. 123 del 29/05/2003.
References
CAMPANA, E.F.; LIUZZI, G.; LUCIDI, S.; PERI, D.; PICCIALLI, V.; PINTO A. (2005), New
global optimization methods for ship design problems, Techn. Rep. INSEAN, 2005 – 1, submitted
to Optimization and Engineering.
CLERK, M.; KENNEDY, J. (2002), The Particle Swarm-explosion, stability and convergence
in multidimensional complex space, IEEE Trans. Evolutionary Computation 6(1)
DUVIGNEAU, R.; VISONNEAU, M.; DENG, G. (2003). On the role played by turbulence
closures for hull shape optimization at model and full scale, J. Marine Science and Technology
153/8
GIUNTA, A.A.; BALABANOV, V.; KAUFMAN, M.; BURGEE, S.; GROSSMAN, B.;
HAFTKA, R.T.; MASON, W.H.; WATSON, L.T. (1997), Variable-complexity response surface
design of an HSCT configuration, Multidisciplinary Design Optimization, SIAM, Philadelphia
JACQUIN, E.; DERBANNE Q.; BELLEVRE, D.; CORDIER, S.; ALESSANDRINI, B.; ROUX,
Y. (2004), Hull form optimization using a free-surface RANSE solver, Symp. Naval Hydrodynamics,
St. John’s
JONES, D.R.; PERTTUNEN, C.D.; STUCKMAN, B.E. (1993). Lipschitzian Optimization
Without the Lipschitz Constant, J. Optimization Theory and Application, Vol. 79, No. 1,
October 1993, pp.157-181.
KENNEDY, J.; EBERHART, R. (1995), Particle swarm optimization, IEEE Int. Conf. Neural
Networks, Perth, IV:pp.1942-1948.
485

MEYERS W.G.; APPLEBEE T.R.; BAITIS, A.E. (1981), User’s manual for the standard ship
motion program SMP, David Taylor internal report DTNSRDC/SPD-0936-01
MEYERS W.G.; BAITIS A.E. (1985), SMP84: improvements to capability and prediction
accuracy of the standard ship motion program SMP84, David Taylor internal report
DTNSRDC/SPD-0936-04
NELDER J.A.; MEAD R. (1965), A simplex method for function minimization, Computer J. 7,
pp.308-313
PAYER H.G. (2004), Challenges in ship design, fabrication and inspection - A class view,
PRADS Symp., Lubeck-Travemunde
PERI, D.; CAMPANA, E.F. (2003), Multidisciplinary design optimization of a naval surface
combatant, J. Ship Research 47/1, pp.1-12
PERI, D.; CAMPANA, E.F. (2005), High fidelity models and multiobjective global optimization
algorithms in simulation based design, J. Ship Research 49
PERI, D.; CAMPANA, E.F.; STERN, F.; TAHARA, Y. (2005), A comparison of global optimization
methods with application to ship design, 5th Osaka Colloquium, Osaka
PERI, D.; MANDOLESI, F. (2005), Multiobjective optimization of an IACC sailing yacht by
means of CFD high-fidelity solvers, 17 th Chesapeake Sailing Yacht Symp., Annapolis
PERI, D.; ROSSETTI, M.; CAMPANA, E.F. (2001), Design optimization of ship hulls via CFD
techniques, J. Ship Research 45/2, pp.140-149
PINTO, A.; PERI, D.; CAMPANA, E.F. (2004), Global optimization algorithms in naval hydrodynamics,
Ship Technology Research 51/3, pp.123-133
SEDERBERG, T.W.; PARRY, S.R. (1986), Free-form deformation of solid geometric models,
SIGGRAPH ’86, 20/4, pp.151-161
SHI, Y.H.; EBERHART, R.C. (1998), Parameter selection in particle swarm optimization, 7th
Annual Conf. Evolutionary Programming, San Diego
SHI, Y.H., EBERHART, R.C. (2001), Particle swarm optimization: developments, applications
and resources, IEEE Congress on Evolutionary Computation, pp.27-30
SCHUBERT, B. (1972), A sequential method seeking the global maximum of a function, SIAM
J. Numerical Analysis 9, pp.379-388
STATNIKOV, R.B.; MATUSOV, J.B. (1995), Multicriteria optimization and engineering, Chapman
& Hall
TAHARA, Y.; PERI, D.; CAMPANA, E.F.; STERN, F. (2005), CFD-based multiobjective optimization
of a surface combatant, 5th Osaka Colloquium, Osaka
TÖRN, A.A.; ŽILINSKAS A. (1989), Global optimization, Springer
VENTER, G.; SOBIESZCZANSKI-SOBIESKI, J. (2004), Multidisciplinary optimization of a
transport aircraft using particle swarm optimization, Structural and Multidisciplinary Optimization
26/1-2, pp.121-131
YANG, G.; REINSTEIN, L.E.; PAI, S.; XU, Z.; CARROLL, D.L. (1998), A new genetic algorithm
technique in optimization of permanent 125-I prostate implants, Medical Physics 25/12,
pp.2308-2315
486

Abstract
Maneuvering Simulations for Ships and Sailing Yachts using
FRIENDSHIP-Equilibrium as an Open Modular Workbench
Tanja Richardt, Stefan Harries, Karsten Hochkirch, FRIENDSHIP-Systems GmbH,
Richardt@FRIENDSHIP-Systems.com
An open modular workbench called FRIENDSHIP-Equilibrium has been developed for the analysis
of stationary and instationary modes of motion. FRIENDSHIP-Equilibrium offers an integration
environment and suitable algorithms for determining the equilibrium of forces and moments acting on
ships and yachts, following a force model approach. In the stationary mode the steady state properties
of the vessel are determined (hydrostatics, VPP) while in the instationary mode the accelerated rigid
body motions are computed (maneuvering motions). The equations of motions may be solved by means
of various time integration methods one of which being an advanced time-step adapting Runge-Kutta
algorithm. The functionality comprises the computation of added mass and damping as needed for time
simulations. Special consideration is given to the aero- and hydrodynamics of sailing. The program
therefore also constitutes a refined Velocity Prediction Program. Within the paper various maneuvering
situations are presented for both a conventional cargo ship and a contemporary IMS yacht. The
examples serve to show the applicability of the approach and to illustrate the usage of the tool. Attention
will also be given to IT integration.
1. Introduction
The importance of the performance prediction of ships and sailing yachts at an early design stage increases
significantly these days. Besides the prediction of the maximum velocity in a balanced condition
the analysis of the ship motions in unsteady conditions receives growing attention. Of major concern
are the evaluation of the maneuverability for ships and the speed loss while changing courses for racing
yachts.
FRIENDSHIP-Equilibrium has been developed for both velocity predictions and maneuvering simulations.
The forces acting on a ship or sailing yacht are calculated via specific force modules of the
software system. FRIENDSHIP-Equilibrium represents a workbench in which each acting force is taken
into account by an individual module. Using the stationary mode steady state calculations are performed
by balancing the hydrodynamic, aerodynamic, buoyant and gravitational forces. In the maneuvering
mode the equations of motions are integrated to record instationary behavior. The state model comprises
linearized equations of motions in six degrees of freedom. The dynamic forces, dependent on the
velocity and the acceleration, are considered via the instationary terms in the equations of motion. The
instationary mode therefore enables a simulation of motions, especially maneuvering, in which the
different state variables can be regarded as functions of time. Hence, with the maneuvering simulations
the behavior of the vessel in unsteady conditions can be assessed and improved before the first sea trials
commence. Naturally, the quality of the simulation depends on the validity and accuracy of the available
force modules.
2. Software system – FRIENDSHIP-Equilibrium
FRIENDSHIP-Equilibrium is an advanced workbench for the analysis of stationary and instationary
modes of motion of both ships and sailing yachts. The external forces acting on a vessel for a given
state are calculated via various force modules. Each force type like buoyant forces, gravitational forces,
rudder forces, keel forces, hull resistance, aerodynamic forces, added resistance in waves, windage etc.
is calculated in specific modules. All forces are added up by the program to determine the resulting
forces on the vessel.
These modules can be added to and taken out from the simulations individually depending on the design
487

Conditions States Excitation
Input files
Boat Name FShip
Water {
Density 1.
Temperature 18
}
DegreesOfFreedom Speed |
Leeway | Sink | Heel
Module Displacement
Module Mass
Module Rudder
Module Keel
Module GenericRig
above upper limit
axis symmetry
@include hydrostatic.feq 4
7 extra
Labels Heel Angle, CoB
Data

Fig. 2: Modules used in FRIENDSHIP-Equilibrium
For all calculations the desired degree of freedom can be chosen by the user. Up to all six degrees of
freedom may be considered in the simulations. The link between the degrees of freedom and the free
variables is summarized in Table I. The applications of FRIENDSHIP-Equilibrium for typical scenarios
are shown in Table II. The free variables used within these operations are marked with ’X’. The required
variables for hydrostatic calculations are indicated as ’input’.
Fig. 3 illustrates the structure of FRIENDSHIP-Equilibrium. The used modules and the required parameters
are defined in one or several input files, see also Fig. 1. The acting forces are determined for
specified environmental conditions. Depending on the force modules these conditions are part of the
required input. For instance the force calculation on sailing yachts requires the wind speed and the wind
direction as input.
Table II: Typical scenarios in FRIENDSHIP-Equilibrium (free variables are marked with ’X’)
Scenario Mode V S λ dz ϕ θ δ r δ t
Hydrostatics hydrostatic X input X
Curves of form hydrostatic input input input
IMS type standard sailing yacht VPP stationary X (X) X
4 DOF sailing yacht VPP stationary X X X X
Advanced sailing yacht VPP stationary X X X X X X X
VPP self propulsion stationary X X X
Maneuvering instationary X X X X X X X
489

INPUT Simulation MODES OUTPUT
Ship / yacht
Conditions
Stationary mode
Velocities
Module file(s):
- Hull data
- Keel data
- Rig data
- Mass
- Rudder
- Propeller
- User module
- ...
- True wind speed vs
- True wind angle b
States
T
Equilibrium
mode via
Newton Raphson
Hydrostatic mode
- Ship speed vs
- Heel angle
- Leeway angle
- Rudder angle
- Trim angle
- Sink z
Hydrostatic
Sailing trim
- Heel angle
- Heel angle
- Trim angle
- Sink z
Equilibriuum
in Fz, My
Force Module
Displacment
Floating position
- Trim
- Sink
Curves of form
Excitation
- Maneuver
- Rudder angle
- Tab angle
- Course
(Autopilot)
Instationary mode
Time-Step-Mode
with
Integration-Method
(e.g. Cash -Karp
Runge-Kutta)
Motion
- Path: longitude
latitude
- State: x,y,z,
. . . . . .
x,y,z,
.. .. .. .. .. ..
x,y,z,
Fig. 3: Modes within FRIENDSHIP-Equilibrium
Three simulation modes are offered by the program for different applications:
– stationary mode
– hydrostatic mode
– instationary mode
2.1. Stationary mode
In the stationary mode the steady state of the ship will be determined for specified environmental conditions.
The program will resolve the equilibrium in which the sum of all forces add up to zero in the
defined degrees of freedom by a nonlinear equation solver. The balance will be computed by means of a
Newton-Raphson algorithm. Velocity predictions in steady conditions may also be calculated within this
mode. Depending on the considered degrees of freedom, the output contains the state variables displayed
in Table I.
In addition, an arbitrarily set of trim parameters may be defined in the force modules. These parameters
are optimized to achieve the maximum speed. Various optimizations routines are available within the
program and may be selected by the user. Consequently, desired parameters must be implemented in the
modules. The usage of trim parameters is shown in the second example, see section .
2.2. Hydrostatic mode
The floating position will be calculated depending on the heel angle in the hydrostatic mode. In this
mode the equilibria for vertical, roll and pitch movements are resolved. Furthermore, curves of form are
determined.
2.3. Instationary mode
For the analysis of motions the program offers an instationary mode. For instationary analysis the excitation
forces have to become part of the input. Maneuvering simulations for instance operate with
changing rudder angles. Fixed rudder angles can be set. The rudder angles may also be controlled by
490

Instationary mode
Parameters Initial values Output parameters
TWS, TWA
Rudder
S 0
INPUT
Ship / yacht
Maneuver
Time
Force modules
State function Integration routine Output function
Controller (autopilot)
F( S )
OUTPUT
t i+1= t i + tstep Integration method Longitude,
State vector
(4th order, 5th order, latitude,
S
variable time . step,..) heading
S
next
= f ( s, s,t)
solve F = m a
S
Fig. 4: Maneuvering simulation within FRIENDSHIP-Equilibrium
the use of predefined maneuvers. A PID-controller (Proportional Integral Derivative) is implemented as
autopilot to keep a desired course. An additional manual maneuvering module offers the possibility to
steer the boat interactively with a joystick. Either way, steering changes are accounted for while running
the process.
The motions are described via the equations of motions including all external forces, calculated by their
respective force modules. Additional added mass and damping forces are determined via a further force
module and are then considered as part of the excitation force. A module for linear coefficients of added
mass and damping is readily available. Alternatively, an additional module which describes these forces
can be defined by the user. Nonlinear coefficients as used by Masayuma et al. (1995) for instance, may
be implemented in more advanced modules. The accelerations are calculated by solving the equation of
motions via a time-step method with a chosen integration routine. FRIENDSHIP-Equilibrium currently
makes available a fourth-order Runge-Kutta scheme, a fifth-order Runge-Kutta-Feldberg scheme as well
as a fifth-order Cash-Karp Runge-Kutta variable time step scheme. In the variable time step integration
the time step is adjusted so that the difference of the result using a fourth order Runge-Kutta scheme and
the result using a fifth order scheme is less than a selected tolerance for each of the state variables. A
time scale can be set such that the maneuver is executed in real time or a specified fraction of that. The
process flow of the time-stepping procedure is sketched in Fig. 4.
The velocity and acceleration are combined into one state vector:
s = (x,y,z,φ,θ,ψ,ẋ,ẏ,ż, ˙φ, ˙θ, ˙ψ,ẍ,ÿ, ¨z, ¨φ, ¨θ, ¨ψ) T . (1)
All state variables are computed as functions of time. The trajectory is displayed in global coordinates.
Moreover, any desired state variable can be plotted during the operation.
3. Mathematical model
3.1. Coordinate systems
The coordinate systems used are displayed in Fig. 5. All systems are right handed and orthogonal. The
forces are calculated in absolute coordinates A which is a partially body fixed moving coordinate system.
The x-axis is directed along the vessel’s centerline while the z-axis is perpendicular to the undisturbed
free surface. The heel and trim angles are determined via the rotation between the body fixed coordinate
system B and the absolute coordinates A. The hydrodynamic coordinate system H is a moving coordinate
system directed along the track to determine the leeway angle. The boat’s track is shown in the global
coordinate system which represents the earth-bound coordinates.
491

Latitude
Apparent Wind CS
[+]
Leeway
VS
X A
X B
X H
View from above
Y
Y B A
Y H
[+]
Hydrodynamic Tab
CS
[+]
Delta
A absolute coordinate system
Longitude
x along the centerline forward
x-y plane in undisturbed free surface
y directed to port side
B body fixed coordinate system
[-]
Heel
x along the centerline forward
x-y plane in designed water plane
y perpendicular to the mast
H hydrodynamic coordinate system
Z H
Z ZA
x system along the track horizontally
B
to the water plane
x-y plane in water plane
G global coordinate system
Y
Y A
earth coordinates
H
x-y ebene in water plane
Y B
Body Fixed
Absolute CS
Global Coordinate System (CS)
Absolute CS
Hydrodynamic
CS
[+]
AWA
[+]
TWA
Body Fixed
View from behind
X AW
Y AW
X MW
TWS
Mean Wind CS
Y MW
[180 - 360]
YAW
MW mean wind coordinate system
x along the true wind direction
AW apparent wind coordinate system
x along the apparent wind direction
Fig. 5: Coordinate systems used in FRIENDSHIP-Equilibrium
492

Fig. 6: Definition of ship coordinate systems in six degrees of freedom
The location of the origin must be body fixed but can be arbitrarily selected, e.g. the center of gravity.
The transformation of the forces from a body fixed system B to the absolute coordinate system A is
accomplished by left multiplication with the transformation matrix
⎡
T BA
= ⎣
cosθ sinϕsinθ cosϕsinθ
0 cosϕ −sinϕ
−sinθ sinϕcosθ cosϕcosθ
for arbitrary heel and pitch angles ϕ and θ, respectively.
⎤
⎦ (2)
3.2. Specification of ship motions
The ship motions comprises in six degrees of freedom – three translations and three rotations. These
motions are described in the absolute coordinate system illustrated in Fig. 6.
Table III: Generalized displacements of a vessel
x Translation in longitudinal direction surge
y Translation in transversal direction sway
z Translation in vertical direction heave
φ Rotation about the longitudinal axis roll
θ Rotation about the transversal axis pitch
ψ Rotation about the vertical axis yaw
The state variables are expressed in vector form:
x = (x,y,z,φ,θ,ψ) T
ẋ = ( ẋ,ẏ,ż, ˙φ, ˙θ, ˙ψ ) T
ẍ = ( ẍ,ÿ, ¨z, ¨φ, ¨θ, ¨ψ ) T
3.3. Equations of motion
According to Newton’s second law the motion of a rigid body in the earth-bound coordinate system can
be expressed as follows:
F external = M · ẍ (3)
493

The forces and moments are combined in a generalized force vector
F = (F x ,F y ,F z ,M x ,M y ,M z ) T
while the accelerations are given in the state vector
ẍ = ( ẍ,ÿ, ¨z, ¨φ, ¨θ, ¨ψ ) T
.
The mass matrix M then contains the following components:
⎛
M =
⎜
⎝
⎞
m 0 0 0 m · z CG −m · y CG
0 m 0 −m · z CG 0 m · x CG
0 0 m m · y CG −m · x CG 0
0 −m · z CG m · y CG I xx −I xy −I xz
⎟
m · z CG 0 −m · x CG −I yx I yy −I yz
⎠
−m · y CG m · x CG 0 −I zx −I zy I zz
with m = ρ · ∇ for steady conditions.
A linear force system is assumed to specify the acting forces on the vessel. The hydrodynamic forces are
divided into their translation, velocity and acceleration components.
F Hydrodynamic = −A · ẍ − B · ẋ −C · x (4)
The matrix A includes the added mass coefficients and B refers to the damping coefficients. Hydrostatic
forces are included in the third term. Velocity and acceleration depend on the reference system. Therefore,
the centripetal acceleration a cp must be considered in the accelerated absolute coordinate system,
see e.g. Gummert ; Reckling (1985). Forces resulting from wind and waves and all other additional
external forces are combined in so-called further environmental forces F Environmental to be determined by
the appropriate modules of the program.
The following equations are solved by the integration routine:
(M + A) · (ẍ − a cp ) = −B · ẋ −C · x + F Environmental (5)
3.4. Coefficients
In order to solve the equations of motion the matrices of the added mass and damping coefficients must
be determined. In general, several methods are available to identify these coefficients:
• Estimation of the coefficients from simple shapes
• Formulas developed by Clarke
• Lewis transformation applying conformal mapping and strip theory
• Inverse Fourier transformation of frequency dependent coefficients
• Viscous flow simulations
• Model experiments
• (Full scale measurements)
494

Latitude [m]
-200.0-100.0 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0
-900.0-800.0-700.0-600.0-500.0-400.0-300.0-200.0-100.0 0.0 100.0
Longituide [m]
Fig. 7: Turning test for cargo ship
turning rate [rad/s]
-0.02 -0.01 -0.01 0.0 0.0
0 200 400 600 800 1000
time [s]
Fig. 8: Turning rate ψ during turning test
The order in this list roughly corresponds the associated effort, the quality of the outcome being proportional.
For a first estimation of the added mass the formulas for simple shapes like cylinders and
ellipsoids as published by Saunders (1957) can be utilized. Clarke, see Lewis (1988), developed formulas
depending on the ship’s geometry to evaluate linear coefficients for added mass and damping. More
accurate values of the coefficients can be derived from conformal mapping of each section by applying
Lewis transformation and utilizing strip theory. Here the three-dimensional flow problem is solved via
the integration of two-dimensional sub-domains along the hull. This method is by definition only valid
for slender bodies, but reasonable values can be obtained. Bohlmann (1990) for instance used this theory
to identify the coefficients for submarines and provided formulas to calculate the damping coefficients.
The hydrodynamic mass in x-direction can be calculated from the the added mass for an ellipsoid given
in Bertram (2000). However, this yields only rough estimates for typical sailing yacht bow and stern
shapes.
Frequency dependent coefficients can be obtained from seakeeping calculations. A routine to transform
these coefficients with an inverse Fourier transformation from frequency-domain to time-domain in
order to identify the coefficients in the state space (Schmiechen, 1973) has been studied by Richardt
(2004) for implementation into FRIENDSHIP-Equilibrium. Finally, the determination of the coefficients
by model testing as carried out by Wolff (1981) for example is recommended, of course, but expensive
with regard to both time and money.
4. Simulations
Maneuvering simulations were processed for a representative cargo ship and a typical sailing yacht. For
the former a Mariner ship was selected which is a common test case. For the latter the full scale research
yacht DYNA was chosen. DYNA resembles a 10m IMS sailing yacht and was developed at the Technical
University Berlin, Hochkirch (2000). Full scale experiment data are available for this yacht which can
be used for validation purposes.
4.1. Maneuver simulations for a cargo ship
For the force calculations of the Mariner ship a simple module which includes the estimation of the
propeller thrust, the hull resistance and the rudder forces was integrated. The main parameters were
taken from Wolff (1981). The coefficients for added mass and damping were determined by the formulas
of Clarke as published in Lewis (1988). For the maneuverability analysis various common test maneuvers
are implemented. The standard maneuvers like turning and zig zag tests are readily available as
495

Latitude [m]
-600.0 -400.0 -200.0 0.0 200.0 400.0
0 1000 2000 3000 4000 5000
Longitude [m]
Fig. 9: Zig zag test for cargo ship (scaled 2.5:1)
maneuvering modules. The rudder angle and the maximum course angle are free to be specified. The
fourth-order Runge-Kutta integration method with a time step of 0.2 seconds was applied for these simulations.
The calculated track for a turning test with a rudder angle of 20 ° is displayed in Fig. 7. Fig. 8
shows the turning rate during this simulation. After 1000 seconds a constant turning rate was reached.
The tactical diameter of 670 meters as determined from Fig. 7 is met after 10 minutes.
The zig zag test is typically executed to investigate turning capabilities. Different rudder angles and
maximum course angles can be used. The track for a zig zag test with a rudder and a maximum course
angle of 20 ° is displayed in Fig. 9. For lack of space, the longitude and latitude axis are scaled 2.5:1.
4.2. Velocity prediction for a sailing yacht
In a second example the FRIENDSHIP-Equilibrium was used for the velocity prediction of a 10m IMS
yacht. Various modules have been developed from research results for that yacht, see Hochkirch (2000).
The forces acting on keel and rudder were defined in the modules called ’Keel’ and ’Rudder’. The
aerodynamic rig forces were calculated with the module ’GenerigRig’. Different modules were used for
displacement, mass, crew and windage. So as to demonstrate the application of trim parameters a set of
different trim parameters was included in the ’GenericRig’ module. These parameters are explained in
Table IV.
Table IV: Example of trim parameters in the module ’GenericRig’
σ reef V S −→ max reefing of the sails to be adjusted so as to gain optimum speed
τ flat V S −→ max flatening of the sails to be adjusted so as to gain optimum speed
t twist V S −→ max reduction of the center of effort of the aerodynamic forces so as to improve
the overall performance of the boat when sailing upwind, see Jackson
(2001) for details
The offsets of the hull and geometric data are given in the input file. Parameters like water density,
gravity etc. can be defined in either the input file or in the program. Before calculating the equilibrium
for sailing conditions the model must be in hydrostatic balance. Therefore, the equilibrium for trim and
sinkage in rest position is determined first. The states to be calculated can be defined in the ’Cycle Range’
window as indicated in Fig. 2. In the example the true wind velocity VWT is considered from 4 m/s to
9 m/s for all courses between an angle of 35 ° to 180 ° with an increment of 5 °. In the output table the
velocities for the equilibrium of all states is listed as pictured in Fig. 10. In this figure a polar diagram is
also shown for the six wind speeds.
496

Fig. 10: VPP for a sailing yacht
4.3. Maneuver simulations for a sailing yacht
For the instationary calculations an additional module was defined to compute the added mass and damping.
The module was called ’AddedMass’ and the coefficients were determined by means of Lewis transformation
as explained in section . The dynamic changes of the effective angles at the keel, rudder and
the sails during the motions are accounted for in the lift calculations. The conditions were chosen to meet
the situation encountered during full-scale measurements. The tacking simulations were processed with
a true wind velocity of 9.59 m/s. The close-hauled courses were steered at 37 ° to the wind. The rudder
angle was automatically adjusted by the autopilot. The factors of the PID controller can be adapted to
the problem and consequently influence the course keeping capabilities. Tacks can also be simulated in
manual maneuvers which enables the users of the program to steer themselves by means of a joystick. A
tacking maneuver in which the rudder is linked to a maximum angle until a certain course angle on the
other tack is reached can be applied. The fifth-order Cash-Karp integration routine was used to solve the
equations of motions.
Fig. 11 depicts the FRIENDSHIP-Equilibrium running in the maneuvering mode. The settings of the
autopilot can be seen in the ’ManeuverEditor’ on the upper left. Several graphs are integrated in the
’Maneuvering’ window. On the left the velocity as function on time is displayed. In the other graphs the
track and the heeling angle are plotted. Naturally, the quantities to be shown can be selected as needed.
The results of the tacking simulations are compared to data of the full scale measurements. The yaw
angle is displayed in Fig. 12 while the associated heel angle is shown in Fig. 13. The oscillation of
the full-scale data was caused by heavy seas and strong unsteady winds during the measurements.
Nevertheless, a rather good correlation between the simulated and the measured data can be observed.
From the starting course to head wind the tack needs 7 seconds. A stable heel angle is achieved after
497

Fig. 11: Maneuvering simulation for a 10m sailing yacht
43 seconds and the new course is fixed after about one minute. In real life these results depend on the
helmsman. In the simulations the value may be optimized by adjusting the autopilot. The optimum
speed is reached after about 82 seconds. The sail trim was idealized during the simulated tack. Naturally,
this typically is not the case in reality. Therefore, additional parameters will have to be integrated in the
future so as to take into account the time needed by the crew to trim the sails optimally.
5. Conclusion
FRIENDSHIP-Equilibrium is an open modular workbench which follows a force approach. All forces
and moments are defined in separate modules. A wide range of force modules is readily available within
the software system like hydrostatics, mass, hydrodynamics from model tests, added resistance in waves,
Delft series for resistance of sailing yachts and keels (Keuning ; Sonnenberg, 1999), lifting surfaces
such as keels and rudder, IMS type rig models and many more. Additional modules to accommodate
individual forces and scenarios can be easily integrated for specific simulations.
FRIENDSHIP-Equilibrium supports stationary, hydrostatic and instationary simulation modes. The accuracy
of the results, naturally depends on the implementation of the underlying mathematical model
used in the force modules. For instationary conditions reasonable estimations of added mass and damping
terms are of importance since the simulations are sensitive to these forces. An accurate identification
of this terms is required for realistic results.
Special focus was given on instationary simulations for which examples were presented for two types
of vessels – a cargo ship and a sailing yacht – to show the applicability and the potential usage of the
system. The sailing yacht maneuver presented was the tacking of a 10m IMS yacht. It comprised a
498

Yaw angle [deg]
-60 -40 -20 0 20 40 60
simulation
full-scale measurements
0 50 100 150 200 250
Time [s]
Fig. 12: Yaw angle
Heel angle [deg]
-40 -30 -20 -10 0 10 20 30 40
simulation
full-scale measurements
0 50 100 150 200 250
Time [s]
Fig. 13: Heel angle
comparison between the simulations based on FRIENDSHIP-Equilibrium and experimental data from
full-scale sailing tests which showed very promising correlation.
References
BERTRAM, V. (2000), Practical Ship Hydrodynamics, Butterworth - Heinemann
BOHLMANN, H. J. (1990), Berechnung hydrodynamischer Koeffizienten von U-Booten zur Vorhersage
des Bewegungsverhaltens, IfS Report 513, Technische Universität Hamburg
GUMMERT, P.; RECKLING, K.-A. (1985), Mechanik, F. Vieweg & Sohn
HANSEN, H.; JACKSON, P. S.; HOCHKIRCH, K. (2003), Real-time velocity prediction program for
wind tunnel testing of sailing yachts, Int. Conference on the Modern Yacht, Southampton
HOCHKIRCH, K. (2000), Entwicklung einer Meßyacht zur Analyse der Segelleistung im Originalmaßstab,
Mensch & Buch Verlag, Berlin, ISBN 3-89820-119-8, PhD-Thesis, Technische Universität Berlin
JACKSON, P. (2001), An improved upwind sail model for VPP’s, 15 th Chesapeake Sailing Yacht Symposium,
Annapolis
KEUNING, J. A.; SONNENBERG, U. B. (1999), Approximation of the calm water resistance on a sailing
yacht based on the ’Delft Systematic Hull Series’, 14 th Chesapeake Sailing Yacht Symp., Annapolis
LEWIS, E. V. (Editor) (1988), Principles of Naval Architecture Vol.III, SNAME
MASAYUMA, Y.; FUKASAWA, T.; SASAGAWA, H. (1995), Tacking simulation of sailing yachts -
Numerical integration of equation of motion and application of neural network technique, 12 th Chesapeake
Sailing Yacht Symp., Annapolis
RICHARDT, T. (2004), Simulation dynamischer Bewegungsvorgänge von Segelyachten, Diploma-thesis,
ILS Technischen Universität Berlin
SAUNDERS, H. E. (1957), Hydrodynamics in ship design Vol.I, SNAME
SCHMIECHEN, M. (1973), On state space models and their application to hydromechanic systems,
NAUT Report 5002, Dept. of Naval Architecture, University of Tokyo
WOLFF, K. (1981), Ermittlung der Manövriereigenschaften fünf repräsentativer Schiffstypen mit Hilfe
von CPMC-Modellversuchen, IfS Report 412, Technischen Universität Hamburg
499

!
"
#$%"
!
" " #
" $ % " "
# & '"
"( ")
*"+" # "
,*&% +""
& " !
-
" "
&$
. " " +"
""/ +" "
" " " " " " " "
( " ") %& " " ( ") +"
"" " " "
" 0 (" ) " %
&"1 &" *
" " " "
" " " " "* "
" " " "
" " & "
& &+" "# " #
" " "
" " +" " * " "
" " " 0
+0 " "
%( 0 ) "*"

" " "
( ) +" "/
("" ) &"" " 1
( " " " ) +" " & "
" "!
* "" " "
# & " " " 0 "/
" ( ) ""(")
-* " "
"
+"" " "
+" & "# *%& "
0
" " " # * 1
%& & " " "
&% " "! "
" & " %
" " " " +"
% " & 1 "+"
"" "# * 1%& , "
" " +"
# 3 " " "
"*0 " " ""
# * * 4
* " " % +"
" & % "
"" 5 & " " " *
+"*"
" " "
" +" " * % *
"(%& # ) (*
*1%& ) "" "
(/)" "
'$
+" 1 %
" % " "
" " &""%
+" " 6 "
& " 0 (" 0
%) " "" "
. "% "&"" % "
. " % "%
+" " " "& 1
"+"" "
" " " +" " "
%& * "%
"# # . "
2

"
" &
+" &,
• "(8) "(+8)
•
• "1
• "1
• 8
+" 8/ "5
. " " "()
" " (8 9 )+" "
"(+8) +8 9 & "
+"* " " % "8 9 +8 9 +"% "
:1 ",
7
7
= ( ∗
) + ( ∗
) (2)
&",!6 (& ")
+" &"" "
& " " 6 "
+" " ,
Ρ = %( $ # " ) (7)
&",
$ 6
# 6
" 6
6 "/
+" " " %+"&%"
" * 1%& & "
" &% & " +" &% "
" " +"
" *"( #),"
(" "" ) "
"
+" 6"16 " +"
". " " ""1
& " " " 0 & & " "
* 0 . "&% "
" "" "&"" " % " "
% &" " . " "
" "" "( 9 ) "
"( 9 ) " "& "1
"" " " ""
+" " 0 " "1
& " " " &" "
+" " " " "1
" 0 " & "
7

"1+" %
" " " " "1 "
"
'())*+ " * " "1
"1 " "" " ""1 "
"0 +" " " "
< (< ∈ 2) +" "1 % "
" " +" " "
"# 1%&
+"
&%"
""1& "
" +" " &, "
" " " , & &"
" "+" = ">& " ".
&= "> " , ( ? , )+&" " " "
& " +" "*
, ,* " < "
2
. " & " "
" "
" 1 %& " 0 + " " &
"
($) "
-*"& " "
+" ""& 6"& "
% +" " & " # +"
& &,&
" +" " & & " " 2 7 ; @A +"
"& "(2% ) "2 & +"
6 "1 +" &
,
"1(&"1B@°A)
" " "
&"1 " " "
+" " 8 9 +8 9 5 "
" " "" *
" " " "
+" & +" " . 2 & "
+" & &,
2 8+8
7 "1
; "
C "1
;

($#$*" " " "
+" " #"&
+" "
" 8 9 +8 9 +" & "1 " 8 9 +8 9
&*D 2+" "& *
8 9 +" "". "& "
"* " ""& "
[Nm]
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
L=100 [m] L=200 [m] L=300 [m]
CPA average
CPA min
CPA max
D 2,8 9 "
+" " . &" "
%& " ( ) "
+" +8 9 "
.& " """ "
[min]
30.00
25.00
20.00
15.00
10.00
5.00
0.00
L=100 [m] L=200 [m] L=300 [m]
TCPA average
TCPA min
TCPA max
D 7+8 9 "
($&$+
"1& " " +" 1*
" "" "0 - '*../+
C

$ " "" " 6 "" " " "
% "* .& " "
" " "& "D ;+"
""& " " " &"( )
+" "( " ) " "
D ;D C
315°
3.00
[Nm]
2.00
1.00
45°
Ship's domain
L=100[m]-L=300[m]
Ship's domain
L=100[m]-L=200[m]
270°
0.00
90°
Ship's domain
L=100[m]-L=100[m]
225°
135°
180°
D ;,E2" & ""27; "
315°
[Nm]
0°
3.00
2.00
1.00
45°
Ship's domain
L=300[m] L=300[m]
Ship's domain
L=100[m]-L=300[m]
270°
0.00
90°
225°
135°
180°
D C,E"& " "2; & ";"
+" +"
&"1 " ()
& " +" & " & "
+" # &"" " 8 9 "
& " 1"

. " "&" "*" "
" "& " ""D
270°
315°
0°
3.00
[Nm]
2.00
1.00
0.00
45°
90°
Average domain:
Ship L=100[m]
Average domain:
Ship L=200[m]
Average domain:
Ship L=300[m]
225°
135°
180°
D , "& " "27;@A
. "
+" "" "&"+"# &" * "
% " ""& " &+"
& "(2; ")&*+"" " &
& " "D F
[Nm]
0°
3.00
Ship's domain
L=100[m]-L=300[m]
315°
2.00
45°
Ship's domain
L=300[m]-L=100[m]
1.00
270°
0.00
90°
225°
135°
180°
D F,E"2;
($'$," "
+" " & "
+" " "*
# "
" "& " " "
F

" " (8 9D ) " "
"(+8 9D )D G+"&* H
D G,8 "" 8 9D
! " "8 9D & γ∈?2I(6
2 6 ) +"
* "# .& " &
"1" "8 9D D J
D J,8 9D ""1 "()K);K)7)2
($($+
"1 & " L
&%& " & "* %& #
'*..0+ ! " " &
+"" 1'())2++""1
G

& &/ ,/ .
&"& " 1*(
# )! " "" "( )
"# 6. "&
"" " " "
+" -*
" ; 2 "& D M & " " +"
& " % " "
)
)
D M,"1,)"; / & ""; "K)"2
6 & ""2 "
% " 8 9 " " (8 9D ) "
% " ""(&"1
" " ) -* "
" "(&"@°A)"&D 2
)
)
D 2, D " ; ( ) & " " " "
( C ),) "2J K) "7G )
-$
+" " " "
4 " " " "1
+" " """
J

" " +"*
1%& "+"""
+" " "
" ""1 % ""
" " +"
" " & "
0 '())/+
)"
.-+5NO:!$ :.N(72)P 3.D88
8 8172-9
.-+5NO:!$ :. N(7;) 3 22 " $
8 . . L ..L
.-+5NO:!$ :.N(7;)4 M " . 8
" 5 5
.-+5NO:!$ :. NK 5.N Q(7C) 5 ; 8!.+
5+:!$ :EK.9.R:.K5+:!$ :.9(2MMG)6 !
$ L$ &/9
NS!QK$ NK$ LHD(2MM;) QL CF
M

!
!"!
!
" #
$ %
& & &
' ' ( )
*
+
*
"#
# $ $ % $ &
' (!!) *$ + ,!,-
. /!)0%12$0 %
1!1$! " $# $
3!
4 -%.
/ ,5 ! ) 661 3
- / ,-../0 + 37
!-8 % % 9
+:+!!/
" " %
! 3 %
$ " !
(!;# $

% %% "!?3" " =%
. % $ ! 3 "
:$ " :.".%""
! < %
!
$#%&
# $ % ! $ %
3)4 9 + !)6+$ +
% !2$ , @! "4 3
! 2*, % ! 7
% $% 606$ + !%
-+:*!&!/%
% 0 $% % !8%
" $ !
# $ % % "
% % " % !4%
% % % A 4 % ! 3
9 9 % " %
% ! % "
B)))! - C %
4!&!/!7$ !!)%
% " !0% 12,
% 2 "4 !% %$%
"B)B! %% "
$ 2,6! % -2*/ 9
% % 3D
2*,!
$#"#&#
E % "%3>
3 ' ' ! 3 % " 0
4 ! 4 % ! 9 "
$%1,23330
% 7"
6@@ : F , 6@ % ! )
+%= $!
7% !7
. = 9 "" B<
!
4 # $ % % !
-/@> :3=GD
-" $/! % 20 !

"0% $H0
%% % ,!
49I "% 0% $"%@
*"*% % !9 "
"%$ !4"
% " $ % + %
6@06,!
(% % J220>>
-66*/%)#0+-666+/ ?0+-66@/3 ""4 ,23350!(!+
%)#0+""C666! -)#0+
+4DK/"$$!4($0' 26
> % % $"4 ,233503
$"% %$ !
8 % "".
!" 9 "
$%. %$
I" " !
3;;%%%! "!$+!;!%"!!
(!+!;3 )#0+"" $666C
% % $
" !
79,2+ B

N=OJ+6+; + 0$ % =!
"GJ+;4"% !)% . B

% !4
""$"%,0 !"
% " !&
! ) " %$
" %""0
" ' ( $! 4 7>?3 9
!) ""$%$
" % " $ "
% " !
%;
• 3=;2929*
• 3%;*$
• ?;+$"%
• F%;+9,' -/
• ?%;" $'
• &;+! 2
•

( 0" 6,23370
'#$#!./-
0 " H ! '
" !
F0%$" !)%
" $ I = .
! ? 9 " $ !
4$
=9!' %
$!
< "!
9 !)
90 -/ " !
9 %0$%
% 9="9!
0 - / " $ !
4 "
" !
-. /
!7@0* "% %!
% % " : %
9: !
0!
= "-0
/" 9!
!
3% !
% ! ' "
;
•
•
3% %: :
"$!4
!< =%%
=% % =
!
3 % 0 ! )
% !
4 $0: 0"%
L$M!
" "
!

#&7 % %
: %!
% % !
%! $%
" $ I !
% :%
!40,7 " 9 !
' ! <
9 " :9
" :%" % !
=
% ! "
" ! %
" ! ) $
!
,7%"%
" %I!

40 ." "%0
% !%
%9 %0 %!"
$ " 9 0
%!3 0 % %
9 ! .
" % "
" $!4
" % 6$;

F 4 % % % " % ! F "
B< % %$ ! B< .
00 ""! "
3' ' % 9"
!
) % = ! C
"!! ="
"! 4
" !A "
"" % !4 %$ % B<
! " $ $ %
!

(!*!;4#4A

(!6!;E +
9 4#4A< %$ 9
!"
! " % 9! E
"% !
0#$#
F "% " B

C)33!H

!
!" #
!$ !$
%
& %
% % '
&
"
!#
!"#
!"! $
"#
$ %&#% '!
### ### ())*++,"
(
$
$
$
$ ! )
$
###! !
* & + , )! ,
! - )&.#(/#
### (*0'+
* '+
1 ( '
2 3 4 ''5 %
!
6
! !,
, '!7 ! 384
92 %8'! '
& %
38'*&:/# )+
( $ )

!"% & '$
< !
'$1 )
) !0 &
5 *5+ ! -
,..."+ 5
% 5 9 5*95+ )'5*'5+
% 5
! ! 7
< !
7 55 *&
+ ! ! 5%
!95 !
%" &$
5 $ )
7 (
: 9! = . 7 = &
! !
8
; >2 ? )!
/ @ ,!
%"!
! !
7>!? 6& ! !!
! !& A )!82
' *82'+ !
1 !
) 6B! 7
!%( 5
C DB
0 ;
:
'
:")
:(;;

%"%
! 82'7
!(
• 1 !8E6
1 8 !5
A *5A + 7 :)41
8>?)8 ! $
! !
• 2 ! !88 !5A
88
5A !
!7 #41 ! : (")
: !)
!)

!!7
0 !
')?

; >A ?

?> ? > ?
') !
!)!! !!
!!) !!)
!
)" $$
)"!
> ? * :"
38'+ (
• !
• ! ! *. +
7 + !
*+
• ! *
!+
• 6! *
6 6 +
• 6!!
• 6
• 6 * +
1 * ) $ 7 +
• 3 )
!
! &
(
• !) (
• 7( 7 !
6 6
• ' ( )
• 6( ) 8
• ( 7
)
• 5 ( !
! 5
) )
3&
!!&
3 ) *!+ )
& !') H
4 )

; 6, = I
)"%
< 5 7
1 ! %%
!
< !! !
!%%(8 !! 5
8
&
2 !
&
!
<
!
2 !
)") -$
' )!
F ! &
& 95
'5
' )!! <
! !!
! ! !
7 ! !
> ? E **++*"+
!5% ! ! !
5%
! %
1! ! 7
7?E
D

$ & ! <
& ! ! !
A ! !
!*D#&:;#+)
*##&;#+!% !

! " #
$%&' (
)*("!* " !
+( + **+"
! * ! ! + ! ! , "
* " -.* #*+!
+!!*""!!! "
!! % ! ( !! ! ! + */
(!!!!*+!+* !
0** ! * " !+ **! !!
+!**!"" !!!!"
"(+* ! ! !"###$0**!
!!+("( ,!+*
*!**!(#*(!"" "( 1
*!,(#*!" "*!#
"" +!!!!""
,1""((#*!+
2 + ! ! * * " "" "! % *
**!"" !!+""(3
,* !*""!""! 4 2
"" . * *"" !
!"!!+"$%&!!"(
% , 56%)6 "* * *!
*"" * (*!"!!*(#*
+ " , (#* + " * ( * #"
(**!5,""!!" *
5&! *
!"#$
.7( """+!# &!+/ !*
"""" !""!

Governor
Command
Propulsion
Control
System
θ
Pitch
Control
System
Disturbances
*
θ
Propulsion
machine
$ )*
+ -
$ 5"
Propeller
Torque
9
Propeller
Thrust
. 5"
+
.)"
Ship
Resistance
-
)
Shaft
rotation
dynamics
7
: π&
9
÷
%
1-w
7
)
Disturbances
.7-,"""+!#
Ship
translation
dynamics
0" "(+*!+ !+(""
" ! ' ( *! * + ! *! (
!!!*" )-
7
% = ⋅ !-
= % + ;
0 ** "( (+ !+(""
1&( "1( !!!
!** )-
' = ⋅
& ⋅
7
: π
!& " -
= ' +
;
: π ⋅ &
& "" 1 , "" 1 ! +
!"*"(*"" !-
: 8
= ρ ⋅
⋅ ⋅ )
(
θ
:
' = ρ ⋅ ⋅ ⋅ ) (
θ
,""".:/ ,/ *
* (
= " !1*+ '
= ρ ⋅
⋅ ⋅ )
& "!! !/ ""+ &
! 2*""!<
$%,%= )# ! 2 ! + ! ( (
% 2+ ("! "*""
**!+**1!
!%&'(
,!" "!* 2!!**!(*
!"##+$0 !
!" ""(.7 2 )!**!*
! "/ """>! ?" * ,
"" ! "! ! !
2 , *>!""?(.:+
;
;
:
8

2 ,+!#!(>!""?8"-*1
$ * ! "" "!@!+!!. " (#*+!
!(#*!7/( ,*("!+! ( (+!
+ ! + * ! . !- $ * ! + ! ! +
! *!*(!( ,"" "!@
! ! +""!!(! (
$ )*
Shaft
rotation
dynamics
7
: π&
θ
$ 5"
Propeller
Torque
9
+ -
9
÷
Propeller
Thrust
%
. 5"
1-w
+
7
.)"
Ship
Resistance
-
)
Disturbances
.:-,!""+!#
Ship
translation
dynamics
Disturbances
"" +! ! ( ! ( *
! +"$ * @!(!"/+
' +! " ! " ! !" *
+! ! * " =* ! *
! 2" "!!!(*+!#! ,(
+( * " ! + *
**!+(! "" "!%!"
* 2""!1!"*""+
#-
* !"##+$ ( *1!
+*""" "A
"*",+&
&
τ ≡ : π ⋅
'
;
;
;
,+&-5"*1! ≡ ⋅ ≡ ⋅
+*>!""?
)
∂(
)
; θ = ,
;
∂(
θ = ,
,+!" ; !" * θ ∂)
θ
;
;
∂)
1 +"!
≡ ⋅ ≡ ⋅
)
∂θ
)
;
( = ,
;
∂θ
( = ,
,"B B !*! (* "
" " 5 + " 1 * " (
* "" ! & * A " " ( +
(!"*1!+*"""**! )"
**!**"*1$ * "" "!@!+!
C (#* +! C( ( + " A "
" =))"!**!! +*
, **))"!+-
(
∂)
;
τ
)
≡
%
⋅
(
;
;
∂)

-
= /- + .
= ,- +
/ 4 . " 4 , " 4 **( !
!" 4
,>!""?"))"!*+- 7
D
: −
7 ∂α
D
− −
D
;
−
D
∂
τ τ ∂
τ τ τ ∂'
=
⋅ +
⋅
D
− −
D
D
∂
:
:
∂
7 ∂
−
− ; −
τ
D
τ
τ
τ
τ
∂θ
D
∂α
D
D
D
∂
7
; ∂
∂
=
+
⋅ ; ; ; ;
⋅ '
D
D
∂
∂
D
; 7 ; ; ; ; ∂
D
∂θ
,""" " &**
*!***"*!E "++"""(
! ' ))"!(4"E +-
D
: −
7 ∂α
D
− −
D
;
−
D
∂
τ τ ∂
τ τ τ ∂'
=
⋅ +
⋅
D
− −
D
D
∂
:
:
∂
7 ∂
−
− ; −
τ
D
τ
τ
τ
τ
∂θ
D
D
∂α
∂
7 ; ;
; ; ;
D
D
D ∂
∂'
= ⋅ +
⋅
∂
; 7
D
; ; ; ;
∂
D
∂
D
∂)
−
; ; − +
D
∂θ
!!)#
)! "" ! !" 1 + " * (! = "
" ! !* ! !" " ; , "
"B B +"1 ",+&&

.-64" *="
.+"* (-%; ;7-1 ; 8F
("/78 ,*"$ * (
7;G*1!; ;7" " (8 FG ,*
" 78 ( "! * 1 % 7; *
" (" *H
,+&&-!+"!
!"" ;
&!
""
*" ""
" "
τ = 8 A τ
= HI
= −: IF = −8 A7
= 8 I = A A
*
% $%& ! 56%)6 + " (! !"+ *
"" !(, !+
!"##+$, !"+*! !"!*(!""
)+1 **! !"" *"
" + "" *! (! ! ( (
!!!
, * *! + " "" " (!
( ,! !*+"*+
. **! *"
*"
* !**** 1 ,*
+" *!
)!! "! ! !*(#* "
+** 1* +
,!"!+"* (!-
*$'
, ! ((#
*"+*(#* &!
(#*
"" !(#*
!(#*
-
= + + ) (!(#*+++(
. * + ! ( ! ! *
,
+ ( " * ! + "? + **! (
!!"+(#!*
F

%" (( 4"! ,
!( *"? ,(# !*+
! !
% " ! ( !
&*!*!""" " !++
*
"(!*"!++- = − ,"
!!
+ ! (
!""! ((#*
#!!( !!"!+
= + + + +
**! (
-
+ %
% #*! (#*!"
!+!(
*!
.!!! !*!++"+!!
! * + " + ( ! !
== """ !1 -
∂Φ 7
:
= −ρ
− ρ( ∇φ
⋅∇φ
−
) − ρ
+
∂
:
φ +!" ,+"!+""-
7 ,!"""2((*(*!
"!"" +- − ρ + J
7
:
: , ! " − ρ( ∇φ
⋅∇φ
− )
:
!+ " "
(!"" " J
∂Φ
," − ρ " * (*
∂
7
:
< ( ! − ρ( ∇φ
⋅∇φ
−
) !" ! %"" 2
:
∂Φ
!+!**! − ρ = ρζ
∂
,"* +- = + ρ −
+ ζ $**
***!*" *""!
**''+
,! >!""?+! !*(** 1!+
! )!"*"* **!"
*1+" ,"*(1"
+-
+ = % 7
−
−
(
)
%
,"?!+"( !*!
,"" . "" +"" " ,"!*!
. " " *!++*! "?" %
H

"!!*!

=! ! !#" !(-"! +
( $&$0 ! (! , * !
(->! **/"*!#?)&)0>! *E *!#?
$&)0>! *E +"!?)&)0>*+!#! ?
= ! " "! ! 5& ! &"
! **! +( ! * + +
! &!*! "*! *!#K
' ! "!"*! ! "!,
!*"!! !" ! ," *""!+
!! "
''.('$
,! "" ""! +"*">! **/"
*!#?. ,>! **/"*!#?/! # #-
= −
0 = )
+ ) )
+
(E " E E ! !**!
,1 -
'
= )
⋅ 0 = )
)
+ ) + )
/-0' ('$
/1023'$
'4 ('$
& ! ! ! !" * ! E L M >! !"?
%4" (.A 0+!#!!!*
*! ," !( ! (&(* !
*( "(( !!
&*E #" *+!#4 "(!+"" * +
*+!#!!! +""

("!!E ( +
!""" "!! " %$&)0""!
)
! "+ .F = !+ E ( N "
"!+! ( 1!#* !E ! +!"*,
! (45&!**! ,! -
= −
)
)
= )
0 = )
⋅
)
− )
⋅
)
+ )
+ )
⋅
)
⋅
)
+ )
+ )
)
⋅
)
⋅
+
.F- *E N +*!#
'4 (5
' E ! "!""*+ %)&)0!
(.H!+#"""
.H- *E +"!
.I-*+!#!
87

,! # #-
)
= )
−
)
θ = ) ⋅ + θ
)
@ "" "!* *"*"" "!# ,
**! ! ( ! "! . * "!
!! %"!!+
"!!
6'$
," **! ?*+!#! ?,!(!"!
!*!#,"!1!)!"" 1
( (+4"!*"( !!%
*"( *!"+ .I(
"*!
,&
, 2""+*""+
*1! &!+*""+ *
/ !" "! + * 2
"" , + + # !" ( 2 (
&" " "!"
, !" + !" ( ! "! * (
! !! * !+ * ( *1! + , !
! ( .7; (! +( ( *1!
!*1!!"" 7 ,""#"""4!*4
""*""
.7;-' !*1! O 7
. *( * *! * (# * +! " . "" E *
!"(.77 0 ! 2
1 )-
• , " **!"++( +! ""
1$ "" **"( **!""
, 2 "(1!**!
8:

• ,(!*. "" !" (##!!!
! ,!+**
!("!="
• , 56%)6 !" " ! !
(#,!>2?"!**!
=" !!
• ,*I; (*(4.77
$(#!!# *>2?"!*
; 7H;
&("+"!**!**"1"" "!
! (#* +! ! " E . "!
!!!+("+ !!!""( ,
*"!**!("E (.7: ! **!
!**! E ( *1! , **! * (#* +! E
! ( ( ! *1! , ! + 4" * (- ( *1!
+ (!"( *!*!"
& **!"( (
"!"**! %"*1!"
*!(#*
! *!#"+
D
∂
.77-,**!* 2/ *-
D
∂
D
∂%
( **! * (# */" $ - ( **! * (#
D
∂
8

∂
. "" -
∂
D
)
D
(**!E *(#
N ! * !# ! + ! (#* +! ! +
!"*+1*"+"" "!
N1!*"!( *1!
P; 7*!E !.7:

- '
,* (*! "" -
• *+!#! .IJ
• ! **"+*!#J
• ! *E N +*!#.FJ
• ! *E +"!.H
&!!"*!**! " +*
E
% ! * ! *1! " (! ! *1!
"+ ! >! * ? = ! ( *1! +
!+; 7H; !*1!(+ )""
#"""4! #"!*
- )
K t
variations
normalised by K variations of n control
t shaft
1.6
1.4
1.2
1
0.8
0.6
0.4
n shaft
control by fuelrack
no control
K t
& V s
control by fuelrack
0.2
10 −2 10 −1 ω [rad/s]
enc,(1−w)
10 0
.7-E (*! "
,*(.7 64!"*; ;7"! **
" * E > *+!# ! ? >E N ! ? (
!"+ + 6"! ; 7 *! ! * E /
! . E L N / ! ( 4"! + " * *
D
∂)
*!
D
∂'
&*1! !E * %" 4"
*! ! #" ! * ! *1! %
*1! 1 **! + ,
" !+"" 4"!
**!
% (*1!! *E N E *"!
,"++!+!*N ! "E ! " % (
!*1!"" "
8

+"!(!" "!! !
(#(!"!/"*7%"**"!"*E
(!+&" !"!"!( +
( + 4"! !
*1!! *E +"!( *!!*E +
D
∂) **!
D
∂θ
- !)
, " ! ( ( .78 , * ( #
+#!!-
• !*1!+"/!"*7/( J
• * ω
7−
,!!#"""
""4!!; 7H; % !
,+&&&J
• ! * E + "! "+ ( # " & * (
( E ! G & ( 7 E
!F;G &"2"!!+
!(J
• 4"! (! * " +*!#+"*
!"*(
.78-E (+(!*1!
,+&&&-% 2" !!"" ;
0" !
)8;;; " P ;
)A;;; " P ;
)87H; " P ;
ω
7−
; :8
; :F
7 7
8A

1
& !! "" ! ! + **! * !#
4" !**! "" + %
*!!"!!!+*! "
!"##+$ & * ( ! *1! " !
!**!+*"! *! +*!#
! +"" "!! +! .*1!!
!+(1("" "!! !**!
! "
, 2 "" " "! * *
*! *1! , * *! ( *
**!"+(! "!*!#,*
2!*+*/
."!**!4"!*"!
"" ! ( ! * "" # !! + *
"!!*" , !
"" ! ( * !# + +!
"*!!
$
,(#+"+""*"!5!
>56%)6? (! % ( $%&
!" , 56%)6 "! + "! * + *
"" **/! ,""!* !#(
)'
),%56)$% :;;8
- E&$/5.)/:;;/7A8 & =
N6E

!"#$$$
%
! " #$$$ !
!! & ' (
)
! "#
!""# ""$%
& "'! # (" "" " " "
'" )! " *
&'+""'*""'* !+
#("""
& "+ !'""
"&++" '"
'*
!!! *""'+"!!'""++
'"!!!'+!!
" "* ! !!' ! "'
' "'* * !","
+"" ! -" ! "
!"
!!!'!'' !!** "
)! "+ !!'"++!!"!
'+"*)"!!!'!!!'
!!'""+".+!*'*&/+
"0*!/!'"01 ! !!!'
"" !' ! * '+ , ""
)"+
"+ '+ !!'" "+ + ,!
)+'!!' * ""+ )
"""2 "'+'
)""''+""'''"3'
*+!4 !*'!.!!!'
'* " "& " !" ) " 5*

!""+,+"""
7 ! ! !!" " "!" ! !
"+")"' ''+
!"!!!#"'+""
! '+
$%%
7 " * 8998 8999 :4 ; .38;& " +
"" 4'%
o 1!!!'!+1!4
o 5" !!!'+
o 1 !'!"'*!!!'
o 5 "< !
1 " ' ! !!' + " !
!' ! "' . ;! " :&
"'" " !4"+ !
!4+ "'*
38; +"+!'+""'! "' "
+"++" *!!!'"!'" +
*'*! *"')* !'
" ! " + " " * ""
+""+!!
&'()+ !" '+'
'+38;' :" :
!#'+')"*# !" + 4
"!4:*#'+'."" +&
5!!'+'"+!41!"
#'+'+"+!!!:4 +'
+ ! #'+ ' * ! #'+
'"+:4!'"*" !!"!
, " : " * * " '
!*: ' *"!
*+,) :4 + .& )" " ,!"" +
'"*'- "38;:4
"+(;2:4"+*

'+ "* ! '+ + ) "
"" '+ 1 "" ! " '
#'+' ! !4!", '+
"'""! )" !#'+'*
)=+ 38;' +"
". 1 1& "'+!!'
+* #'+ '* :4 ) !
.#'+$*:& " ! * 3 7 +
" " ' + + '" ! +*
! *!!'1="'+
+ "1='"+ * "
" * + "" )" " !
'+"!'* !'
" !4 + +" * ' !4
""!
/* ! 00%
/!!$111!0
! < ' " !'" '
!! *!!'" "'*+
' "" '* " '* .
!'" 3 '* " ; * " "
! '" !'"'&
!!* * "!%""
!! 4 ! ! " ,! "
! '+ ! " ! " " " '*
"!!'
/$02
5 * ! * !! ! :"
2".:2&'* " :!!'";

! " 2*#"! !
*$#
" + +* ! * "
;B +

#!38;': 2;,++ *"
'" ! * " ! !"
! !4""*""!""
-""'"
4$,7-6
""+""*!!!!'
!'")*'!!!
" ! + * + )*
,'+F"!!) + !'""%
-6 0 6 , ' !4 ' "
!'""* '

o !4""+" "
o !""+"""
o $+'+'
o #'!!'""+"
o $+"!"
'* "
8,
* """.38;38H3&!'" '*
!"+!"* " ,
"'++
""'+* '*"+"!4
! "!!'""+
7 ,! * . +* " & :4
2"+-"*"'** !

++" !*+'
+'%
o :
o "".#:*!!*"&
o ".'"'""""&
o D
o @'*+!!*
)
** !!"!"

+"!-"!!
' + * ' " "
++!!"' "!!'
+;*! !4 #
!!!!'" !3#
";+L'+,'*M2@ ""
! *"'!!+NN" "';
' ' /0
5"+'"3" +!!"
' "*!(*"
"#"' ""!!*
!""""" "" !"
"" ,
$+ "+ "" < + 'O 1( !" " +
@'@ ' "+ ' " " "+
""*" !@'@+!*"!"
!!

"+5 !)*+"*"""/"0
. !& " " " * $( ."
'!& !!

;0 !!
8999 ; !'"* !' +"
"*"+' " !!
" " " +" "
""!" !'""'*+
++"" '*"*"
!!"! -
!4'++ !"!! -
!!'!'""++ *"
!4"!!!'
"'!"* !! 2
!' ! ' !" + "
# * " !!' ' " "* '
+'*"'"'
R

!
"#
#$
%&
%
%&$
%
%
%#
%
'#
(
)
*
*++
*$
*#
*
*#
*#
*#
*#
,
,
,
,
,
,$$
-
.
.
.
.#
.
/
/#
/
/!+
01
01#
0
0
0
0!
0!+
23
2#
2##
2$
4
4
45
4+
4
61
6$
6
61
6
6#15
7
7$
7$#
7$#
7
7&
7#
7+$+
8
8
95
9+
:1
:
:
:
:1
;
;
;
; #
;

COMPIT'06
!"" #$$%
&
!"
!#
$%
$&' $'
&
'& -.
()$*+ ,*#
/$
01 + $2
11 2)$)
)30 %$*
(&
4#030 +" $*
*# +3$*5
+$1
*# $
3 ' $ 67
# 0%$890-8: ;.
; ##-:.;
www.oudpoelgeest.nl
) & # #3 ;
3 /##69
& ?:;:>;8::9 @3A
"#*$"*#$$% + '
69;:6;8::B
:7;:?;8::B
88;:?;8::B
)& $$, -.
&h.t.grimmelius@wbmt.tudelft.nl
www.3ME.TUDelft.nl/COMPIT06
-&C