Download - Academy Publisher

Where: G
i
is the selection field of PMU
corresponding to LMU (i)
; m
i
is the number of PMU
in G i
; i is an integer and ranges from 0 to N-1; N is
the number of sub-tasks, namely the quantity of LMU in
LMP.
So, for the whole networked manufacturing task—
LMP described in ⑴, all PMU subsets can be obtained
and described as:
G = { G0,
G1,
⋅⋅⋅,
GN
−1}
⑶
This also is the selection fields of EMP,
2) Objective functions
For the whole networked manufacturing tasks
formulated by ⑴, EMP is orderly composed of N
PMU-s, marked as:
EMP = { PMU (0, k ),
PMU (1, k ), ⋅ ⋅ ⋅,
0
1
⑷
PMU ( N − 1, k N
)}
−1
Where: k
i
∈[ 0, mi
−1]
; PMU i,
k ) is the k i
-th
PMU in
G
i
;
i
(
i
m is the number of PMU in
G
i
.
In order to obtain the optimal EMP, each EMP
should be evaluated in terms of some qualitative or
quantitative criterions. In this paper, the following
three criterions will be considered: the least total
running cost—C, the least total running time—T and
the best total machining quality — Q. Thus, the
objectives functions are formulated by ⑸.
⎧
minC
⎪
= min( C + C
N −1
N − 2
) = min( ∑ C
i
( j)
+ ∑ C
i = 0
i = 0
in tr
⎪
⎪
⎨minT
= min( T
N −1
N − 2
+ T )= min( ∑ T ( j)
+ ∑ T
tr
i
in
i
⎪
i = 0
i = 0
⎪
⎪
⎪
minQ
⎩
N −1
= min ∑ (1 - Q
i
( j))
i = 0
i,
,
i
i
+ 1
+ 1
( j,
k ))
( j,
k ))
Where: PMU ( i,
j)
is the j -th in G
i
,
j ∈ [ 0, mi −1],
k ∈[0,
m i + 1
−1]
, i ∈[ 0, N −1]
m
i
is the number of PMU in G
i
, C i
( j)
is the
machining cost inside PMU ( i,
j)
, C i , i + 1
( j , k ) is the
transportation cost between PMU ( i,
j)
in G i
and
PMU ( i + 1, k)
in G
i + 1
, T i
( j)
is the machining time
inside PMU ( i,
j)
, T i , i+
1( j,
k)
is the transportation time
between PMU ( i,
j)
in G
i
and PMU ( i + 1, k)
in
G
i+1
, Qi ( j)
is the machining quality, which is
guaranteed by PMU ( i,
j)
, expressed by the rate of
certified parts quantity divided by all parts quantity.
3) Restriction conditions
For LMP, R and D are assumed as the released time
and the delivery time. C T and Q T are respectively
assumed as the total cost restriction and the total quality
restriction. During [R, D], all LMU-s in LMP must be
completed. Similarly, LMU (i) has a released time R i and
a delivery time D i , and has the cost, time and quality
restrictions expressed by C i , T i and Q i . During [R i , D i ],
all work procedures of LMU (i) must be completed. Thus,
the restriction conditions of networked manufacturing
resources optimization deployment for complicated part
include:
⑸
The sequence restriction of sub-tasks:if LMU(i)
must be completed before LMU(j), then
i i i j
R + T ≤ D ≤ R . ⑹
The running time restrictions of LMU (i):
i i
⎪
⎧maxT
( j)
≤ T ≤ ( D
i
N −1
N −2
⎨
max( ∑T
( j)
+ ∑T
i
i,
⎪⎩ i=
0
i=
0
i
− R )
( j,
k))
≤ ( R − D)
The running cost restrictions of LMU (i):
i
⎪
⎧maxCi
( j)
≤ C
N −1
N −2
⎨
max( ∑Ci
( j)
+ ∑Ci
⎪⎩ i=
0
i=
0
i+
1
, i+
1
( j,
k))
≤ C
The total quality restrictions of LMU (i):
N
⎪
⎧
∑ −
T
min 1 Q ( j) / N ≥ Q
i
⎨ i=
i
⎪⎩ minQ ( j)
≥ Q
i
T
⑺
⑻
0
⑼
Ⅳ. OPTIMIZING DEPLOYMENT ALGORITHMS
BASED ON GENETIC ALGORITHM
GA is widely applied in advanced manufacturing
fields, such as the optimum scheduling of workshop
resources, the partner selection of virtual enterprise. In
this paper, for the convenience and speediness of
computation, we transform the multi-objectives
optimization problem formulated by ⑸ into a single
objective optimization problem to solve with GA.
Exterior information is not almost used when
searching the best solution by GA, and only the value
of fitness function is taken into consideration. In order
to make the optimization result impersonal and precise,
we introduce the relative membership degree to the best
member of fuzzy mathematics into the designing of
relative fitness function.
A. Coding method
According to the characteristics of networked
manufacturing resources optimization deployment, the
integer coding method is applied in GA. The coding
regulations include:
• Coding the manufacturing subtask: the code is
0,1,…,N-1 (N is the number of subtasks, namely the
number of LMU in LMP).
• A gene of a chromosome corresponds to a LMU in
LMP, and the length of a chromosome, namely the
quantity of genes in a chromosome, is equal to the
quantity of LMU in LMP.
• Coding the manufacturing resources: the code is 0,
1,…, m −1, where m
i
i
is the quantity of PMU in G i
.
• A gene value of a chromosome corresponds to a
manufacturing resource, namely a PMU.
• x i (the i -th gene value of a chromosome) expresses
the xi
-th PMU in G i , and the corresponding
manufacturing subtask is the i -th LMU in LMP.
x is integer and 0 ≤ x p m .
i
i
• A chromosome corresponds to an EMP. For the
chromosome expressed by ⑽, the corresponding
EMP expressed by ⑾.
X [ x x ⋅⋅⋅ x ⋅⋅⋅ ]
i
x
⑽
1
=
0 1
N −
i
203