SEKE 2012 Proceedings - Knowledge Systems Institute

Multi-Objective Optimization of
Fuzzy Neural Networks for Software Modeling
Kuwen Li, Marek Z. Reformat, Witold Pedrycz
Electrical and Computer Engineering
University of Alberta
Edmonton, AB, Canada
{kuwen, reformat, wpedrycz}@ualberta.ca
Jinfeng Yu
College of Computer Science and Technology
Harbin, Heilongjiang Province
China, 150001
Abstract—Software modeling is used to provide better
understanding of features and attributes describing software
artifacts. This knowledge is applied to improve practices
leading to development of software that is easier to maintain
and reuse.
In the paper we use Fuzzy Neural Networks (FNNs) for
modeling purposes. This type of models allow for extracting
knowledge in the form of if-then rules. The process of
constructing FNN models involves structural as well as
parametric optimization. Additionally, software data
representing different classes of artifacts is often unbalanced
creating difficulties in building models that “cover” all classes
evenly.
We propose an application of Multi-Objective Evolutionary
Computing as a tool for constructing FNN models. We use
combinations of different measures to represent quality of
developed models from the point of view of their classification
capabilities. We extract rules from the constructed models, and
prune them to obtain clear and simple representations of
software artifacts.
I. INTRODUCTION
Development of models of different objects and artifacts
is one of the most popular approaches that allow us to gain
knowledge about these objects and artifacts , and provide us
with tractable approxim ations to reality. T here is an
abundance of definitions of the w ord ‘model’. A common
definition, expressed in the wo rds of Neelamkavil [1], is
very illustrative: “A model is a sim plified representation of
a system intended to enhance our ability to understand,
predict and possibly control the behavior of the system.”
Among all different m odels the ones that are of special
interest are white-box models. These models allow us to
“look inside” and find relations that exists between
attributes and features descri bing considered objects and
artifacts. Such an approach is used in software engineering
where software objects are m odeled in order to gain
knowledge about relations between software metrics
describing these objects and their quality attributes.
Development of software object models is challenging due
to imbalance of software data , i.e., uneven distribution of
different classes of software objects. This means that
developed models are not able to model classes of objects
that are poorly represented in the available data. This also
affects extraction of knowledge, i.e., the knowledge about
these classes is incomplete and unreliable.
In this paper we address the problem of building
software models based on imbalanced data via combining a
number of methods and approaches: Fuzzy Neural Networks
(FNNs) as data models w ith abstraction and knowledge
extraction capabilities, Evolutionary Computing (EC) as an
optimization tool w ith easiness of introduction of different
objectives, Pareto approach as a m ulti-objective
optimization method with the ab ility to “generate” a set of
results satisfying different objectives, and different
measures as representations of m odel quality: accuracy,
specificity, sensitivity(recall), and precision.
II. FUZZY NEURAL NETWORK MODEL
The fuzzy OR/AND neurons [2] are the fundamental
parts of our Fuzzy Neur al Network model. The OR/ AND
neuron arranges AND and OR neurons in the way illustrated
in Figure 1.
x
w
u
AND
OR
z1
z2
v
OR/AND
Figure 1. Architecture of OR/AND neuron
In essence, the outputs of two “input neurons” are
aggregated (weighted) using the OR neuron located in the
output layer:
z 1 = AND(x; w); z 2 = OR(x; u); y = OR(z; v).
The evident advantage of the OR/AND neurons resides
with their significant interpreta bility capabilities. N ote that
if v 1 = 1 and v 2 = 0 we end up with a “pure” and-wise
aggregation. The combination of v 1 = 0 and v 2 = 1 leads to
the “pure” or-wise aggregation of the inputs. A whole
spectrum of situations in-between the pure and and or
OR
y
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