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Preface
Bob Stern of CRC Press, to whom I am indebted, approached me in late 1999
asking if I was interested in developing a second edition of volume I of the
Practical Handbook of Genetic Algorithms. My immediate response was an
unequivocal “Yes!” This is the fourth book I have edited in the series and each
time I have learned more about GAs and people working in the field. I am proud
to be associated with each and every person with whom I have dealt with over the
years. Each is dedicated to his or her work, committed to the spread of knowledge
and has something of significant value to contribute.
This second edition of the first volume comes a number of years after the
publication of the first. The reasons for this new edition arose because of the
popularity of the first edition and the need to perform a number of functions for
the GA community. These “functions” fall into two main categories: the need to
keep practitioners abreast of recent discoveries/learning in the field and to very
specifically update some of the best chapters from the first volume.
The book leads off with chapter 0, which is the same chapter as the first edition
by Jim Everett on model building, model testing and model fitting. An excellent
“How and Why.” This chapter offers an excellent lead into the whole area of
models and offers some sensible discussion of the use of genetic algorithms,
which depends on a clear view of the nature of quantitative model building and
testing. It considers the formulation of such models and the various approaches
that might be taken to fit model parameters. Available optimization methods are
discussed, ranging from analytical methods, through various types of hillclimbing,
randomized search and genetic algorithms. A number of examples
illustrate that modeling problems do not fall neatly into this clear-cut hierarchy.
Consequently, a judicious selection of hybrid methods, selected according to the
model context, is preferred to any pure method alone in designing efficient and
effective methods for fitting parameters to quantitative models.
Chapter 1 by Roubos and Setnes deals with the automatic design of fuzzy rulebased
models and classifiers from data. It is recognized that both accuracy and
transparency are of major importance and we seek to keep the rule-based models
small and comprehensible. An iterative approach for developing such fuzzy rulebased
models is proposed. First, an initial model is derived from the data.
Subsequently, a real-coded GA is applied in an iterative fashion, together with a
rule-based simplification algorithm to optimize and simplify the model,
respectively. The proposed modeling approach is demonstrated for a system
identification and a classification problem. Results are compared to other
approaches in the literature. The proposed modeling approach is more compact
and interpretable.
Goldberg and Hammerham in Chapter 2, have extended their contribution to
Volume III of the series (Chapter 6, pp 119–238) by describing their current
research, which applies this technology to a different problem area, designing
automata that can recognize languages given a list of representative words in the
language and a list of other words not in the language. The experimentation
carried out indicates that in this problem domain also, smaller machine solutions
are obtained by the MTF operator than the benchmark. Due to the small variation
of machine sizes in the solution spaces of the languages tested (obtained
empirically by Monte Carlo methods), MTF is expected to find solutions in a
similar number of iterations as the other methods. While SFS obtained faster
convergence on more languages than any other method, MTF has the overall best
performance based on a more comprehensive set of evaluation criteria.
Taplin and Qiu, in Chapter 3, have contibuted material that very firmly grounds
GA in solving real-world problems by employing GAs to solve the very complex
problems associated with the staging of road construction projects. The task of
selecting and scheduling a sequence of road construction and improvement
projects is complicated by two characteristics of the road network. The first is that
the impacts and benefits of previous projects are modified by succeeding ones
because each changes some part of what is a highly interactive network. The
change in benefits results from the choices made by road users to take advantage
of whatever routes seem best to them as links are modified. The second problem
is that some projects generate benefits as they are constructed, whereas others
generate no benefits until they are completed.
There are three general ways of determining a schedule of road projects. The
default method has been used to evaluate each project as if its impacts and
benefits would be independent of all other projects and then to use the resulting
cost-benefit ratios to rank the projects. This is far from optimal because the
interactions are ignored. An improved method is to use rolling or sequential
assessment. In this case, the first year’s projects are selected, as before, by
independent evaluation. Then all remaining projects are reevaluated, taking
account of the impacts of the first-year projects, and so on through successive
years. The resulting schedule is still sub-optimal but better than the simple
ranking.
Another option is to construct a mathematical program. This can take account of
some of the interactions between projects. In a linear program, it is easy to specify
relationships such as a particular project not starting before another specific
project or a cost reduction if two projects are scheduled in succession. Fairly
simple traffic interactions can also be handled but network-wide traffic effects
have to be analysed by a traffic assignment model (itself a complex programming
task). Also, it is difficult to cope with deferred project benefits. Nevertheless,
mathematical programming has been used to some extent for road project
scheduling.
The novel option, introduced in this chapter, is to employ a GA which offers a
convenient way of handling a scheduling problem closely allied to the travelling
salesman problem while coping with a series of extraneous constraints and an
objective function which has at its core a substantial optimising algorithm to
allocate traffic.
The authors from City University of Hong Kong are Zhang, Chung, Lo, Hui, and
Wu. Their contribution, Chapter 4, deals with the optimization of electronic
circuits. It presents an implementation of a decoupled optimization technique for
the design of switching regulators. The optimization process entails selection of
the component values in the regulator to meet the static and dynamic
requirements. Although the proposed approach inherits characteristics of
evolutionary computations that involve randomness, recombination, and survival
of the fittest, it does not perform a whole-circuit optimization. Consequently,
intensive computations that are usually found in stochastic optimization
techniques can be avoided. In the proposed optimization scheme, a regulator is
decoupled into two components, namely, the power conversion stage (PCS) and
the feedback network (FN). The PCS is optimized with the required static
characteristics such as the input voltage and output load range, whils”t the FN is
optimized with the required static characteristics of the whole system and the
dynamic responses during the input and output disturbances. Systematic
procedures for optimizing circuit components are described. The proposed
technique is illustrated with the design of a buck regulator with overcurrent
protection. The predicted results are compared with the published results
available in the literature and are verified with experimental measurements.
Chapter 5 by Hallinan discusses the problems of feature selection and
classification in the diagnosis of cervical cancer. Cervical cancer is one of the
most common cancers, accounting for 6% of all malignancies in women. The
standard screening test for cervical cancer is the Papanicolaou (or “Pap”) smear,
which involves visual examination of cervical cells under a microscope for
evidence of abnormality.
Pap smear screening is labour-intensive and boring, but requires high precision,
and thus appears on the surface to be extremely suitable for automation. Research
has been done in this area since the late 1950s; it is one of the “classical”
problems in automated image analysis.
In the last four decades or so, with the advent of powerful, reasonably priced
computers and sophisticated algorithms, an alternative to the identification of
malignant cells on a slide has become possible.
The approach to detection generally used is to capture digital images of visually
normal cells from patients of known diagnosis (cancerous/precancerous condition
or normal). A variety of features such as nuclear area, optical density, shape and
texture features are then calculated from the images, and linear discriminant
analysis is used to classify individual cells as either “normal” or “abnormal.” An
individual is then given a diagnosis on the basis of the proportion of abnormal
cells detected on her Pap smear slide.
The problem with this approach is that while all visually normal cells from
“normal” (i.e., cancer-free) patients may be assumed to be normal, not all such
cells from “abnormal” patients will, in fact, be abnormal. The proportion of
affected cells from an abnormal patient is not known a priori, and probably varies
with the stage of the cancer, its rate of progression, and possibly other factors.
This means that the “abnormal” cells used for establishing the canonical
discriminant function are not, in fact, all abnormal, which reduces the accuracy of
the classifier. Further noise is introduced into the classification procedure by the
existence of two more-or-less arbitrary cutoff values – the value of the
discriminant score at which individual cells are classified as “normal” or
“abnormal,” and the proportion of “abnormal” cells used to classify a patient as
“normal” or “abnormal.”
GAs are employed to improve the ability of the system to discriminate and
therefore enhance classification.
Chapter 6, dealing with “Algorithms for Multidimensional Scaling,” offers
insights into looking at the potential for using GAs to map a set of objects in a
multidimensional space. GAs have a couple of advantages over the standard
multidimensional scaling procedures that appear in many commercial computer
packages. The most frequently cited advantage of Gas – the ability to avoid being
trapped in a local optimum – applies in the case of multidimensional scaling.
Using a GA or at least a hybrid GA, offers the opportunity to freely choose an
appropriate objective function. This avoids the restrictions of the commercial
packages, where the objective function is usually a standard function chosen for
its stability of convergence rather than for its applicability to the user’s particular
research problem. The chapter details genetic operators appropriate to this class of
problem, and uses them to build a GA for multidimensional scaling with fitness
functions that can be chosen by the user. The algorithm is tested on a realistic
problem, which shows that it converges to the global optimum in cases where a
systematic hill-descending method becomes entrapped at a local optimum. The
chapter also looks at how considerable computation effort can be saved with no
loss of accuracy by using a hybrid method. For hybrid methods, the GA is
brought in to “fine-tune” a solution, which has first been obtained using standard
multidimensional scaling methods.
Chapter 7 by Lam and Yin describes various applications of GAs to transportation
optimization problems. In the first section, GAs are employed as solution
algorithms for advanced transport models; while in the second section, GAs are
used as calibration tools for complex transport models. Both sections show that,
similar to other fields, GAs provide an alternative powerful tool to a wide variety
of problems in the transportation domain.
It is well-known that many decision-making problems in transportation planning
and management could be formulated as bilevel programming models (singleobjective
or multi-objectives), that are intrinsically non-convex and it is thus
difficult to find the global optimum. In the first example, a genetic-algorithmsbased
(GAB) approach is proposed to solve the single-objective models.
Compared with the previous heuristic algorithms, the GAB approach is much
simpler in principle and more efficient in applications. In the second example, the
GAB approach to accommodate multi-objective bilevel programming models is
extended. It is shown that this approach can capture a number of Pareto solutions
efficiently and simultaneously which can be attributed to the parallelism and
globality of GAs.
Varela, Vela, Puente, Gomez and Vidal in Chapter 8 describe an approach to
solve job shop scheduling problems by means of a GA which is adapted to the
problem in various ways. First, a number of adjustments of the evaluation
function are suggested; and then it is proposed that a strategy to generate a
number of chromosomes of the initial population allows the introduction of
heuristic knowledge from the problem domain. In order to do that, the variable
and value ordering heuristics proposed by Norman Sadeh are exploited. These are
a class of probability-based heuristics which are, in principle, set to guide a
backtracking search strategy. The chapter validates all of the refinements
introduced on well known benchmarks and reports experimental results showing
that the introduction of the proposed refinements has an accumulative and
positive effect on the performance of the GA.
Chapter 9, developed by Raich and Ghaboussi, discusses an evolutionary-based
method called the implicit redundant representation genetic algorithm (IRR GA)
is applied to evolve synthesis design solutions for an unstructured, multi-objective
frame problem domain. The synthesis of frame structures presents a design
problem that is difficult, if not impossible, for current design and optimization
methods to formulate, let alone search. Searching for synthesis design solutions
requires the optimization of structures with diverse structural topology and
geometry. The topology and geometry define the number and the location of
beams and columns in the frame structure. As the topology and geometry change
during the search process, the number of design variables also change. To support
the search for synthesis design solutions, an unstructured problem formulation
that removes constraints that specify the number of design variables is used.
Current optimization methods, including the simple genetic algorithm (SGA), are
not able to model unstructured problem domains since these methods are not
flexible enough to change the number of design variables optimized. The
unstructured domain can be modeled successfully using the location-independent
and redundant IRR GA representation.
The IRR GA uses redundancy to encode a variable number of locationindependent
design variables in the representation of the problem domain. During
evolution, the number and locations of the encoded variables dynamically change
within each individual and across the population. The IRR GA provides several
benefits: redundant segments protect existing encoded design variables from the
disruption of crossover and mutation; new design variables may be designated
within previously redundant segments; and the dimensions of the search space
dynamically change as the number of design variables represented changes. The
IRR GA synthesis design method is capable of generating novel frame designs
that compare favorably with solutions obtained using a trial-and-error design
process.
Craenen, Eiben and Marchiori in Chapter 10 develop a contribution that describes
evolutionary algorithms (EAs) for constraint handling. Constraint handling is not
straightforward in an EA because the search operators mutation and
recombination are “blind” to constraints. Hence, there is no guarantee that if the
parents satisfy some constraints the offspring will satisfy them as well. This
suggests that the presence of constraints in a problem makes EAs intrinsically
unsuited to solve this problem. This should especially hold when the problem
does not contain an objective function to be optimized, but only constraints – the
category of constraint satisfaction problems. A survey of related literature,
however, indicates that there are quite a few successful attempts to evolutionary
constraint satisfaction. Based on this survey, the authors identify a number of
common features in these approaches and arrive at the conclusion that EAs can be
effective constraint solvers when knowledge about the constraints is incorporated
either into the genetic operators, in the fitness function, or in repair mechanisms.
The chapter concludes by considering a number of key questions on research
methodology.
Chapter 11 provides a very valuable approach to fine-tuning fuzzy rules. The
chapter presents the design of a fuzzy logic controller (FLC) for a boost-type
power factor corrector. A systematic offline design approach using the genetic
algorithm to optimize the input and output fuzzy subsets in the FLC is proposed.
Apart from avoiding complexities associated with nonlinear mathematical
modeling of switching converters, circuit designers do not have to perform timeconsuming
procedures of fine-tuning the fuzzy rules, which require sophisticated
experience and intuitive reasoning as in many classical fuzzy-logic-controlled
applications. Optimized by a multi-objective fitness function, the proposed
control scheme integrates the FLC into the feedback path and a linear
programming rule on controlling the duty time of the switch for shaping the input
current waveform, making it unnecessary to sense the rectified input voltage. A
200-W experimental prototype has been built. The steady-state and transient
responses of the converter under a large-signal change in the supply voltage and
in the output load are investigated.
In Chapter 12, Grundler, from the University of Zagreb describes a new method
of complex process control with the coordinating control unit based upon a
genetic algorithm. The algorithm for the control of complex processes controlled
by PID and fuzzy regulators at the first level and coordinating unit at the second
level has been theoretically laid out. A genetic algorithm and its application to the
proposed control method have been described in detail. The idea has been verified
experimentally and by simulation in a two-stage laboratory plant. Minimal energy
consumption criteria limited by given process response constraints have been
applied, and improvements in relation to other known optimizing methods have
been made. Independent and non-coordinating PID and fuzzy regulator parameter
tuning have been performed using a genetic algorithm and the results achieved are
the same or better than those obtained from traditional optimizing methods while
at the same time the method proposed can be easily automated. Multilevel
coordinated control using a genetic algorithm applied to a PID and a fuzzy
regulator has been researched. The results of various traditional optimizing
methods have been compared with an independent non-coordinating control and
multilevel coordinating control using a genetic algorithm.
Chapter 13 discusses GA approaches to cancer treatment. The aim of radiation
therapy is to cure the patient of malignant disease by irradiating tumours and
infected tissue, whilst minimising the risk of complications by avoiding
irradiation of normal tissue. To achieve this, a treatment plan, specifying a
number of variables, including beam directions, energies and other factors, must
be devised. At present, plans are developed by radiotherapy physicists, employing
a time-consuming iterative approach. However, with advances in treatment
technology which will make higher demands on planning soon to be available in
clinical centres, computer optimisation of treatment plan parameters is being
actively researched. These optimisation systems can provide treatment solutions
that better approach the aims of therapy. However, direct optimisation of
treatment goals by computer remains a time-consuming and computationally
expensive process. With the increases in the demand for patient throughput, a
more efficient means of planning treatments would be beneficial. Previous work
by Knowles (1997) described a system which employs artificial neural networks
to devise treatment plans for abdominal cancers. Plan parameters are produced
instantly upon input of seven simple values, easily measured from the CT-scan of
the patient. The neural network used in Knowles (1997) was trained with fairly
standard backpropagation (Rumelhart et al., 1986) coupled with an adaptive
momentum scheme. This chapter focuses on later work in which the neural
network is trained using evolutionary algorithms. Results show that the neural
network employing evolutionary training exhibits significantly better
generalisation performance than the original system developed. Testing of the
evolutionary neural network on clinical planning tasks at Royal Berkshire
Hospital in Reading, UK, has been carried out. It was found that the system can
readily produce clinically useful treatment plans, considerably quicker than the
human-based iterative method. Finally, a new neural network system for breast
cancer treatment planning was developed. As plans for breast cancer treatments
differ greatly from plans for abdominal cancer treatments, a new network
architecture was required. The system developed has again been tested on clinical
planning tasks at Royal Berkshire Hospital and results show that, in some cases,
plans which improve on those produced by the hospital are generated.
For those of you who are well-entrenched in the field, there are authors that you
will recognise as being some of the best; and for those of you who are new to
Gas, the same will apply – these are names you will certainly come to know and
respect. The contributors to this edition come from a cross-section of academia
and industry – theoreticians and practitioners. All make a significant contribution
to our understanding of and ability to use GAs.
One of the main objectives of the series has been to develop a work that will allow
practitioners to take the material offered and use it productively in their own work.
This edition maintains that objective. To that end, some contributors have also
included computer code so that their work can be duplicated and used productively
in your own endeavours. I will willingly e-mail the code to you if you send a
request to lchambers@transport.wa.gov.au or it may be found on the CRC Press
web site at www.crcpress.com.
The science and art of GA programming and application has come a long way in
the last 5 years since the publication of the first edition. However, I consider GAs
as still being a “new science” that has a long way to go before the bounds of the
effects are well-defined and their ability to contribute in a meaningful manner to
many fields of human endeavour are exhausted. We are, metaphorically, still
“scratching the surface” of our understanding and applications of GAs. This book
is designed to help scratch that surface just a little bit deeper and a little bit more.
As in the previous volumes, authors have come from countries around the world.
In a world, which we are told is continually shrinking, it is pleasing to obtain first
hand evidence of this shrinkage. As in the earlier volumes all communications
were by e-mail which has dramatically sped up the whole process. But even so, a
work of this nature invariably takes time.
The development of a chapter contribution to any field of serious endeavour is a
task that must, of need, be taken on only after serious consideration and
contemplation. I am happy to say that I believe all the authors contributing to this
volume have gone through those processes and I believe that because of the
manifest quality of the work presented.
Lance Chambers
Perth, Western Australia
lchambers@transport.wa.gov.au
Note: I have not Americanised (sic) the spelling of English spelling contributors.
So, as you read, you will find a number of words with s’s where you may expect
z’s, and you may find a large number of u’s where you might least expect them as
in the word, “colour” and “behaviour.” Please do not be perturbed. I believe the
authors have the right to see their work in a form each recognises. I also have not
altered the referencing forms used (we all understand the various forms and this
should not detract from the book, but hopefully add some individuality) by the
authors.
Ultimately, however, I am responsible for all alterations, errors and omissions.

Contents
Chapter 0 Model Building, Model Testing and Model Fitting
0.1 Uses of Genetic Algorithms
0.1.1 Optimizing or Improving the Performance of Operating Systems
0.1.2 Testing and Fitting Quantitative Models
0.1.3 Maximizing vs. Minimizing
0.1.4 Purpose of this Chapter
0.2 Quantitative Models
0.2.1 Parameters
0.2.2 Revising the Model or Revising the Data?
0.2.3 Hierarchic or Stepwise Model Building: The Role of Theory
0.2.4 Significance and Meaningfulness
0.3 Analytical Optimization
0.3.1 An Example: Linear Regression
0.4 Iterative Hill-Climbing Techniques
0.4.1 Iterative Incremental Stepping Method
0.4.2 An Example: Fitting the Continents Together
0.4.3 Other Hill-Climbing Methods
0.4.4 The Danger of Entrapment on Local Optima and Saddle Points
0.4.5 The Application of Genetic Algorithms to Model Fitting
0.5 Assay Continuity in a Gold Prospect
0.5.1 Description of the Problem
0.5.2 A Model of Data Continuity
0.5.3 Fitting the Data to the Model
0.5.4 The Appropriate Misfit Function
0.5.5 Fitting Models of One or Two Parameters
0.5.6 Fitting the Non-homogeneous Model 3
0.6 Conclusion
Reference
Chapter 1 Compact Fuzzy Models and Classifiers through Model
Reduction and Evolutionary Optimization
1.1 Introduction
1.2 Fuzzy Modeling
1.2.1 The Takagi-Sugeno Fuzzy Model
1.2.2 Data-Driven Identification by Clustering
1.2.3 Estimating the Consequent Parameters
1.3 Transparency and Accuracy of Fuzzy Models
1.3.1 Rule Base Simplification
1.3.2 Genetic Multi-objective Optimization
1.4 Genetic Algorithms
1.4.1 Fuzzy Model Representation
1.4.2 Selection Function
1.4.3 Genetic Operators
1.4.4 Crossover Operators
1.4.5 Mutation Operators
1.4.5.1 Constraints
1.5 Examples
1.5.1 Nonlinear Plant
1.5.2 Proposed approach
1.6 TS Singleton Model
1.7 TS Linear Model
1.7.1 Iris Classification Problem
1.7.2 Solutions in the literature
1.7.3 Proposed Approach
1.8 Conclusion
References
Chapter 2 On the Application of Reorganization Operators for Solving a
Language Recognition Problem
2.1 Introduction
2.1.1 Performance across a New Problem Set
2.1.2 Previous Work
2.2 Reorganization Operators
2.2.1 The Jefferson Benchmark
2.2.2 MTF
2.2.3 SFS
2.2.4 Competition
2.3 The Experimentation
2.3.1 The Languages
2.3.2 Specific Considerations for the Language Recognition Problem
2.4 Data Obtained from the Experimentation
2.5 General Evaluation Criteria
2.6 Evaluation
2.6.1 Machine Size
2.6.2 Convergence Rates
2.6.3 Performance of MTF
2.7 Conclusions and Further Directions
References
Chapter 3 Using GA to Optimise the Selection and Scheduling of Road
Projects
3.1 Introduction
3.2 Formulation of the Genetic Algorithm
3.2.1 The Objective
3.2.2 The Elements of the Project Schedule
3.2.3 The Genetic Algorithm
3.3 Mapping the GA String into a Project Schedule and Computing
the Fitness
3.3.1 Data Required
3.3.2 Imposing Constraints
3.3.3 Calculation of Project Benefits
3.3.4 Calculating Trip Generation, Route Choice and Link Loads
3.4 Results
3.4.1 Convergence of Solutions to the Problem
3.4.2 The Solutions
3.4.3 Similarity and Dissimilarity of Solutions: Euclidean Distance
3.5 Conclusions: Scheduling Interactive Road Projects by GA
3.5.1 Dissimilar Construction Schedules with High and Almost Equal Payoffs
3.5.2 Similar Construction Schedules with Dissimilar Payoffs
References
Chapter 4 Decoupled Optimization of Power Electronics Circuits Using
Genetic Algorithms
4.1 Introduction
4.2 Decoupled Regulator Configuration
4.2.1 Optimization Mechanism of GA
4.2.2 Chromosome and Population Structures
4.2.3 Fitness Functions
4.3 Fitness Function for PCS
4.3.1 OF1 for Objective (1)
4.3.2 OF2 for Objective (2)
4.3.3 OF3 for Objective (3)
4.3.4 OF4 for Objective (4)
4.4 Fitness function for FN
4.4.1 OF5 for Objective (1)
4.4.2 OF6 and OF8 for Objective (2) and Objective (4)
4.4.3 OF8 of Objective (3)
4.5 Steps of Optimization
4.6 Design Example
4.7 Conclusions
References
Chapter 5 Feature Selection and Classification in the Diagnosis of
Cervical Cancer
5.1 Introduction
5.2 Feature Selection
5.3 Feature Selection by Genetic Algorithm
5.3.1 GA Encoding Schemes
5.3.2 GAs and Neural Networks
5.3.3 GA Feature Selection Performance
5.3.4 Conclusions
5.4 Developing a Neural Genetic Classifier
5.4.1 Algorithm Design Issues
5.4.2 Problem Representation
5.4.3 Objective Function
5.4.4 Selection Strategy
5.4.5 Parameterization
5.5 Validation of the Algorithm
5.5.1 The Dataset
5.5.2 Experiments on Two-Dimensional Data
5.5.3 Results of Two-Dimensional Data Experiments
5.5.4 Lessons from Artificial Data
5.5.5 Experiments on a Cell Image Dataset
5.6 Parameterization of the GA
5.6.1 Parameterization Experiments
5.6.2 Results of Parameterization Experiments
5.6.3 Selecting the Neural Network Architecture
5.7 Experiments with the Cell Image Dataset
5.7.1 Slide-Based vs. Cell-Based Features
5.7.2 Comparison with the Standard Approach
5.7.3 Discussion
References
Chapter 6 Algorithms for Multidimensional Scaling
6.1 Introduction
6.1.1 Scope of This Chapter
6.1.2 What is Multidimensional Scaling?
6.1.3 Standard Multidimensional Scaling Techniques
6.2 Multidimensional Scaling Examined in More Detail
6.2.1 A Simple One-Dimensional Example
6.2.2 More than One Dimension
6.2.3 Using Standard Multidimensional Scaling Methods
6.3 A Genetic Algorithm for Multidimensional Scaling
6.3.1 Random Mutation Operators
6.3.2 Crossover Operators
6.3.3 Selection Operators
6.3.4 Design and Use of a Genetic Algorithm for Multidimensional Scaling
6.4 Experimental Results
6.4.1 Systematic Projection
6.4.2 Using the Genetic Algorithm
6.4.3 A Hybrid Approach
6.5 The Computer Program
6.5.1 The Extend Model
6.5.2 Definition of Parameters and Variables
6.5.3 The Main Program
6.5.4 Procedures and Functions
6.5.5 Adapting the Program for C or C++
6.6 Using the Extend Program
References
Chapter 7 Genetic Algorithm-Based Approach for Transportation
Optimization Problems
7.1 GA-Based Solution Approach for Transport Models
7.1.1 Introduction
7.1.2 GAB Approach for Single-Objective Bilevel Programming Models
7.1.3 GAB Approach for Multi-Objective Bilevel Programming Models
7.1.4 Summary
7.2 GAB Calibration Approach for Transport Models
7.2.1 Introduction
7.2.2 Review of TFS
7.2.3 Calibration Measures
7.2.4 GAB Calibration Procedure
7.2.5 Calibration of TFS
7.2.6 Case Study
7.2.7 Summary
7.3 Concluding Remarks
References
Appendix I: Notation
Chapter 8 Solving Job-Shop Scheduling Problems by Means of Genetic
Algorithms
8.1 Introduction
8.2 The Job-Shop Scheduling Constraint Satisfaction Problem
8.3 The Genetic Algorithm
8.4 Fitness Refinement
8.4.1 Variable and Value Ordering Heuristics
8.5 Heuristic Initial Population
8.6 Experimental Results
8.7 Conclusions
References
Chapter 9 Applying the Implicit Redundant Representation Genetic
Algorithm in an Unstructured Problem Domain
9.1 Introduction
9.2 Motivation for Frame Synthesis Research
9.2.1 Modeling the Conceptual Design Process
9.2.2 Research in Frame Optimization
9.3 The Implicit Redundant Representation Genetic Algorithm
9.3.1 Implementation of the IRR GA Algorithm
9.3.2 Suitability of the IRR GA in Conceptual Design
9.4 The IRR Genotype/Phenotype Representation
9.4.1 Provision of Dynamic Redundancy
9.4.2 Controlling the Level of Redundancy in the IRR GA Initial Population
9.5 Applying the IRR GA to Frame Design Synthesis in an
Unstructured Domain
9.5.1 Unstructured Design Problem Formulation
9.5.2 IRR GA Genotype/Phenotype Representation for Frame Design Synthesis
9.5.3 Use of Repair Strategies on Frame Design Alternatives
9.5.4 Generation of Horizontal Members in Design Synthesis Alternatives
9.5.5 Specification of Loads on Unstructured Frame Design Alternatives
9.5.6 Finite-Element Analysis of Frame Structures
9.5.7 Deletion of Dynamically Allocated Nodal Linked Lists
9.6 IRR GA Fitness Evaluation of Frame Design Synthesis
Alternatives
9.6.1 Statement of Frame Design Objectives Used as Fitness Functions
9.6.2 Application of Penalty Terms in IRR GA Fitness Evaluation
9.7 Discussion of the Genetic Control Operators Used by the IRR GA
9.7.1 Fitness Sharing among Individuals in the Population
9.7.2 Tournament Selection of New Population Individuals
9.7.3 Multiple Point Crossover of Binary Strings
9.7.4 Single-Bit Mutation of Binary Strings
9.8 Results of the Implicit Redundant Representation Frame
Synthesis Trials
9.8.1 Evolved Design Solutions for the Frame Synthesis Unstructured Domain
9.8.2 Synthesis versus Optimization of Frame Design Solutions Using IRR GA
9.9 Concluding Remarks
References
Chapter 10 How to Handle Constraints with Evolutionary Algorithms
10.1 Introduction
10.2 Constraint Handling in EAs
10.3 Evolutionary CSP Solvers
10.3.1 Heuristic Genetic Operators
10.3.2 Knowledge-Based Fitness and Genetic Operators
10.3.3 Glass-Box Approach
10.3.4 Genetic Local Search
10.3.5 Co-evolutionary Approach
10.3.6 Heuristic-Based Microgenetic Method
10.3.7 Stepwise Adaptation of Weights
10.4 Discussion
10.5 Assessment of EAs for CSPs
10.6 Conclusion
References
Chapter 11 An Optimized Fuzzy Logic Controller for Active Power Factor
Corrector Using Genetic Algorithm
11.1 Introduction
11.2 FLC for the Boost Rectifier
11.2.1. Switching Rule for the Switch SW
11.2.2 Fuzzy Logic Controller (FLC)
11.2.3 Defuzzification
11.3 Optimization of FLC by the Genetic Algorithm
11.3.1 Structure of the Chromosome
11.3.2 Initialization of Si
11.3.3 Formulation of Multi-objective Fitness Function
11.3.4 Selection of Chromosomes
11.3.5 Crossover and Mutation Operations
11.3.6 Validation of SI: Recovery of Valid Fuzzy Subsets
11.4 Illustrative Example
11.5 Conclusions
References
Chapter 12 Multilevel Fuzzy Process Control Optimized by Genetic
Algorithm
12.1 Introduction
12.2 Intelligent Control
12.3 Multilevel Control
12.3.1 Optimal Control Concept
12.3.2 Process Stability during Genetic Algorithm Optimizing
12.3.3 Optimizing Criteria
12.4 Optimizing Aided by Genetic Algorithm
12.4.1 Genetic Algorithm Parameters
12.5 Laboratory Cascaded Plant
12.6 Multilevel Control Using Genetic Algorithm
12.6.1 Non-coordinated Multilevel Control Using a PID Controller
12.7 Fuzzy Multilevel Coordinated Control
12.7.1 Decision Control Table
12.8 Conclusions
References
Chapter 13 Evolving Neural Networks for Cancer Radiotherapy
13.1 Introduction and Chapter Overview
13.2 An Introduction 13.2.1 Radiation Therapy Treatment Planning (RTP)
13.2.2 Volumes
13.2.3 Treatment Planning
13.2.4 Recent Developments and Areas of Active Research
13.2.5 Treatment Planning
13.3 Evolutionary Artificial Neural Networks
13.3.1 Evolving Network Weights
13.3.2 Evolving Network Architectures
13.3.3 Evolving Learning Rules
13.3.4 EPNet
13.3.5 Addition of Virtual Samples
13.3.6 Summary
13.4 Radiotherapy Treatment Planning with EANNs
13.4.1 The Backpropogation ANN for Treatment Planning
13.4.2 Development of an EANN
13.4.3 EANN Results
13.4.4 Breast Cancer Treatment Planning
13.5 Summary
13.6 Discussion and Future Work
Acknowledgments
References
Figures
Figure 0.1 Simple linear regression
Figure 0.2 Iterative incremental stepping method
Figure 0.3 Fitting contours on the opposite sides of an ocean
Figure 0.4 Least misfit for contours of steepest part of continental shelf
Figure 0.5 The fit of the continents around the Atlantic
Figure 0.6 Entrapment at a saddle point
Figure 0.7 Cumulative distribution of gold assays, on log normal scale
Figure 0.8 Assay continuity
Figure 0.9 Log correlations as a function of r, the inter-assay distance
Figure 0.10 Correlations as a function of r, the inter-assay distance
Figure 0.11 Fitting model 0: ρ(r) = a
Figure 0.12 Fitting model 1: ρ(r) = exp(-kr)
Figure 0.13 Fitting model 2: ρ(r) = a.exp(-kr)
Figure 0.14 Comparing model 0, model 1 and model 2
Figure 0.15 Fit of model 3 using systematic projection
Figure 0.16 Fit of model 3 using the genetic algorithm
Figure 1.1 Example of a linguistic fuzzy rule
Figure 1.2 Fuzzy sets are defined by fitting parametric functions (solid
lines) to the projections (dots) of the point-wise defined fuzzy sets in the
fuzzy partition matrix U
Figure 1.3 Transparency of the fuzzy rule base premise
Figure 1.4 Similarity-driven simplification
Figure 1.5 Two modeling schemes with multi-objective GA optimization
Figure 1.6 Input u(k), unforced system g(k), and output y(k) of the plant in
(Equations 15 and 16)
Figure 1.7 Initial fuzzy sets and fuzzy sets in the reduced model
Figure 1.8 Local singleton models and the response surface
Figure 1.9 Simulation of the six-rule TS singleton model and error in the
estimated output
Figure 1.10 Local linear TS-model derived in five steps: (a) initial model
with ten clusters, (b) set merging, (c) GA-optimization, (d) set-merging,
(e) final GA optimization
Figure 1.11 Simulation of the six-rule TS singleton model and the error in
the estimated output
Figure 1.12 Local linear TS model and the response-surface
Figure 1.13 Iris data: setosa (×), versicolor (Ο), and virginica (∇)
Figure 1.14 Initial fuzzy rule-based model with three rules and 33
misclassifications
Figure 1.15 Optimized fuzzy rule-based model with three rules and three
misclassifications (Table 1.3-B)
Figure 1.16 Optimized and reduced fuzzy rule-based model with three
rules and four misclassifications (Table 1.3-E)
Figure 2.1 16-state/148-bit FSA genome (G1) map
Figure 2.2 Outline of the Jefferson benchmark GA. The two inserts will be
extra steps used in further sections as modifications to the original
algorithm
Figure 2.3 An example of the crossover used
Figure 2.4 An example of the mutation operator used
Figure 2.5 Outline of the MTF operator
Figure 2.6 Four tables depiction of MTF algorithm on a four-state FSM
genome
Figure 2.7 Outline of the SFS operator
Figure 2.8 Standardization formula for SFS algorithm (Step 2b, Figure 2.7)
Figure 2.9 Pictorial description of Figure 2.8 for max_num_states = 32
Figure 2.10 Table depiction of SFS algorithm on a four-state FSM genome
Figure 2.11 Outline of competition procedure
Figure 2.12 16-state/148-bit FSA genome (G2) map
Figure 2.13 Table of parameters for the languages
Figure 2.14 The seeds used to initialize the random number generator for
each run
Figure 2.15 Number of generations required to find a solution
Figure 2.16 Number of generations required to find a solution
Figure 2.17 Minimal number of states found in a solution
Figure 2.18 Minimal number of states found in a solution
Figure 2.19 Rankings of methods for each language based on machine size
Figure 2.20 Recommendations of methods for each language based on
efficiency
Figure 2.21 Recommendations of languages for each method based on
efficiency
Figure 3.1 The genetic algorithm for the road project construction
timetable problem
Figure 3.2 Relationship between the timetable analysis period and project
sub-periods
Figure 3.3 Procedure for calculation of the objective function value
Figure 3.4: Comparison of the Steps in the Improvement of the Objective
Function Values of the best individuals over GA generations in ten
experiments
Figure 3.5 Euclidean distance between two vectors in a R3 space
Figure 3.6 Hypothetical superior solutions and surrounding inferior
solutions
Figure 4.1 Block diagram of power electronics circuits: chromosome
structures and the fitness functions
Figure 4.2 Objective functions
Figure 4.3 Typical transient response of vd
Figure 4.4 Flowchart of the optimization steps of PCS
Figure 4.5 Reproducion process
Figure 4.6 Buck regulator with overcurrent protection
Figure 4.7 Φp and ΦF vs. the number of generation gen
Figure 4.8 Simulated start-up transients when vin is 20 V and RL is 5 Ω
Figure 4.9 Experimental start-up transients when vin is 20 V and RL is 5 Ω
Figure 4.10 Simulated start-up transients when vin is 60 V and RL is 5 Ω
Figure 4.11 Experimental start-up transients when vin is 60 V and RL is 5 Ω
Figure 4.12 Simulated transient responses when vin is changed from 20 V to
40 V
Figure 4.13 Experimental transient responses when vin is changed from 20
V into 40 V
Figure 4.14 Simulated transient responses when RL is changed from 5 Ω to
10 Ω and vin is 40 V
Figure 4.15 Experimental transient responses when RL is changed from 5 Ω
to 10 Ω and vin is 40 V
Figure 4.16 Simulated transient responses when RL is changed from 10 Ω
to 5 Ω and vin is 40 V
Figure 4.17 Experimental transient responses when RL is changed from 10
Ω to 5 Ω and vin is 40 V
Figure 5.1 Automated diagnosis from digital images
Figure 5.2 Architecture of the neural network
Figure 5.3 Organization of a chromosome coding for a simple three-layer
neural network
Figure 5.4 Two dimensional training data
Figure 5.5 ROC curves for 2-D data: select 2 from 7 features, training set
Figure 5.6 ROC curves for 2-D data: select 2 from 7 features, test set
Figure 5.7 Performance of a “good” classifier (Run 1) compared with that
of a “poor” classifier (Run 3) on training and validation data
Figure 5.8 Histogram of cell nuclear area
Figure 5.9 Correlation of AUC on the training data with maximum fitness
for the parameterization experiments
Figure 5.10 The presence of abnormal cells shifts the distribution of a
feature measured across all cells on a slide
Figure 5.11 ROC curves for test on train results
Figure 5.12 ROC curves for test on test results
Figure 5.13 ROC curves for test on train results
Figure 5.14 ROC curves for test on test results
Figure 5.15 Generalizability of the MACs classifiers
Figure 6.1 Global and local optima for the one-dimensional example
Figure 6.2 Misfit function (Y) for the one-dimensional example
Figure 6.3 Projected mutation
Figure 6.4 The genetic algorithm control panel
Figure 6.5 Systematic projection from ten random starting configurations
Figure 6.6 Genetic algorithm using the same ten random starting
configurations
Figure 6.7 Starting from Eigen vectors and from the Alscal solution
Figure 6.8 The Extend model
Figure 6.9 The Extend simulation setup screen
Figure 7.1 Example network 1
Figure 7.2 Demand multiplier versus generation number
Figure 7.3 Example network 2
Figure 7.4 Pareto optimal solutions
Figure 7.5 Flowchart of GAB calibration algorithm
Figure 7.6 Tuen Mun corridor network
Figure 7.7 Integral network cost vs. perception error coefficient
Figure 7.8 Total trip cost vs. perception error coefficient
Figure 7.9 Link choice entropy vs. perception error coefficient
Figure 7.10 Path choice entropy vs. perception error coefficient
Figure 7.11 NCV vs. OD variation coefficient
Figure 7.12 Path choice entropy vs. perception error coefficient in the pilot
tests
Figure 7.13 NCV vs OD variation coefficient in the pilot tests
Figure 7.14 Maximum fitness vs population size, generation, length of
chromosome
Figure 7.15 Maximum fitness vs. crossover probability and mutation
probability
Figure 7.16 Fitness vs perception error coefficient in the TFS calibration
Figure 7.17 Fitness vs OD variation coefficient in the TFS calibration
Figure 8.1 A JSS problem instance with three jobs
Figure 8.2 (a) Scheduling produced by the fitness1 strategy to the problem
of Figure 8.1 from the individual (3 3 1 1 1 2 2 2). The fitness1 value is 13.
(b) Scheduling produced from the same individual by the fitness2 strategy.
The fitness2 value is 11
Figure 8.3 Results of convergence of six versions of the GA
Figure 8.4 Results about convergence of four versions of the GA along
1000 generations
Figure 8.5 Comparison of various versions of the GA in solving the FT10
problem instance
Figure 9.1 C++ code for main() function that implements the IRR GA
Figure 9.2 SIndividual data structure used for the population individuals
Figure 9.3 Comparison of generic IRR GA and SGA genotype
representations
Figure 9.4 Dynamic redundancy provided by the IRR GA compared to the
SGA
Figure 9.5 Models of structured and unstructured frame design problem
formulations
Figure 9.6 Definition of design variables encoded in the IRR GA genotype
Figure 9.7 SNodeData structure for storing design variables
Figure 9.8 Definition of SaveNodes() function called by EvaluateBinary()
Figure 9.9 Definition of CreateNodeForList() and slsStore() called by
SaveNodes()
Figure 9.10 Assembly of complete structure from design variables
Figure 9.11 Linked lists of SNodeData structures for frame structure
defined in Figure 9.10
Figure 9.12 Definition of SStructure and SNode data structure for frame
alternatives
Figure 9.13 EvaluateBinary() code segment for structures with less than
two supports
Figure 9.14 Code segment for EvaluateBinary() and function
DeleteSingleNode()
Figure 9.15 EvaluateBinary() code segment and function
MakeSameNodes()
Figure 9.16 Common list functions called by DeleteSingleNode() and
MakeSameNodes()
Figure 9.17 Implementation of CreateHorzMembers()
Figure 9.18 SLoadVector data structure for structural loads and forces
Figure 9.19 Application of alternating span live loading to an example
structure
Figure 9.20 Implementation of SetGravityLoad()
Figure 9.21 Application of wind loading to the exterior nodes of two
example structures
Figure 9.22 SetWL() applies wind loading in each direction to frame
structures
Figure 9.23 Deletion of arrays of linked lists created dynamically by the
IRR GA program
Figure 9.24 Implementation of CalcVolumeFitness() and
CalcFloorFitness()
Figure 9.25 Code segment of CalcHorzDeflPenalty()
Figure 9.26 Implementation of CalcVertDeflPenalty()
Figure 9.27 Implementation of CalcNodeSymPenalty()
Figure 9.28 Code segment from SelectString() implementing tournament
selection
Figure 9.29 CrossoverBinary() code to set the number and location of
multiple crossover sites
Figure 9.30 Frame design solutions for four trials represented by the fittest
population individual of each IRR GA trial
Figure 9.31 Individuals in top 25% of the population ranked by fitness after
one generation
Figure 9.32 Individuals in top 25% of the population after 50 generations
Figure 9.33 Individuals in top 25% of the population after 200 generations
Figure 9.34 Maximum fitness and average fitness of the IRR GA
population over 500 generations for a single trial
Figure 11.1 Block diagram of the boost rectifier with APFC and FLC
Figure 11.2 Behavioral model of the APFC
Figure 11.3 Structure of the fuzzy subsets and chromosomes
Figure 11.4 Inference method
Figure 11.5 Flowcharts
Figure 11.6 Typical output response of the boost rectifier
Figure 11.7 Crossover and mutation operations
Figure 11.8 Validation of Si
Figure 11.9 GA-trained membership functions
Figure 11.10 Steady-state experimental waveforms when RL = 110 Ω
Figure 11.11 Transient responses when RL is changed from 110 Ω to 220
Ω
Figure 11.12 Transient responses when RL is changed from 220 Ω to 110
Ω
Figure 11.13 Transient responses when vin is changed from 110 V to 90 V
Figure 11.14 Transient responses when vin is changed from 90 V to 130 V
Figure 11.15 Transient output and control voltages when vin is changed
from 90 V to 130 V (Ch 1: output voltage (100 V/div); Ch2: control
voltage (2 V/div); Timebase: 20 ms/div)
Figure 12.1 Block diagram of a coordinate control concept
Figure 12.2 Block diagram of laboratory plant
Figure 12.3 Photo of laboratory plant
Figure 12.4 Block diagram of laboratory plant
Figure 12.5 Block diagram of the first stage of plant
Figure 12.6 Block diagram of the second stage of plant
Figure 12.7 Block diagram of the connecting tube
Figure 12.8 First process stage response for Zeigler-Nichols and GA tuned
PID, controller for step input qk1u from qk1u = 0.5 l/min to qk1u = 1.0 l/min
Figure 12.9 Second process stage response for Ziegler-Nicholos and GA
tuned PID2 controller for step input qk1u from qk1u = 0.5 l/min to qk1u = 1.0
l/min
Figure 12.10 First stage response to step disturbance qk1u (from qk1u = 0.5
l/min to qk1u = 1.0 l/min) controlled with genetic algorithm tuned decision
tables
Figure 12.11 First stage response to step disturbance qk1u (from qk1u = 0.5
l/min to qk1u = 0.2 l/min) controlled with genetic algorithm tuned decision
tables
Figure 12.12 Second stage response to step disturbance qk1u (from qk1u = 0.5
l/min to qk1u = 1.0 l/min) controlled with genetic algorithm tuned decision
tables
Figure 12.13 Second stage response to step disturbance qk1u (from qk1u = 0.5
l/min to qk1u = 0.2 l/min) controlled with genetic algorithm-tuned decision
tables
Figure 12.14 Comparison of energy consumption for both stages, at
different input step disturbances
Figure 12.15 Comparison of cumulative energy consumption for both
stages of the laboratory plant for total of six steps input disturbances
Figure 12.16 Response of the first stage of a plant controlled by fuzzy
controllers (decision tables are GA-tuned) for set point Tr = 37 °C
Figure 12.17 Response of the second stage of a plant controlled by fuzzy
controllers (decision tables are GA tuned) for set point Tr = 64.4°C
Figure 12.18 Behavior of the first stage of a plant controlled by fuzzy
controllers (decision tables are GA tuned) for set point Tr = 28.6°C
Figure 12.19 Behavior of the second stage of a plant controlled by fuzzy
controllers (decision tables are GA tuned) for set point Tr = 47.5°C
Figure 12.20 First stage response with nonlinear characteristic of thyristor
converter
Figure 12.21 Second stage response with nonlinear characteristic of
thyristor converter
Figure 12.22 First stage process response for various optimizing criteria
Figure 12.23 Second stage process response for various optimizing criteria
Figure 13.1 A schematic showing a typical beam setup for treatment of a
prostate cancer
Figure 13.2 The Philips multi-leaf collimator
Figure 13.3 A typical plot of the dose to a target volume plotted on a dosevolume
histogram
Figure 13.4 A cost function vs. gantry angle plot with the allowed gantryangle-
windows also displayed
Figure 13.5 A typical routine for evolution of connection weights. (From
X. Yao, 1996.)
Figure 13.6 A typical cycle of the evolution of architectures. (From X.
Yao, 1996.)
Figure 13.7 A typical cycle of the evolution of learning rules. (From X.
Yao, 1996.)
Figure 13.8 Input measurements taken from a patient's CT-scan for input to
the neural network. Inputs 1, 2, and 3 are lengths and inputs 4, 5, and 6 are
angles
Figure 13.9 Neural network architecture showing inputs and outputs (some
connection lines are not shown)
Figure 13.10 Encoding of the connection weights on a chromosome
Figure 13.11 A plot of training set error and validation set error against
generation for the EANN
Figure 13.12 A plot of training set error and validation set error against
epoch for SAM
Tables
Table 1.1 Singleton TS fuzzy models for the dynamic plant
Table 1.2 Linear TS fuzzy models for the dynamic plant
Table 1.3 Fuzzy rule-based classifiers for the Iris data derived by means of
scheme 1 (A,B,C) and scheme 2 (D,E,F)
Table 2.1 Four-state FSM with start state Q13
Table 2.2 FSM with of Table 2.1 after Step 1 of MTF
Table 2.3 FSM of Table 2.2 after Next States for Q0 reassigned
Table 2.4 FSM of Table 2.1 after MTF
Table 2.5 Four-state FSM with start state Q13
Table 2.6 FSM with of Table 2.5 after Step 1 of SFS
Table 2.7 FSM of Table 2.6 after Next States for Q0 Reassigned
Table 2.8 FSM of Table 2.5 after SFS
Table 3.1 Details of road projects proposed for the rural road network in
the Pilbara and adjoining regions in Western Australia
Table 3.2 Effects of a project on travel time (TT) on link i
Table 3.3 Vehicle travel time on link i in year t: TTi(t)
Table 3.4 Values of the best ten GA I\individuals in each of experiments 1
and 2
Table 3.5 Summary of the best ten investment sequences
Table 3.6 Project sequence for the best solution converted to annual
investment
Table 3.7 Road project construction timetable determined by the best
solution
Table 3.8 Euclidean distances between the best ten solutions
Table 3.9 Differences between solutions: Euclidean distance and program
similarities
Table 3.10 Comparison of project implementation in the best and second
best solutions (Euclidean distance = 4.99)
Table 4.1 Parameters in GA optimization
Table 4.2(a) Initial values of L and C and the results after 500 generations
Table 4.2(b) Initial component values for the controller and the results after
500 generations
Table 5.1 Variables in the 2-D artificial data set
Table 5.2 Two-dimensional data: Selecting two features from seven
Table 5.3 Performance of run 3 with early stopping
Table 5.4 Description of BCCA dataset.
Table 5.5 Parameterization of the genetic algorithm
Table 5.6 Performance of slide-based and cell-based classifiers at various
operating points
Table 5.7 Confusion matrix for stepwise linear discriminant analysis at
operating point X
Table 5.8 Confusion matrix for best GA/NN at operating point Y
Table 5.9 Performance of the GA/NN and SLDA at the QC and PS
operating points
Table 6.1 An example data matrix of inter-object distances dij
Table 6.2 Inter-city flying mileages
Table 7.1 Input data for example network 1
Table 7.2 Solutions with alternative algorithms
Table 7.3 Input data for example network
Table 7.4 Pareto optimal solutions
Table 7.5 OD matrix (passenger car units per hour)
Table 7.6 The link data of the network
Table 8.1 Individual and aggregate demands of the initial state of the
problem of Figure. 8.1 for all tasks and resources over the time intervals
Table 8.2 Survivabilities of all ten tasks in the initial state of the problem
of Figure 8.1 over the time intervals
Table 8.3 Comparison of six versions of the GA against the ORR & FSS
heuristics
Table 8.4 Comparison of the heuristic strategies to generate individuals
Table 9.1 Values of scalar constants for calculating the fitness and penalty
function
Table 10.1 Specific features of three implemented versions of H-GA
Table 10.2 Specific features of Arc-GA
Table 10.3 Main features of Glass-Box GA
Table 10.4 Main features of the GLS algorithm
Table 10.5 Main features of the co-evolutionary algorithm
Table 10.6 Main features of heuristic-based microgenetic algorithm
Table 10.7 Main features of the SAW-ing algorithm
Table 12.1 Comparison of optimizing results of PID controllers
Table 12.2 49-element control decision table
Table 12.3 Comparison of energy consumption for fuzzy controllers
Table 12.4 Decision control table tuned by genetic algorithm for the first
process
Table 12.5 Decision control table tuned by genetic algorithm for the second
process
Table 13.1 Summary of EANN training times
Table 13.2 Comparison of SAM and EANN generalisation performance
Table 13.3 Summary of EANN and SAM generalisation performance
Table 13.4 Best validation set errors at various training set errors for
EANN and SAM
Table 13.5 Best validation set errors at various low training set errors for
EANN and SAM
Table 13.6 Summary of breast cancer treatment plans produced by the
EANN

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