Evolutionary Computation
A Unified Approach
Kenneth A. De Jong
A Bradford Book
The MIT Press
Cambridge, Massachusetts
London, England
Contents
Introduction
2
1.1 Basic Evolutionary Processen
3
1.2 EV: A Simple Evolutionary System
1.3 E V oii a Simple Fitness Landscape ö
1.4 EV on a Morc Complcx Fitness Landscape 15
19
1.5 Evolutionary Systems as Problem Solvers
Ol
1.6 Exerciscs
2 3
A Historical Perspective
2.1 Early Algorithmic Views -'^
24
2.2 T h e Catalytie 1960s
2r
2.3 T h e Explorativc 1970s >
2o
2.3.1 Evolutionary P r o g r a m m i n g
2,r
2.3.2 Evolution Strategies >
26
2.3.3 Genetic Algorithms
27
2.4 T h e Exploitativc 1980s
27
2.4.1. Optimization Applications
28
2.4.2 Other E A Applications
2.4.3 S u m m a r y
29
2.5 T h e Unifying 1990s
2
2.6 The Twenty-hrst Century: M a t u r e Expansion 9
2.7 Summary
3 3
Canonical Evolutionary Algorithms
33
3.1 Introduction
33
3.2 EV(m.n)
3.3 Evolutionary P r o g r a m m i n g '"
A6
3.4 Evolution Strategies
40
3.5 Genetic Algorithms
3.5.1 Multi-parcnt Rcproduction 41
43
3.5.2 Universal Genetic Codes
47
3.6 Summary
CONTENTS
A Unifled View of Simple EAs 49
4.1 A Common Framework jo
4.2 Population Sizc r ,,
4.2.1 Parcnt Population Sine m 50
4.2.2 Oftspring Population Sizc n 52
4.3 Sclection -,,
o4
4.3.1 Choosing Selection MechaiÜHins 5g
4.3.2 Survival Sclection: A Special Gase 59
4.3.3 Sclection Summary gg
4.4 Repioductive Mechanisms ßi
4.4.1 Mutation ,.-,
4.4.2 Recombinatiou £•>
4.4.3 Crossover or Mutation? gg
4.4.4 Representation Lssucs 57
4.4.5 Clioosiiig Effeetivc Repioductive Meclianisms 68
4.5 Summary f.q
Evolutionary Algorithms as Problem Solvers 71
5.1 Simple EAs as Parallel Adaptive Search j[
5.1.1 Representation 72
5.1.1.1 Fixed-Length Linear Objects 73
5.1.1.2 Nonlincar Objects 73
5.1.1.3 Variable-Length Objects 74
5.1.1.4 Nonlinear, Variable-Lcngth Objects 75
5.1.2 Reproductive Operators 7,5
5.1.3 Objective Fitness Evaluation 7g
5.1.4 Population Sizes and Dynamics 77
5.1.5 Convergcnce and Stopphig Criteria 78
5.1.6 Retuniing an Answer 70
5.1.7 Summary on
5.2 EA-based Optimization on
5.2.1 O P T - E A s '•'.'•'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'. W
5.2.1.1 Fitness Scaling ^1
5.2.1.2 Convergcnce and Elitism g2
5.2.1.3 Summary ^3
5.2.2 Parameter Optimization ^3
5.2.2.1 Pheiiotypic Representations and Operators 84
5.2.2.2 Genotypic Representations and Operators $4
5.2.2.3 Clioosiiig Representations and Operators 85
5.2.2.4 Beal-Valued Parameter Optimization 85
5.2.2.5 Integer-Valued Parameter Optimization 93
5.2.2.6 Symbolic Parameter Optimization 95
5.2.2.7 Non-liomogencons Parameter Optimization 97
5.2.3 Constraiiied Optimization 97
5.2.4 Data Structure Optimization 1 Q.Q
vii
CONTENTS
5.2.4.1 Variablc-Length Data Structurcs 102
5.2.5 Multi-objective Optlmization 103
5.2.6 Summary LM
5.3 EA-Based Soarch 1()5
]
5.4 EA-Based Macliine Learning 07
5.5 EA-Based Automatcd Programming 109
5.5.1 Represcntmg Programs 109
5.5.2 Evaluatmg Programm HO
5.5.3 Summary H2
5.6 EA-Bascd Adaptation H2
5.7 Summary H3
6 Evolutionary Computation Theory 115
u
6.1 Inlroductioii 5
6.2 Analyzing EA Dynamics H'
6.3 Sclcction-Only Models 120
6.3.1 Noii-overlapping-Gencration Models 120
6.3.1.1 Uniform (Neutral) Selection 121
6.3.1.2 Fitness-Biased Selection 123
6.3.1.3 Non-overlapping-Generation Models with n ^ m 132
6.3.2 Ovcrlapping-Generation Models 134
6.3.2.1 Uniform (Neutral) Selection 135
6.3.2.2 Fitness-Biased Selection 136
6.3.3 Selection in Standard EAs 137
6.3.4 Reduciug Selection Sampling Variance 138
6.3.5 Selection Summary 140
6.4 Reproduction-Oiüy Models 141
6.4.1 Noii-oveiiapping-Gcucration Models 141
6.4.1.1 Reproduction for Fixed-Length Discrete Linear Gcnomes . . 143
6.4.1.2 Reproduction for Othcr Genome Types 152
6.4.2 Ovcrlapping-Generation Models 158
6.4.3 Reproduction Summary 159
6.5 Selection and Reproduction Interactions 160
6.5.1 Evolvability and Priee's Theorem 160
6.5.2 Selection and Discrete Recombination 162
6.5.2.1 Discrete Recombination from a Schema Perspective 162
6.5.2.2 Crossover-Induced Diversity 163
6.5.2.3 Crossovcr-lndueed Fitness Improvements 166
6.5.3 Selection and Other Recombination Operators 169
6.5.4 Selection and Mutation 1"!
6.5.4.1 Mutation from a Schema Perspective 172
6.5.4.2 Mutation-Indueed Diversity 172
6.5.1.3 Mutation-Indueed Fitness Improvements 175
6.5.5 Selection and Other Mutation Operators 177
6.5.6 Selection and Multiple Reproduetive Operators 177
vm CONTENTS
6.5.7Selcction. Reproduction, and Population Size 180
6.5.7.1 Non-overlapphig-Gcncration Models 181
6.5.7.2 Overlapping-Generation Models 183
6.5.8 Summary 185
6.6 Representation 185
6.6.1 Capturing I m p o r t a n t Application Features 185
6.6.2 Defining Effective Reproduction Operator« 186
6.6.2.1 Effective M u t a t i o n Operators 187
6.6.2.2 Effective Recombination O p e r a t o r s 187
6.7 Landscape Aiialysis 188
6.8 Models of Canonical EAs 189
6.8.f Infinite Population Models for Simple GAs 189
6.8.2 Expected Value Models of Simple GAs 191
6.8.2.1 GA Schema Theory 192
6.8.2.2 Summary 199
6.8.3 Markov Models 199
6.8.3.1 Markov Models of Finitc Population EAs 200
6.8.3.2 Markov Models of Simple GAs 201
6.8.3.3 Summary 203
6.8.4 Statistical Meclianics Models 203
6.8.5 S u m m a r y 205
6.9 Application-Oriented Theories 205
6.9.1 Optimization-Oriented Theorics 205
6.9.1.1 Convergence and R a t e s of Coiivergence 206
6.9.1.2 ESs and Real-Valucd P a r a m e t e r Optiinization Problems . . . 206
6.9.1.3 Simple EAs and Discrete Optimization Problems 207
6.9.1.4 Optimizing with Genetic Algorithms 208
6.10 Summary 209
A d v a n c e d E C Topics 211
7.1 Self-adapting EAs 211
7.1.1 A d a p t a t i o n at EA Design Time 212
7.1.2 A d a p t a t i o n over Multiple EA Runs 212
7.1.3 A d a p t a t i o n during an EA R u n 213
7.1.4 S u m m a r y 213
7.2 Dynamic Landscapes 213
7.2.1 S t a n d a r d EAs on Dynamic Landscapes 214
7.2.2 Modificd EAs for Dynamic Landscapes 215
7.2.3 Categorizing Dynamic Landseapes 216
7.2.4 T h e Iinportance of the R a t e of Change 216
7.2.5 T h e Iniportance of Diversity 217
7.2.6 Summary 219
7.3 Exploiting Parallelism 219
7.3.1 Coarse-Gralncd Parallel EAs 220
7.3.2 Finc-Graiiied Models 220
ix
CONTENTS
7.3.3 Snmmary 221
7.4 Evolving Executable Objecto 221
7.4.1 Representation of Bchaviors 22 L
7.4.2 Summary 223
7.5 Mnlti-objective EAs 223
7.6 Hybrid EAs 224
7.7 Biologically lnspired Extensions 225
7.7.1 Non-raudom Mating and Spcciation 225
7.7.2 Coevolutioiiary Systems 226
7.7.2.1 CoEC Architectures 227
7.7.2.2 CoEC Dynamics 227
7.7.3 Generative Represcntations and Morphogenesis 228
7.7.4 Inclusion of Lamarekian Propcrties 229
7.7.5 Agent-Orient.ed Models 229
7.7.6 Snmmary 230
7.8 Snmmary 230
231
8 The Road Ahead
8.1 Modeling General Evolutionary Systems 231
2;
8.2 Morc Unification • ^2
8.3 Snmmary 232
233
Appendix A: Source Code Overview
A.l EC1: A Vcry Simple EC System 233
A.l.l EC1 Code Structnre 234
A.1.2 EC1 Parameters 235
A.2 EC2: A Morc Interestmg EC System 236
A.3 EC3: A Morc Flexible EC System 237
A.4 EC4: An EC Research System 240
24
Bibliography 1
253
Index
