ISBN: 3-540-66950-7
TITLE: Evolutionary Algorithms
AUTHOR: Spears, William M.
TOC:

Notation XIII
Part I. Setting the Stage
1. Introduction 3
1.1 Evolutionary Algorithms 3
1.2 Overview of Related Work 9
1.3 Issues and Goals 15
1.4 Outline 17
2. Background 19
2.1 No Free Lunch 19
2.2 A Boolean Satisfiability Problem Generator 21
2.3 Using SAT to Create Multimodal and Epistatic Problems 24
2.4 Speciation 28
2.5 Summary 34
Part II. Static Theoretical Analyses
3. A Survival Schema Theory for Recombination 39
3.1 Introduction 39
3.2 Framework 40
3.3 Survival Theory for n-point Recombination 42
3.4 Graphing Disruption 45
3.5 Estimates Using Population Homogeneity 47
3.6 Survival Theory for P_0 Uniform Recombination 51 
3.7 Expected Number of Offspring in H_k 56
3.8 Summary 58
4. A Construction Schema Theory for Recombination 59
4.1 Introduction 59
4.2 Construction Theory for n-point Recombination 60
4.3 Graphing Construction 62
4.4 Construction Theory for P0 Uniform Recombination 64
4.5 Expected Number of Offspring in H_k 72
4.6 Summary 74
5. Survival and Construction Schema Theory for Recombination 77
5.1 Introduction 77
5.2 Survival and Construction 77
5.3 Expected Number of Offspring in Hk 81 
5.4 Summary 82
6. A Survival Schema Theory for Mutation 83
6.1 Introduction 83
6.2 Framework 84
6.3 Summary 90
7. A Construction Schema Theory for Mutation 91
7.1 Introduction 91
7.2 Framework 91
7.3 Summary 99
8. Schema Theory: Mutation versus Recombination 101
8.1 Introduction 101
8.2 Survival 101
8.3 Construction 104
8.4 Survival and Construction 113
8.5 Summary 114
9. Other Static Characterizations of Mutation and Recombination 117
9.1 Introduction 117
9.2 Exploratory Power 118
9.3 Positional Bias 121
9.4 Distributional Bias 122
9.5 Summary 125
Part III. Dynamic Theoretical Analyses
10. Dynamic Analyses of Mutation and Recombination 129
10.1 Introduction 129
10.2 The Limiting Distribution for Recombination 129
10.3 The Limiting Distribution for Mutation 137
10.4 The Limiting Distribution for Mutation and Recombination 144
10.5 Summary 145
11. A Dynamic Model of Selection and Mutation 147
11.1 Introduction 147
11.2 Selection and Mutation 147
11.3 Summary 151
12. A Dynamic Model of Selection, Recombination, and Mutation 155
12.1 Introduction 155
12.2 EA Performance 155
12.3 Overview of Markov Chains 156
12.4 The Nix and Vose Markov Chain Model for EAs 159
12.5 Instantaneous Transient Behavior of EAs 161
12.6 Summary and Discussion 167
13. An Aggregation Algorithm for Markov Chains 169
13.1 Introduction 169
13.2 The Aggregation Algorithm at a High Level 170
13.3 The Aggregation Algorithm in More Detail 171
13.4 Special Cases in Which Aggregation Is Perfect 176
13.5 Error Analysis and a Similarity Metric 181
13.6 Some Experiments 183
13.7 Related Work 187
13.8 Summary 189
Part IV. Empirical Analyses
14. Empirical Validation 193
14.1 Introduction 193
14.2 The Multimodal Problem Generator 194
14.3 The Relationship of Multimodality to Epistasis 198
14.4 Summary 201
Part V. Summary
15. Summary and Discussion 205
15.1 Summary and Contributions 205
15.2 Future Work 208
15.3 Conclusions 209
Appendix: Formal Computations for Aggregation 211
References 213
Index 219
END
