Zhang / Sanderson Adaptive Differential Evolution

A Robust Approach to Multimodal Problem Optimization
1. Auflage 2009
ISBN: 978-3-642-01527-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1, 164 Seiten

Reihe: Adaptation, Learning, and Optimization

The fundamental theme of this book is theoretical study of differential evolution and algorithmic analysis of parameter adaptive schemes. The book offers real-world insights into a variety of large-scale complex industrial applications.

Autoren/Hrsg.

Zhang, Jingqiao

Sanderson, Arthur C.

Inhaltsverzeichnis

1;Foreword;6
2;Contents;9
3;Acronyms;13
4;Introduction;14
4.1;Research Motivation;15
4.2;Research Contribution;16
5;Related Work and Background;18
5.1;Evolutionary Algorithms;18
5.1.1;Evolution Strategies;19
5.1.2;Evolutionary Programming;20
5.1.3;Genetic Algorithms;20
5.1.4;Genetic Programming;20
5.2;Differential Evolution;21
5.3;Parameter Control;22
5.4;Multi-objective Optimization;24
5.5;No Free Lunch Theorem and Domain Knowledge Utilization;25
6;Theoretical Analysis of Differential Evolution;27
6.1;Introduction;27
6.2;Properties of Differential Evolution;29
6.2.1;DE/rand/k/bin without Crossover;29
6.2.2;Properties of Mutation;29
6.2.3;Properties of Selection;30
6.3;An Approximate Model of DE;31
6.4;Analyses of the Evolution Process of DE;33
6.4.1;Mathematical Formulation of DE;33
6.4.2;Calculation of E(z);34
6.4.3;Calculation of $\sigma_{z1}$;38
6.4.4;Calculation of $\sigma_{z2}$;39
6.4.5;From $\{\vec{z}_{i,g}\}$ to $\{\vec{x} _{i,g+1}\}$;41
6.5;Numerical Evaluation and Discussions;42
6.5.1;Performance Metrics;42
6.5.2;Progress Rate ;43
6.5.3;Evolution of $\sigma^{*}_{x1}$ and $\sigma^{*}_{x2}$;43
6.5.4;Steady Point;45
6.5.5;Dynamic Behavior of DE;45
6.5.6;Effect of Mutation Factor;46
6.6;Summary;48
6.7;Appendix;49
6.7.1;Proof of Property 3.3;49
6.7.2;Proof of Eqs. (3.16) and (3.34);50
7;Parameter Adaptive Differential Evolution;51
7.1;Introduction;51
7.2;Adaptive DE Algorithms;53
7.2.1;DESAP;53
7.2.2;FADE;53
7.2.3;SaDE;54
7.2.4;SaNSDE;55
7.2.5;jDE;55
7.2.6;Algorithms Comparison;56
7.3;JADE: A New Adaptive Differential Evolution Algorithm;58
7.3.1;Initialization;58
7.3.2;Mutation;58
7.3.3;Crossover;60
7.3.4;Selection;60
7.3.5;Adaptation of $µ_{CR}$;61
7.3.6;Adaptation of $µ_{F}$;62
7.3.7;Explanation of Parameter Adaptation;63
7.3.8;Discussion of Parameter Settings;64
7.3.9;Algorithm Complexity;64
7.4;Performance Analysis for Low- to Moderate-Dimensional Problems;64
7.4.1;Comparison of JADE with Other Evolutionary Algorithms;66
7.4.2;Benefit of JADE’s Components;74
7.4.3;Evolution of $µ_{F}$ and $µ_{CR}$ in JADE;75
7.4.4;Parameter Values of JADE;76
7.5;Performance Analysis in a Noisy Environment;76
7.6;Scalability Analysis for High-Dimensional Problems;79
7.6.1;Comparison of Different Adaptive DE Algorithms;80
7.6.2;Scalability of Different Adaptive DE Algorithms;85
7.6.3;Comparison of JADE+ with Coevolutionary Algorithms;87
7.7;Summary;88
7.8;Appendix: Stochastic Properties of the Mutation and Crossover of JADE;89
7.8.1;A Simplified Model;89
7.8.2;Mathematical Analysis;90
7.8.3;Proof of Proposition 4.1;91
8;Surrogate Model-Based Differential Evolution;95
8.1;Introduction;95
8.2;Adaptive Differential Evolution;96
8.3;RBF Surrogate Model;97
8.4;DE-AEC: Differential Evolution with Adaptive Evolution Control;98
8.4.1;Procedure of DE-AEC;98
8.4.2;Explanation of q, S and K;100
8.5;Performance Evaluation;101
8.5.1;Success Rate and Success Performance;101
8.5.2;Simulation Results;101
8.6;Summary;104
9;Adaptive Multi-objective Differential Evolution;106
9.1;Introduction;106
9.2;Multi-objective Evolutionary Algorithms;108
9.2.1;PAES;108
9.2.2;SPEA2;108
9.2.3;PESA;109
9.2.4;NSGA and NSGA-II;109
9.2.5;Differential Evolution Based MOEAs;109
9.3;JADE for Multi-objective Optimization;111
9.3.1;Pareto Dominance and Crowding Density;111
9.3.2;Selection;111
9.3.3;Mutation;113
9.4;Performance Comparison;114
9.4.1;Comparison Based on Conventional Performance Metrics;115
9.4.2;Pareto-Compliant Performance Metrics;116
9.4.3;Experimental Results;121
9.5;Summary;124
10;Application to Winner Determination Problems in Combinatorial Auctions;125
10.1;Introduction;125
10.2;Problem Description and Current Approaches;127
10.2.1;Winner Determination in Combinatorial Auctions;127
10.2.2;Current Approaches;127
10.3;Utilization of Domain Knowledge;128
10.3.1;Representation Scheme for Discrete Optimization;128
10.3.2;Regeneration Operation;129
10.3.3;Seeding JADE;131
10.4;Performance Comparison;131
10.4.1;Experimental Setting;132
10.4.2;Comparison Results;132
10.5;Summary;135
11;Application to Flight Planning in Air Traffic Control Systems;136
11.1;Introduction;136
11.2;Problem Formulation;137
11.3;Utilization of Domain Knowledge;139
11.4;Simulation;140
11.5;Summary;143
12;Application to the TPM Optimization in Credit Decision Making;144
12.1;Introduction;144
12.2;Problem Formulation;146
12.3;Utilization of Domain Knowledge;148
12.4;Simulation;149
12.4.1;Performance Comparison;150
12.4.2;Comparison of Optimized TPM with Empirical Data;153
12.5;Summary;154
13;Conclusions and Future Work;155
13.1;Summary;155
13.2;Future Work;156
13.2.1;Coevolutionary Algorithms;157
13.2.2;Constrained Optimization;157
13.2.3;Optimization in a Noisy Environment;158
14;References;159
15;Index;170