Multiobjective optimization methodology : a jumping gene approach

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
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The first book to focus on jumping genes outside bioscience and medicine, Multiobjective Optimization Methodology: A Jumping Gene Approach introduces jumping gene algorithms designed to supply adequate, viable solutions to multiobjective problems quickly and with low computational cost.

Better Convergence and a Wider Spread of Nondominated Solutions

The book begins with a thorough review of state-of-the-art multiobjective optimization techniques. For readers who may not be familiar with the bioscience behind the jumping gene, it then outlines the basic biological gene transposition process and explains the translation of the copy-and-paste and cut-and-paste operations into a computable language.

To justify the scientific standing of the jumping genes algorithms, the book provides rigorous mathematical derivations of the jumping genes operations based on schema theory. It also discusses a number of convergence and diversity performance metrics for measuring the usefulness of the algorithms.

Practical Applications of Jumping Gene Algorithms

Three practical engineering applications showcase the effectiveness of the jumping gene algorithms in terms of the crucial trade-off between convergence and diversity. The examples deal with the placement of radio-to-fiber repeaters in wireless local-loop systems, the management of resources in WCDMA systems, and the placement of base stations in wireless local-area networks.

Offering insight into multiobjective optimization, the authors show how jumping gene algorithms are a useful addition to existing evolutionary algorithms, particularly to obtain quick convergence solutions and solutions to outliers.

Author Notes

Kit Sang Tangreceived his BSc from the University of Hong Kong in 1988 and his MSc and PhD from City University of Hong Kong in 1992 and 1996, respectively. He is currently an associate professor in the Department of Electronic Engineering at City University of Hong Kong. He has published over 90 journal papers and five book chapters, and coauthored two books, focusing on genetic algorithms and chaotic theory.

Tak Ming Chanreceived his BSc in applied physics from Hong Kong Baptist University in 1999 and his MPhil and PhD in electronic engineering from City University of Hong Kong in 2001 and 2006 respectively. He was a research associate in the Department of Industrial and Systems Engineering at the Hong Kong Polytechnic University from 2006 to 2007 and a postdoctoral fellow in the Department of Production and Systems Engineering, University of Minho, Portugal from 2007 to 2009.

Richard Jacob Yinobtained his BEng in Information Technology in 2004 and his PhD in Electronic Engineering in 2010 from the City University of Hong Kong. He is now an Electronic Engineer at ASM Assembly Automation Hong Kong Limited.

Kim Fung Manis a Chair Professor and head of the electronic engineering department at City University of Hong Kong. He received his PhD from Cranfield Institute of Technology, UK. He is currently the co-editor-in-chief of IEEE Transactions of Industrial Electronics. He has co-authored three books and published extensively in the area.

Preface	p. ix
About the Authors	p. xi
1 Introduction	p. 1
1.1 Background on Genetic Algorithms	p. 1
1.2 Organization of Chapters	p. 4
References	p. 5
2 Overview of Multiobjective Optimization	p. 9
2.1 Classification of Optimization Methods	p. 9
2.1.1 Enumerative Methods	p. 9
2.1.2 Deterministic Methods	p. 9
2.1.3 Stochastic Methods	p. 10
2.2 Multiobjective Algorithms	p. 11
2.2.1 Multiobjective Genetic Algorithm	p. 11
2.2.1.1 Modified Fitness Assignment	p. 13
2.2.1.2 Fitness Sharing	p. 13
2.2.2 Niched Pareto Genetic Algorithm 2	p. 14
2.2.3 Nondominated Sorting Genetic Algorithm 2	p. 15
2.2.3.1 Fast Nondominated Sorting Approach	p. 15
2.2.3.2 Crowded-Comparison Approach	p. 17
2.2.3.2 Elitism Strategy	p. 19
2.2.4 Strength Pareto Evolutionary Algorithm 2	p. 19
2.2.4.1 Strength Value and Raw Fitness	p. 20
2.2.4.2 Density Estimation	p. 20
2.2.4.3 Archive Truncation Method	p. 22
2.2.5 Pareto Archived Evolution Strategy	p. 22
2.2.6 Microgenetic Algorithm	p. 23
2.2.6.1 Population Memory	p. 24
2.2.6.2 Adaptive Grid Algorithm	p. 24
2.2.6.3 Three Types of Elitism	p. 25
2.2.7 Ant Colony Optimization	p. 25
2.2.8 Particle Swarm Optimization	p. 27
2.2.9 Tabu Search	p. 28
References	p. 29
3 Jumping Gene Computational Approach	p. 33
3.1 Biological Background	p. 33
3.1.1 Biological Jumping Gene Transposition	p. 33
3.1.2 Advantageous Effects of JG on Host Evolution	p. 35
3.2 Overview of Computational Gene Transposition	p. 36
3.2.1 Sexual or Asexual Transposition	p. 36
3.2.2 Bacterial Operations	p. 38
3.2.2.1 Transduction	p. 38
3.2.2.2 Conjugation	p. 39
3.2.2.3 Transformation	p. 40
3.2.3 Other Operations	p. 41
3.3 Jumping Gene Genetic Algorithms	p. 41
3.3.1 Transposons in Chromosomes	p. 42
3.3.2 Cut-and-Paste and Copy-and-Paste Operations	p. 42
3.3.3 Jumping Gene Transposition	p. 43
3.3.4 Some Remarks	p. 44
3.4 Real-Coding Jumping Operations	p. 45
References	p. 49
4 . Theoretical Analysis of Jumping Gene Operations	p. 53
4.1 Overview of Schema Models	p. 53
4.1.1 Schema	p. 53
4.1.2 Holland's Model	p. 53
4.1.3 Stephens and Waelbroeck's Model	p. 55
4.2 Exact Schema Theorem for Jumping Gene Transposition	p. 57
4.2.1 Notations and Functional Definitions	p. 57
4.2.1.1 Notations	p. 57
4.2.1.2 Functional Definitions	p. 57
4.2.2 Exact Schema Evolution Equation for Copy-and-Paste	p. 59
4.2.3 Exact Schema Evolution Equation for Cut-and-Paste	p. 64
4.3 Theorems of Equilibrium and Dynamical Analysis	p. 69
4.3.1 Distribution Matrix for Copy-and-Paste	p. 69
4.3.2 Distribution Matrix for Cut-and-Paste	p. 72
4.3.3 Lemmas	p. 72
4.3.4 Proof of Theorem 4.1	p. 75
4.3.5 Proof of Theorem 4.2	p. 78
4.4 Simulation Results and Analysis	p. 79
4.4.1 Simulation 4.1: Existence of Equilibrium	p. 79
4.4.2 Simulation 4.2: Primary Schemata Competition Sets with Different Orders	p. 80
4.5 Discussion	p. 80
4.5.1 Assumptions	p. 80
4.5.2 Implications	p. 80
4.5.3 Destruction and Construction	p. 82
4.5.4 Finite Population Effect	p. 83
4.5.5 The Effect of the JG in a GA	p. 84
References	p. 87
5 Performance Measures on Jumping Gene	p. 89
5.1 Convergence Metric: Generational Distance	p. 89
5.2 Convergence Metric: Deb and Jain Convergence Metric	p. 90
5.3 Diversity Metric: Spread	p. 91
5.4 Diversity Metric: Extreme Nondominated Solution Generation	p. 92
5.5 Binary e-Indicator	p. 94
5.6 Statistical Test Using Performance Metrics	p. 95
5.7 Jumping Gene Verification and Results	p. 96
5.7.1 JG Parameter Study	p. 96
5.7.2 Comparisons with Other MOEAs	p. 98
5.7.2.1 Mean and Standard Deviation of Generational Distance for Evaluating Convergence	p. 99
5.7.2.2 Mean and Standard Deviation of Spread for Evaluating Diversity	p. 100
5.7.2.3 Diversity Evaluation Using Extreme Nondominated Solution Generation	p. 108
5.7.2.4 Statistical Test Using Binary ¿-Indicator	p. 108
5.7.3 An Experimental Test of Theorems of Equilibrium	p. 111
5.7.3.1 Optimization of Controller Design	p. 120
5.7.3.2 Results and Comparisons	p. 121
References	p. 126
6 Radio-to-Fiber Repeater Placement in Wireless Local-Loop Systems	p. 129
6.1 Introduction	p. 129
6.2 Path Loss Model	p. 132
6.3 Mathematical Formulation	p. 133
6.4 Chromosome Representation	p. 135
6.5 Jumping Gene Transposition	p. 136
6.6 Chromosome Repairing	p. 136
6.7 Results and Discussion	p. 137
6.7.1 Mean and Standard Deviation of Deb and Jain Convergence Metric for Evaluating Convergence	p. 139
6.7.2 Mean and Standard Deviation of Spread for Evaluating Diversity	p. 139
6.7.3 Diversity Evaluation Using Extreme Nondominated Solution Generation	p. 139
6.7.4 Statistical Test Using Binary ¿-Indicator	p. 139
References	p. 147
7 Resource Management in WCDMA	p. 149
7.1 Introduction	p. 149
7.2 Mathematical Formulation	p. 151
7.3 Chromosome Representation	p. 153
7 A Initial Population	p. 154
7.4.1 Power Generation	p. 154
7.4.2 Rate Generation	p. 154
7.5 Jumping Gene Transposition	p. 154
7.6 Mutation	p. 155
7.7 Ranking Rule	p. 157
7.8 Results and Discussion	p. 157
7.8.1 Mean and Standard Deviation of Deb and Jain Convergence Metric for Evaluating Convergence	p. 161
7.8.2 Mean and Standard Deviation of Spread for Evaluating Diversity	p. 162
7.8.3 Diversity Evaluation Using Extreme Nondominated Solution Generation	p. 163
7.8.4 Statistical Test Using Binary s-Indicator	p. 164
7.9 Discussion of Real-Time Implementation	p. 169
References	p. 177
8 Base Station Placement in WLANs	p. 179
8.1 Introduction	p. 179
8.2 Path Loss Model	p. 180
8.3 Mathematical Formulation	p. 181
8.4 Chromosome Representation	p. 183
8.5 Jumping Gene Transposition	p. 184
8.6 Chromosome Repairing	p. 184
8.7 Results and Discussion	p. 185
8.7.1 Mean and Standard Deviation of Deb and Jain Convergence Metric for Evaluating Convergence	p. 186
8.7.2 Mean and Standard Deviation of Spread for Evaluating Diversity	p. 186
8.7.3 Diversity Evaluation Using Extreme Nondominated Solution Generation	p. 187
8.7.4 Statistical Test Using the Binary ¿-Indicator	p. 189
References	p. 199
9 Conclusions	p. 201
References	p. 202
Appendix A Proofs of Lemmas in Chapter 4	p. 203
Appendix B Benchmark Test Functions	p. 221
Appendix C Chromosome Representation	p. 229
Appendix D Design of the Fuzzy PID Controller	p. 231
Index	p. 237

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