Multiobjective Optimization Methodology: A Jumping Gene Approach

by Tang; K.S.

• ISBN13: 9781439899199
• ISBN10: 1439899193
• Format: Hardcover
• Copyright: 2012-05-04
• Publisher: CRC Press

Summary

Complex design problems are often governed by a number of performance merits. These markers gauge how good the design is going to be, but can conflict with the performance requirements that must be met. The challenge is reconciling these two requirements. This book introduces a newly developed jumping gene algorithm, designed to address the multi-functional objectives problem and supplies a viably adequate solution in speed. The text presents various multi-objective optimization techniques and provides the technical know-how for obtaining trade-off solutions between solution spread and convergence.

Table of Contents

Preface	p. ix
About the Authors	p. xi
Introduction	p. 1
Background on Genetic Algorithms	p. 1
Organization of Chapters	p. 4
References	p. 5
Overview of Multiobjective Optimization	p. 9
Classification of Optimization Methods	p. 9
Enumerative Methods	p. 9
Deterministic Methods	p. 9
Stochastic Methods	p. 10
Multiobjective Algorithms	p. 11
Multiobjective Genetic Algorithm	p. 11
Modified Fitness Assignment	p. 13
Fitness Sharing	p. 13
Niched Pareto Genetic Algorithm 2	p. 14
Nondominated Sorting Genetic Algorithm 2	p. 15
Fast Nondominated Sorting Approach	p. 15
Crowded-Comparison Approach	p. 17
Elitism Strategy	p. 19
Strength Pareto Evolutionary Algorithm 2	p. 19
Strength Value and Raw Fitness	p. 20
Density Estimation	p. 20
Archive Truncation Method	p. 22
Pareto Archived Evolution Strategy	p. 22
Microgenetic Algorithm	p. 23
Population Memory	p. 24
Adaptive Grid Algorithm	p. 24
Three Types of Elitism	p. 25
Ant Colony Optimization	p. 25
Particle Swarm Optimization	p. 27
Tabu Search	p. 28
References	p. 29
Jumping Gene Computational Approach	p. 33
Biological Background	p. 33
Biological Jumping Gene Transposition	p. 33
Advantageous Effects of JG on Host Evolution	p. 35
Overview of Computational Gene Transposition	p. 36
Sexual or Asexual Transposition	p. 36
Bacterial Operations	p. 38
Transduction	p. 38
Conjugation	p. 39
Transformation	p. 40
Other Operations	p. 41
Jumping Gene Genetic Algorithms	p. 41
Transposons in Chromosomes	p. 42
Cut-and-Paste and Copy-and-Paste Operations	p. 42
Jumping Gene Transposition	p. 43
Some Remarks	p. 44
Real-Coding Jumping Operations	p. 45
References	p. 49
. Theoretical Analysis of Jumping Gene Operations	p. 53
Overview of Schema Models	p. 53
Schema	p. 53
Holland's Model	p. 53
Stephens and Waelbroeck's Model	p. 55
Exact Schema Theorem for Jumping Gene Transposition	p. 57
Notations and Functional Definitions	p. 57
Notations	p. 57
Functional Definitions	p. 57
Exact Schema Evolution Equation for Copy-and-Paste	p. 59
Exact Schema Evolution Equation for Cut-and-Paste	p. 64
Theorems of Equilibrium and Dynamical Analysis	p. 69
Distribution Matrix for Copy-and-Paste	p. 69
Distribution Matrix for Cut-and-Paste	p. 72
Lemmas	p. 72
Proof of Theorem 4.1	p. 75
Proof of Theorem 4.2	p. 78
Simulation Results and Analysis	p. 79
Simulation 4.1: Existence of Equilibrium	p. 79
Simulation 4.2: Primary Schemata Competition Sets with Different Orders	p. 80
Discussion	p. 80
Assumptions	p. 80
Implications	p. 80
Destruction and Construction	p. 82
Finite Population Effect	p. 83
The Effect of the JG in a GA	p. 84
References	p. 87
Performance Measures on Jumping Gene	p. 89
Convergence Metric: Generational Distance	p. 89
Convergence Metric: Deb and Jain Convergence Metric	p. 90
Diversity Metric: Spread	p. 91
Diversity Metric: Extreme Nondominated Solution Generation	p. 92
Binary e-Indicator	p. 94
Statistical Test Using Performance Metrics	p. 95
Jumping Gene Verification and Results	p. 96
JG Parameter Study	p. 96
Comparisons with Other MOEAs	p. 98
Mean and Standard Deviation of Generational Distance for Evaluating Convergence	p. 99
Mean and Standard Deviation of Spread for Evaluating Diversity	p. 100
Diversity Evaluation Using Extreme Nondominated Solution Generation	p. 108
Statistical Test Using Binary ¿-Indicator	p. 108
An Experimental Test of Theorems of Equilibrium	p. 111
Optimization of Controller Design	p. 120
Results and Comparisons	p. 121
References	p. 126
Radio-to-Fiber Repeater Placement in Wireless Local-Loop Systems	p. 129
Introduction	p. 129
Path Loss Model	p. 132
Mathematical Formulation	p. 133
Chromosome Representation	p. 135
Jumping Gene Transposition	p. 136
Chromosome Repairing	p. 136
Results and Discussion	p. 137
Mean and Standard Deviation of Deb and Jain Convergence Metric for Evaluating Convergence	p. 139
Mean and Standard Deviation of Spread for Evaluating Diversity	p. 139
Diversity Evaluation Using Extreme Nondominated Solution Generation	p. 139
Statistical Test Using Binary ¿-Indicator	p. 139
References	p. 147
Resource Management in WCDMA	p. 149
Introduction	p. 149
Mathematical Formulation	p. 151
Chromosome Representation	p. 153
A Initial Population	p. 154
Power Generation	p. 154
Rate Generation	p. 154
Jumping Gene Transposition	p. 154
Mutation	p. 155
Ranking Rule	p. 157
Results and Discussion	p. 157
Mean and Standard Deviation of Deb and Jain Convergence Metric for Evaluating Convergence	p. 161
Mean and Standard Deviation of Spread for Evaluating Diversity	p. 162
Diversity Evaluation Using Extreme Nondominated Solution Generation	p. 163
Statistical Test Using Binary s-Indicator	p. 164
Discussion of Real-Time Implementation	p. 169
References	p. 177
Base Station Placement in WLANs	p. 179
Introduction	p. 179
Path Loss Model	p. 180
Mathematical Formulation	p. 181
Chromosome Representation	p. 183
Jumping Gene Transposition	p. 184
Chromosome Repairing	p. 184
Results and Discussion	p. 185
Mean and Standard Deviation of Deb and Jain Convergence Metric for Evaluating Convergence	p. 186
Mean and Standard Deviation of Spread for Evaluating Diversity	p. 186
Diversity Evaluation Using Extreme Nondominated Solution Generation	p. 187
Statistical Test Using the Binary ¿-Indicator	p. 189
References	p. 199
Conclusions	p. 201
References	p. 202
Proofs of Lemmas in Chapter 4	p. 203
Benchmark Test Functions	p. 221
Chromosome Representation	p. 229
Design of the Fuzzy PID Controller	p. 231
Index	p. 237
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