Differential Evolution in Electromagnetics (eBook)

Title Page 2
Preface 6
Acknowledgement 10
Contents 11
A Literature Survey on Differential Evolution 18
Motivations 18
Eliminating Inconsistencies 18
Crediting Original Contributions 18
Knowing the State of the Art 18
Gaining Insight 19
Platforms 19
Starting Point 19
Databases 20
Informal Online Resources and Tools 21
Result Refining 22
Books 22
Book Chapters 23
Other Formal Publications 23
Informal Notes 24
Result Analysis 24
Theory of Differential Evolution 24
Fundamentals of Differential Evolution 25
Intrinsic Control Parameters 26
Evaluation of Differential Evolution 26
Applications of Differential Evolution 26
Hybridization 26
Future Actions 27
Open Access 27
Future Update 27
Misconceptions and Misconducts on Differential Evolution 27
References 27
Basics of Differential Evolution 35
A Short History 35
Inception 35
Early Years 36
Key Milestones in and after 1998 38
The Foundational Differential Evolution Strategies 39
Notations 39
Strategy Framework 40
Intrinsic Control Parameters 43
Classic Differential Evolution 44
Initialization 44
Differential Mutation 44
Crossover 46
Dynamic Differential Evolution 52
State of the Art of Differential Evolution 52
Essential Features of Differential Evolution 53
Advantages 53
Disadvantages 54
References 54
A Retrospective of Differential Evolution in Electromagnetics 59
Introduction 59
Coverage 59
Pioneering Works 60
An Overview of Applications of Differential Evolution in Electromagnetics 60
Electromagnetic Inverse Problems 61
A Bird’s Eye View 61
Further Classification 61
Antenna Arrays 64
Conventional Antenna Arrays 64
Time-Modulated Antenna Arrays 65
Moving Phase Center Antenna Arrays 66
Microwave and RF Engineering 66
Design of Microwave and RF Devices 66
Characterization of Microwave and RF Devices 67
Antennas 68
Design of Antennas 68
Measurement of Antennas 69
Electromagnetic Structures 69
Plain Electromagnetic Structures 70
Frequency Selective Surfaces 71
Electromagnetic Composite Materials 72
Modeling of Electromagnetic Composite Materials 72
Retrieval of Effective Permittivity Tensor 72
Frequency Planning 73
Radio Network Design 74
MIMO 74
Radar 75
Computational Electromagnetics 75
Electromagnetic Compatibility 76
Miscellaneous Applications 76
An Outlook to Future Applications of Differential Evolution in Electromagnetics 76
References 77
Application of Differential Evolution to a Two-Dimensional Inverse Scattering Problem 88
Introduction 88
General Description of the Problem 89
Experimental Setup 89
The Optimization Problem 91
Mathematical Nature of the Optimization Problem and Differential Evolution 91
Initial Guess 92
Foldy-Lax Model of Scattering 93
Multiple Signal Classification for Estimating the Scatterer Support 94
Least Square Based Method for Generating Initial Guess for the Relative Permittivity 95
Numerical Results 96
Measurement Setup 96
Control Parameters 96
Numerical Example 1: A Single Cylinder 97
Numerical Example 2: Two Identical Cylinders 102
Numerical Example 3: Two Different Cylinders 105
Numerical Example 4: Two Closely Located Identical Cylinders 109
Numerical Example 5: Kite Cross-Section Cylinder 112
Conclusions 116
References 117
The Use of Differential Evolution for the Solution of Electromagnetic Inverse Scattering Problems 121
Introduction 121
Problem Formulation 122
The Inverse Scattering Formulation 122
Discrete Setting 123
The Inverse Scattering Problem as an Optimization Problem 124
The Iterative Multiscaling Approach 124
Numerical Results 126
Off-Centered Dielectric Cylinder 126
Off-Centered Dielectric Hollow Cylinder 131
Centered Stratified Dielectric Square Cylinder 135
Centered E-Shape Dielectric Cylinder 140
Conclusions 143
References 143
Modeling of Electrically Large Equipment with Distributed Dipoles Using Metaheuristic Methods 146
Introduction 146
Near-Field to Far-Field Transformation 146
Radiating Equipment Modeling with Prefixed Position Dipoles 147
Present Work 148
Electromagnetic Modeling of a Radiating Equipment with Distributed Infinitesimal Dipoles 149
Integral Equations for the Radiation of Electronic Equipment 149
Point-Matching Method with Dirac Delta Basis Functions 150
Ground Plane in Semi-anechoic Chambers 150
Proposed Method for Near-Field to Far-Field Transformation 151
Description of the Method 151
Optimization Problem 153
Source Identification 153
Electromagnetic Optimization by Genetic Algorithms 153
EMOGA v1.0: Genetic Algorithm 154
EMOGA v2.0: Metaheuristic Method 155
Numerical Results 157
Measurement Systems 157
Near-Field Results 160
Far-Field Prediction 162
Conclusions 163
References 164
Application of Differential Evolution to a Multi-Objective Real-World Frequency Assignment Problem 168
Introduction 168
Multi-objective FAP in a GSM Network 169
GSM Components and Frequency Planning 169
Interference Cost 170
Separation Cost 171
Multi-objective Differential Evolution with Pareto Tournaments 172
Algorithm Structure 172
Pareto Tournament 172
Problem Domain Knowledge 173
Multi-objective Variable Neighborhood Search 173
Variable Neighborhood Search 173
Multi-objective Variable Neighborhood Search 174
Greedy Mutation 175
Multi-objective Skewed Variable Neighborhood Search 175
Experiments and Results 176
Experimental Setup 176
Methodology and Metrics 179
Tuning of the DEPT Parameters 179
Empirical Results 186
Conclusions 188
References 188
RNN Based MIMO Channel Prediction 190
Introduction 190
Received Signal Model 191
Received Signal Model 191
Optimization Problem 192
Hybrid PSO-ES-DEPSO Training Algorithm 192
MIMO Channel/Beam-Forming Models 193
Channel Model 193
Channel Estimation Model 195
MIMO Beam-Forming 195
Recurrent Neural Network for Channel Prediction 197
Training Procedure 198
Numerical Results 200
Algorithm Comparison 200
Robustness of PSO-ES-DEPSO Algorithm 201
Linear and Nonlinear Predictors with PSO-EA-DEPSO Algorithm 204
Non-convexity of the Solution Space 205
Performance Measures of RNN Predictors 206
Conclusions 216
References 217
Index 220

"Chapter 1 A Literature Survey on Differential Evolution (p. 1-2)

Anyong Qing

1.1 Motivations

1.1.1 Eliminating Inconsistencies

It has been observed since 2004 that there are many inconsistent or even false claims prevailing in the community of differential evolution [1]. Two measures have been taken to clarify them. The first is a system level parametric study on differential evolution [1]-[4]. The second is the large scale literature survey mentioned here. It is one of the foundation stones of this book.

1.1.2 Crediting Original Contributions

The academic society nowadays has become more and more utilitarian and impetuous. Many researchers dream a shortcut to their academic success. They tend to accept established view points especially those from topical review articles by leading researchers. Original publications are neglected that insufficient credits are given to originality. In some cases, they may not be aware that the original contributions are cited incorrectly [1]. Academic misconducts such as multiple submissions, exaggerated claims, or even plagiarism are not rare. It is one of the objectives of this survey to promote good academic conducts by locating and appropriately crediting original contributions.

1.1.3 Knowing the State of the Art

It has been more than ten years since the inception of differential evolution. However, as far as we know, nobody else has done any comprehensive literature survey on differential evolution. The state of the art of differential evolution is therefore not precisely known to interested researchers. This literature survey aims to fill this gap. It also serves to reveal the popularity of differential evolution.

1.1.4 Gaining Insight

The literature survey involves not only literature collection but also literature analysis among which the latter is more important. Through the analysis, the following questions will be answered
(a) What is differential evolution?
(b) When is differential evolution used and why is it useful?
(c) When will differential evolution fail and why does it fail?"