Adaptive Differential Evolution: A Robust Approach to Multimodal Problem Optimization

Optimization problems are ubiquitous in academic research and real-world applications wherever such resources as space, time and cost are limited. Researchers and practitioners need to solve problems fundamental to their daily work which, however, may show a variety of challenging characteristics such as discontinuity, nonlinearity, nonconvexity, and multimodality. It is expected that solving a complex optimization problem itself should easy to use, reliable and efficient to achieve satisfactory solutions. Differential evolution is a recent branch of evolutionary algorithms that is capable of addressing a wide set of complex optimization problems in a relatively uniform and conceptually simple manner. For better performance, the control parameters of differential evolution need to be set appropriately as they have different effects on evolutionary search behaviours for various problems or at different optimization stages of a single problem. The fundamental theme of the book is theoretical study of differential evolution and algorithmic analysis of parameter adaptive schemes. Topics covered in this book include: * Theoretical analysis of differential evolution and its control parameters * Algorithmic design and comparative analysis of parameter adaptive schemes * Scalability analysis of adaptive differential evolution * Adaptive differential evolution for multi-objective optimization * Incorporation of surrogate model for computationally expensive optimization * Application to winner determination in combinatorial auctions of E-Commerce * Application to flight route planning in Air Traffic Management * Application to transition probability matrix optimization in credit-decision making Title Page......Page 2 Preface......Page 6 Acknowledgement......Page 10 Contents......Page 11 Knowing the State of the Art......Page 18 Starting Point......Page 19 Databases......Page 20 Informal Online Resources and Tools......Page 21 Books......Page 22 Other Formal Publications......Page 23 Theory of Differential Evolution......Page 24 Fundamentals of Differential Evolution......Page 25 Hybridization......Page 26 References......Page 27 Inception......Page 35 Early Years......Page 36 Key Milestones in and after 1998......Page 38 Notations......Page 39 Strategy Framework......Page 40 Intrinsic Control Parameters......Page 43 Differential Mutation......Page 44 Crossover......Page 46 State of the Art of Differential Evolution......Page 52 Advantages......Page 53 References......Page 54 Coverage......Page 59 An Overview of Applications of Differential Evolution in Electromagnetics......Page 60 Further Classification......Page 61 Conventional Antenna Arrays......Page 64 Time-Modulated Antenna Arrays......Page 65 Design of Microwave and RF Devices......Page 66 Characterization of Microwave and RF Devices......Page 67 Design of Antennas......Page 68 Electromagnetic Structures......Page 69 Plain Electromagnetic Structures......Page 70 Frequency Selective Surfaces......Page 71 Retrieval of Effective Permittivity Tensor......Page 72 Frequency Planning......Page 73 MIMO......Page 74 Computational Electromagnetics......Page 75 An Outlook to Future Applications of Differential Evolution in Electromagnetics......Page 76 References......Page 77 Introduction......Page 88 Experimental Setup......Page 89 Mathematical Nature of the Optimization Problem and Differential Evolution......Page 91 Initial Guess......Page 92 Foldy-Lax Model of Scattering......Page 93 Multiple Signal Classification for Estimating the Scatterer Support......Page 94 Least Square Based Method for Generating Initial Guess for the Relative Permittivity......Page 95 Control Parameters......Page 96 Numerical Example 1: A Single Cylinder......Page 97 Numerical Example 2: Two Identical Cylinders......Page 102 Numerical Example 3: Two Different Cylinders......Page 105 Numerical Example 4: Two Closely Located Identical Cylinders......Page 109 Numerical Example 5: Kite Cross-Section Cylinder......Page 112 Conclusions......Page 116 References......Page 117 Introduction......Page 121 The Inverse Scattering Formulation......Page 122 Discrete Setting......Page 123 The Iterative Multiscaling Approach......Page 124 Off-Centered Dielectric Cylinder......Page 126 Off-Centered Dielectric Hollow Cylinder......Page 131 Centered Stratified Dielectric Square Cylinder......Page 135 Centered E-Shape Dielectric Cylinder......Page 140 References......Page 143 Near-Field to Far-Field Transformation......Page 146 Radiating Equipment Modeling with Prefixed Position Dipoles......Page 147 Present Work......Page 148 Integral Equations for the Radiation of Electronic Equipment......Page 149 Ground Plane in Semi-anechoic Chambers......Page 150 Description of the Method......Page 151 Electromagnetic Optimization by Genetic Algorithms......Page 153 EMOGA v1.0: Genetic Algorithm......Page 154 EMOGA v2.0: Metaheuristic Method......Page 155 Measurement Systems......Page 157 Near-Field Results......Page 160 Far-Field Prediction......Page 162 Conclusions......Page 163 References......Page 164 Introduction......Page 168 GSM Components and Frequency Planning......Page 169 Interference Cost......Page 170 Separation Cost......Page 171 Pareto Tournament......Page 172 Variable Neighborhood Search......Page 173 Multi-objective Variable Neighborhood Search......Page 174 Multi-objective Skewed Variable Neighborhood Search......Page 175 Experimental Setup......Page 176 Tuning of the DEPT Parameters......Page 179 Empirical Results......Page 186 References......Page 188 Introduction......Page 190 Received Signal Model......Page 191 Hybrid PSO-ES-DEPSO Training Algorithm......Page 192 Channel Model......Page 193 MIMO Beam-Forming......Page 195 Recurrent Neural Network for Channel Prediction......Page 197 Training Procedure......Page 198 Algorithm Comparison......Page 200 Robustness of PSO-ES-DEPSO Algorithm......Page 201 Linear and Nonlinear Predictors with PSO-EA-DEPSO Algorithm......Page 204 Non-convexity of the Solution Space......Page 205 Performance Measures of RNN Predictors......Page 206 Conclusions......Page 216 References......Page 217 Index......Page 220 I ?rst met Jingqiao when he had just commenced his PhD research in evolutionary algorithms with Arthur Sanderson at Rensselaer. Jingqiao's goals then were the investigation and development of a novel class of se- adaptivedi?erentialevolutionalgorithms, later calledJADE. I had remarked to Jingqiao then that Arthur always appreciated strong theoretical foun- tions in his research, so Jingqiao's prior mathematically rigorous work in communications systems would be very useful experience. Later in 2007, whenJingqiaohadcompletedmostofthetheoreticalandinitialexperimental work on JADE, I invited him to spend a year at GE Global Research where he applied his developments to several interesting and important real-world problems. Most evolutionary algorithm conferences usually have their share of in- vative algorithm oriented papers which seek to best the state of the art - gorithms. The best algorithms of a time-frame create a foundation for a new generationof innovativealgorithms, and so on, fostering a meta-evolutionary search for superior evolutionary algorithms. In the past two decades, during whichinterest andresearchin evolutionaryalgorithmshavegrownworldwide by leaps and bounds, engaging the curiosity of researchers and practitioners frommanydiversescienceandtechnologycommunities, developingstand-out algorithms is getting progressively harder.