Differential Evolution

A Practical Approach to Global Optimization

By: Kenneth Price, Rainer M. Storn, Jouni A. Lampinen

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Paperback | 13 December 2005

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560 Pages

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Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables.

The differential evolution (DE) algorithm is a practical approach to global numerical optimization which is easy to understand, simple to implement, reliable, and fast. Packed with illustrations, computer code, new insights, and practical advice, this volume explores DE in both principle and practice. It is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization.

A companion CD includes DE-based optimization software in several programming languages.

Industry Reviews

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"This book is about an evolutionary method, called differential evolution (DE) ... . the authors claim that 'this book is designed to be easy to understand and simple to use'. Indeed, they have achieved their goal. The book is enjoyable to read, fully illustrated with figures and C-like pseudocodes ... . this book is foremost addressed to engineers ... . Moreover, those interested in evolutionary algorithms will certainly find this book to be both interesting and useful." (Panos M. Pardalos, Mathematical Reviews, Issue 2006 g)

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Non-Fiction Computing & I.T.Computer Programming & Software Development Computer Science Artificial Intelligence Graphical & Digital Media Applications Mathematics Optimisation Linear Programming

Preface	p. VII
Table of Contents	p. XIII
The Motivation for Differential Evolution	p. 1
Introduction to Parameter Optimization	p. 1
Overview	p. 1
Single-Point, Derivative-Based Optimization	p. 6
One-Point, Derivative-Free Optimization and the Step Size Problem	p. 11
Local Versus Global Optimization	p. 16
Simulated Annealing	p. 18
Multi-Point, Derivative-Based Methods	p. 19
Multi-Point, Derivative-Free Methods	p. 20
Differential Evolution - A First Impression	p. 30
References	p. 34
The Differential Evolution Algorithm	p. 37
Overview	p. 37
Population Structure	p. 37
Initialization	p. 38
Mutation	p. 38
Crossover	p. 39
Selection	p. 40
DE at a Glance	p. 41
Visualizing DE	p. 43
Notation	p. 47
Parameter Representation	p. 48
Bit Strings	p. 48
Floating-Point	p. 50
Floating-Point Constraints	p. 52
Initialization	p. 53
Initial Bounds	p. 53
Initial Distributions	p. 56
Base Vector Selection	p. 61
Choosing the Base Vector Index, r0	p. 61
One-to-One Base Vector Selection	p. 63
A Comparison of Random Base Index Selection Methods	p. 64
Degenerate Vector Combinations	p. 65
Implementing Mutually Exclusive Indices	p. 68
Gauging the Effects of Degenerate Combinations: The Sphere	p. 70
Biased Base Vector Selection Schemes	p. 72
Differential Mutation	p. 74
The Mutation Scale Factor: F	p. 75
Randomizing the Scale Factor	p. 79
Recombination	p. 91
Crossover	p. 92
The Role of Cr in Optimization	p. 97
Arithmetic Recombination	p. 104
Phase Portraits	p. 112
The Either/Or Algorithm	p. 117
Selection	p. 118
Survival Criteria	p. 119
Tournament Selection	p. 121
One-to-One Survivor Selection	p. 122
Local Versus Global Selection	p. 124
Permutation Selection Invariance	p. 124
Crossover-Dependent Selection Pressure	p. 125
Parallel Performance	p. 127
Extensions	p. 128
Termination Criteria	p. 128
Objective Met	p. 129
Limit the Number of Generations	p. 129
Population Statistics	p. 129
Limited Time	p. 130
Human Monitoring	p. 130
Application Specific	p. 130
References	p. 131
Benchmarking Differential Evolution	p. 135
About Testing	p. 135
Performance Measures	p. 137
DE Versus DE	p. 139
The Algorithms	p. 139
The Test Bed	p. 142
Phase Portraits	p. 142
Summary	p. 154
DE Versus Other Optimizers	p. 156
Comparative Performance: Thirty-Dimensional Functions	p. 157
Comparative Studies: Unconstrained Optimization	p. 167
Performance Comparisons from Other Problem Domains	p. 171
Application-Based Performance Comparisons	p. 175
Summary	p. 182
References	p. 182
Problem Domains	p. 189
Overview	p. 189
Function and Parameter Quantization	p. 189
Uniform Quantization	p. 190
Non-Uniform Quantization	p. 191
Objective Function Quantization	p. 192
Parameter Quantization	p. 195
Mixed Variables	p. 201
Optimization with Constraints	p. 201
Boundary Constraints	p. 202
Inequality Constraints	p. 206
Equality Constraints	p. 220
Combinatorial Problems	p. 227
The Traveling Salesman Problem	p. 229
The Permutation Matrix Approach	p. 230
Relative Position Indexing	p. 231
Onwubolu's Approach	p. 233
Adjacency Matrix Approach	p. 233
Summary	p. 237
Design Centering	p. 239
Divergence, Self-Steering and Pooling	p. 239
Computing a Design Center	p. 242
Multi-Objective Optimization	p. 244
Weighted Sum of Objective Functions	p. 244
Pareto Optimality	p. 246
The Pareto-Front: Two Examples	p. 247
Adapting DE for Multi-Objective Optimization	p. 250
Dynamic Objective Functions	p. 255
Stationary Optima	p. 256
Non-Stationary Optima	p. 259
References	p. 262
Architectural Aspects and Computing Environments	p. 267
DE on Parallel Processors	p. 267
Background	p. 267
Related Work	p. 267
Drawbacks of the Standard Model	p. 271
Modifying the Standard Model	p. 272
The Master Process	p. 273
DE on Limited Resource Devices	p. 276
Random Numbers	p. 276
Permutation Generators	p. 279
Efficient Sorting	p. 282
Memory-Saving DE Variants	p. 282
References	p. 284
Computer Code	p. 287
DeMat - Differential Evolution for MATLAB	p. 287
General Structure of DeMat	p. 287
Naming and Coding Conventions	p. 288
Data Flow Diagram	p. 291
How to Use the Graphics	p. 293
DeWin - DE for MS Windows: An Application in C	p. 295
General Structure of DeWin	p. 296
Naming and Coding Conventions	p. 300
Data Flow Diagram	p. 300
How To Use the Graphics	p. 304
Functions of graphics.h	p. 305
Software on the Accompanying CD	p. 307
References	p. 309
Applications	p. 311
Genetic Algorithms and Related Techniques for Optimizing Si-H Clusters: A Merit Analysis for Differential Evolution	p. 313
Introduction	p. 313
The System Model	p. 315
Computational Details	p. 317
Results and Discussion	p. 318
Concluding Remarks	p. 325
References	p. 325
Non-Imaging Optical Design Using Differential Evolution	p. 327
Introduction	p. 327
Objective Function	p. 328
A Reverse Engineering Approach to Testing	p. 331
A More Difficult Problem: An Extended Source	p. 334
Conclusion	p. 337
References	p. 337
Optimization of an Industrial Compressor Supply System	p. 339
Introduction	p. 339
Background Information on the Test Problem	p. 340
System Optimization	p. 340
Demand Profiles	p. 341
Modified Differential Evolution; Extending the Generality of DE	p. 342
Component Selection from the Database	p. 343
Crossover Approaches	p. 343
Testing Procedures	p. 348
Obtaining 100% Certainty of the Results	p. 348
Results	p. 349
Summary	p. 350
References	p. 351
Minimal Representation Multi-Sensor Fusion Using Differential Evolution	p. 353
Introduction	p. 353
Minimal Representation Multi-Sensor Fusion	p. 357
Differential Evolution for Multi-Sensor Fusion	p. 361
Experimental Results	p. 364
Comparison with a Binary Genetic Algorithm	p. 372
Conclusion	p. 374
References	p. 375
Determination of the Earthquake Hypocenter: A Challenge for the Differential Evolution Algorithm	p. 379
Introduction	p. 379
Brief Outline of Direct Problem Solution	p. 382
Synthetic Location Test	p. 384
Convergence Properties	p. 385
Conclusions	p. 389
References	p. 389
Parallel Differential Evolution: Application to 3-D Medical Image Registration	p. 393
Introduction	p. 393
Medical Image Registration Using Similarity Measures	p. 395
Optimization by Differential Evolution	p. 398
Parallelization of Differential Evolution	p. 401
Experimental Results	p. 404
Conclusions	p. 408
Acknowledgments	p. 408
References	p. 408
Design of Efficient Erasure Codes with Differential Evolution	p. 413
Introduction	p. 413
Codes from Bipartite Graphs	p. 414
Code Design	p. 418
Differential Evolution	p. 421
Results	p. 423
Acknowledgments	p. 426
References	p. 426
FIWIZ - A Versatile Program for the Design of Digital Filters Using Differential Evolution	p. 429
Introduction	p. 429
Unconventional Design Tasks	p. 432
Approach	p. 435
Examples	p. 444
Conclusion	p. 445
References	p. 445
Optimization of Radial Active Magnetic Bearings by Using Differential Evolution and the Finite Element Method	p. 447
Introduction	p. 447
Radial Active Magnetic Bearings	p. 448
Magnetic Field Distribution and Force Computed by the Two-Dimensional FEM	p. 454
RAMB Design Optimized by DE and the FEM	p. 455
Conclusion	p. 461
Acknowledgments	p. 461
References	p. 462
Application of Differential Evolution to the Analysis of X-Ray Reflectivity Data	p. 463
Introduction	p. 463
The Data-Fitting Procedure	p. 466
The Model and Simulation	p. 469
Examples	p. 471
Conclusions	p. 477
References	p. 477
Inverse Fractal Problem	p. 479
General Introduction	p. 479
Conclusion	p. 495
References	p. 497
Active Compensation in RF-Driven Plasmas by Means of Differential Evolution	p. 499
Introduction	p. 499
RF-Driven Plasmas	p. 500
Langmuir Probes	p. 501
Active Compensation in RF-Driven Plasmas	p. 501
Automated Control System Structure and Fitness Function	p. 502
Experimental Setup	p. 504
Parameters and Experimental Design	p. 505
Results	p. 509
Conclusion	p. 509
Acknowledgments	p. 510
References	p. 510
Appendix	p. 513
Unconstrained Uni-Modal Test Functions	p. 514
Sphere	p. 514
Hyper-Ellipsoid	p. 515
Generalized Rosenbrock	p. 515
Schwefel's Ridge	p. 516
Neumaier #3	p. 517
Unconstrained Multi-Modal Test Functions	p. 518
Ackley	p. 518
Griewangk	p. 519
Rastrigin	p. 520
Salomon	p. 521
Whitley	p. 522
Storn's Chebyshev	p. 523
Lennard-Jones	p. 525
Hilbert	p. 526
Modified Langerman	p. 526
Shekel's Foxholes	p. 528
Odd Square	p. 529
Katsuura	p. 530
Bound-Constrained Test Functions	p. 531
Schwefel	p. 531
Epistatic Michalewicz	p. 531
Rana	p. 532
References	p. 533
Index	p. 535
Table of Contents provided by Ingram. All Rights Reserved.

Differential Evolution

A Practical Approach to Global Optimization

At a Glance

Paperback

Industry Reviews

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How to return your order

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You Can Find This Book In

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