Aguiar E Oliveira Junior / Ingber / Petraglia Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing

1. Auflage 2012
ISBN: 978-3-642-27479-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 35, 207 Seiten

Reihe: Intelligent Systems Reference Library

Stochastic global optimization is a very important subject, that has applications in virtually all areas of science and technology. Therefore there is nothing more opportune than writing a book about a successful and mature algorithm that turned out to be a good tool in solving difficult problems. Here we present some techniques for solving  several problems by means of Fuzzy Adaptive Simulated Annealing (Fuzzy ASA), a fuzzy-controlled version of ASA, and by ASA itself. ASA is a sophisticated global optimization algorithm that is based upon ideas of the simulated annealing paradigm, coded in the C programming language and developed to statistically find the best global fit of a nonlinear constrained, non-convex cost function over a multi-dimensional space. By presenting detailed examples of its application we want to stimulate the reader’s intuition and make the use of Fuzzy ASA (or regular ASA) easier for everyone wishing to use these tools to solve problems. We kept formal mathematical requirements to a minimum and focused on continuous problems, although ASA is able to handle discrete optimization tasks as well. This book can be used by researchers and practitioners in engineering and industry, in courses on optimization for advanced undergraduate and graduate levels, and also for self-study.

Autoren/Hrsg.

Aguiar E Oliveira Junior, Hime

Ingber, Lester

Petraglia, Antonio

Rembold Petraglia, Mariane

Augusta Soares Machado, Maria

Au, Maria

Inhaltsverzeichnis

1;Title Page
;1
2;Preface;5
3;Contents;8
4;Part I: Fundamentals;12
4.1;Introduction;13
4.1.1;Why to Optimize?;13
4.1.2;Kinds of Optimization Problems;15
4.1.3;How to Optimize?;16
4.1.4;References;20
4.2;Global Optimization and Its Applications;21
4.2.1;Introduction;21
4.2.2;Stochastic or Deterministic ?;22
4.2.3;Considerations about General Global Optimization Tasks;23
4.2.4;Some Popular Approaches and Final Comments;28
4.2.5;References;30
4.3;Metaheuristic Methods;31
4.3.1;Introduction;31
4.3.2;Genetic Algorithms;33
4.3.3;Particle Swarm Optimization;34
4.3.4;Differential Evolution;35
4.3.5;Cross-Entropy Method;36
4.3.6;Simulated Annealing;37
4.3.7;References;40
5;Part II: ASA, Fuzzy ASA and Their Characteristics;41
5.1;Adaptive Simulated Annealing;42
5.1.1;Introduction;42
5.1.1.1; LICENSE and Contributions ;43
5.1.1.2; Organization of Chapter ;43
5.1.2;Theoretical Foundations of Adaptive Simulated Annealing (ASA);44
5.1.2.1; Shades of Simulated Annealing ;44
5.1.2.2;Critics of SA;45
5.1.2.3; ``Standard'' Simulated Annealing (SA) ;45
5.1.2.4; Boltzmann Annealing (BA) ;45
5.1.2.5; Simulated Quenching (SQ) ;48
5.1.2.6;Fast Annealing (FA);49
5.1.2.7; Adaptive Simulated Annealing (ASA) ;49
5.1.2.8;VFSR and ASA;53
5.1.3;Practical Implementation of ASA;53
5.1.3.1;Generating Probability Density Function;53
5.1.3.2; Acceptance Probability Density Function ;54
5.1.3.3; Reannealing Temperature Schedule ;54
5.1.3.4; QUENCH_PARAMETERS=FALSE ;55
5.1.3.5;QUENCH_COST=FALSE;56
5.1.3.6;QUENCH_COST_SCALE=TRUE;56
5.1.4;Tuning Guidelines;56
5.1.4.1; The Necessity for Tuning ;56
5.1.4.2; Construction of the Code ;57
5.1.4.3; Motivations for Tuning Methodology ;59
5.1.4.4;Some Rough But Useful Guidelines;59
5.1.4.5;Quenching;61
5.1.4.6;Options for Large Spaces;62
5.1.4.7;Shunting to Local Codes;63
5.1.4.8;Judging Importance-Sampling;64
5.1.4.9; User References ;64
5.1.5;Adaptive OPTIONS;65
5.1.5.1; VFSR ;65
5.1.5.2; ASA_FUZZY ;65
5.1.6;Multiple Systems;65
5.1.6.1; SELF_OPTIMIZE ;65
5.1.6.2; ASA_PARALLEL ;66
5.1.6.3;TRD Example of Multiple Systems;66
5.1.7;Conclusion;67
5.1.8;References;68
5.2;Unconstrained Optimization;72
5.2.1;Fuzzy ASA;72
5.2.2;Unconstrained (or Rectangular Constrained) Optimization Examples;76
5.2.2.1;Rastrigin Function;79
5.2.2.2;Schwefel Function;82
5.2.2.3;Ackley Function;85
5.2.2.4;Krishnakumar Function;87
5.2.2.5;Rosenbrock Function;89
5.2.2.6;Griewangk Function;92
5.2.2.7;Special Function 1;94
5.2.2.8;Special Function 2;97
5.2.3;Conclusion;101
5.2.4;References;102
5.3;Constrained Optimization;103
5.3.1;Introduction;103
5.3.2;Constrained Global Optimization Using ASA and Fuzzy ASA;105
5.3.2.1;Function G01;106
5.3.2.2;Function G02;110
5.3.2.3;Function G03;113
5.3.2.4;Function G04;114
5.3.2.5;Function G05;115
5.3.2.6;Function G06;115
5.3.2.7;Function G07;116
5.3.2.8;Function G08;117
5.3.2.9;Function G09;118
5.3.2.10;Function G10;119
5.3.2.11;Function G11;120
5.3.2.12;Function G12;121
5.3.2.13;Function G13;121
5.3.3;Conclusion;122
5.3.4;References;123
6;Part III Applications;124
6.1;Applications to Signal Processing - Blind Source Separation;125
6.1.1;Introduction;125
6.1.2;Implementation;130
6.1.3;Results;130
6.1.3.1;Example 1 - Separation by TSK MIMO System;130
6.1.3.2;Example 2 - Separation by TSK MIMO System;133
6.1.3.3;Example 3 - Separation by TSK MIMO System;134
6.1.3.4;Example 4 - Separation by TSK MIMO System;135
6.1.3.5;Example 5 - Mixture by PNL Model;138
6.1.4;Conclusion;143
6.1.5;References;144
6.2;Fuzzy Modeling with Fuzzy Adaptive Simulated Annealing;145
6.2.1;Introduction;145
6.2.2;Affine Takagi-Sugeno Fuzzy Systems;146
6.2.3;The Fuzzy Modeling Problem;147
6.2.3.1;Approximation in Lower Dimensions;147
6.2.3.2;Approximation in Higher Dimensions;150
6.2.4;Ideas for Fuzzy Clustering Using ASA;151
6.2.5;Conclusions about the Presented Methods;153
6.2.6;References;154
6.3;Statistical Estimation and Global Optimization;155
6.3.1;Introduction;155
6.3.2;Maximum Likelihood Estimation with ASA;156
6.3.3;Implementation and Experiments;157
6.3.3.1;Exponential Distribution;158
6.3.3.2;Normal Distribution;162
6.3.3.3;Lognormal Distribution;163
6.3.3.4;Cauchy Distribution;164
6.3.3.5;Triangular Distribution;166
6.3.3.6;Mixture (Laplace and Uniform) Distribution;170
6.3.3.7;Gamma Distribution;170
6.3.4;Conclusions;172
6.3.5;References;173
6.4;Nonlinear Equation Solving;174
6.4.1;Introduction;174
6.4.2;Statement of the Problem;175
6.4.3;The Algorithm;176
6.4.4;Examples;177
6.4.4.1;Example 1;177
6.4.4.2;Example 2;181
6.4.4.3;Example 3;183
6.4.4.4;Example 4;186
6.4.4.5;Example 5;186
6.4.4.6;Example 6;187
6.4.4.7;Example 7;189
6.4.5;Conclusions;189
6.4.6;References;192
6.5;Space-Filling Curves and Fuzzy ASA;193
6.5.1;Introduction;193
6.5.2;Key Results from General Topology, Ergodic and Measure Theories;194
6.5.3;Composing Space-Filling Curves and ASA;200
6.5.3.1;Algorithm Description;200
6.5.4;Experiments;201
6.5.5;Conclusions;203
6.5.6;References;205
6.6;Epilogue;206
6.6.1;Final Thoughts;206
7;Index;208