Engineering Optimization: An Introduction with Metaheuristic Applications

✍ Scribed by Xin-She Yang

• Publisher: Wiley
• Year: 2010
• Tongue: English
• Leaves: 378
• Edition: 1
• Category: Library

✦ Synopsis

An accessible introduction to metaheuristics and optimization, featuring powerful and modern algorithms for application across engineering and the sciencesFrom engineering and computer science to economics and management science, optimization is a core component for problem solving. Highlighting the latest developments that have evolved in recent years, Engineering Optimization: An Introduction with Metaheuristic Applications outlines popular metaheuristic algorithms and equips readers with the skills needed to apply these techniques to their own optimization problems. With insightful examples from various fields of study, the author highlights key concepts and techniques for the successful application of commonly-used metaheuristc algorithms, including simulated annealing, particle swarm optimization, harmony search, and genetic algorithms.The author introduces all major metaheuristic algorithms and their applications in optimization through a presentation that is organized into three succinct parts:Foundations of Optimization and Algorithms provides a brief introduction to the underlying nature of optimization and the common approaches to optimization problems, random number generation, the Monte Carlo method, and the Markov chain Monte Carlo methodMetaheuristic Algorithms presents common metaheuristic algorithms in detail, including genetic algorithms, simulated annealing, ant algorithms, bee algorithms, particle swarm optimization, firefly algorithms, and harmony searchApplications outlines a wide range of applications that use metaheuristic algorithms to solve challenging optimization problems with detailed implementation while also introducing various modifications used for multi-objective optimizationThroughout the book, the author presents worked-out examples and real-world applications that illustrate the modern relevance of the topic. A detailed appendix features important and popular algorithms using MATLAB® and Octave software packages, and a related FTP site houses MATLAB code and programs for easy implementation of the discussed techniques. In addition, references to the current literature enable readers to investigate individual algorithms and methods in greater detail.Engineering Optimization: An Introduction with Metaheuristic Applications is an excellent book for courses on optimization and computer simulation at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners working in the fields of mathematics, engineering, computer science, operations research, and management science who use metaheuristic algorithms to solve problems in their everyday work.

✦ Table of Contents

Engineering Optimization: An Introduction with Metaheuristic Applications......Page 6
CONTENTS......Page 8
List of Figures......Page 16
Preface......Page 22
Acknowledgments......Page 24
Introduction......Page 26
PART I FOUNDATIONS OF OPTIMIZATION AND ALGORITHMS......Page 32
1 A Brief History of Optimization......Page 34
1.1 Before 1900......Page 35
1.2 Twentieth Century......Page 37
1.3 Heuristics and Metaheuristics......Page 38
Exercises......Page 41
2.1 Optimization......Page 46
2.2 Type of Optimization......Page 48
2.3 Optimization Algorithms......Page 50
2.5 Order Notation......Page 53
2.6 Algorithm Complexity......Page 55
2.7 No Free Lunch Theorems......Page 56
Exercises......Page 58
3.1 Upper and Lower Bounds......Page 60
3.2 Basic Calculus......Page 62
3.3.1 Continuity and Smoothness......Page 66
3.3.2 Stationary Points......Page 67
3.3.3 Optimality Criteria......Page 69
3.4 Vector and Matrix Norms......Page 71
3.5.1 Eigenvalues......Page 74
3.5.2 Definiteness......Page 77
3.6.1 Linear Functions......Page 79
3.6.3 Quadratic Form......Page 80
3.7.2 Hessian......Page 82
3.7.4 Optimality of multivariate functions......Page 83
3.8.1 Convex Set......Page 84
3.8.2 Convex Functions......Page 86
Exercises......Page 89
4.1 Unconstrained Optimization......Page 92
4.2.1 Newton's Method......Page 93
4.2.2 Steepest Descent Method......Page 94
4.2.3 Line Search......Page 96
4.2.4 Conjugate Gradient Method......Page 97
4.4 Linear Programming......Page 99
4.5.1 Basic Procedure......Page 101
4.5.2 Augmented Form......Page 103
4.8 Lagrange Multipliers......Page 107
4.9 Karush-Kuhn-Tucker Conditions......Page 111
Exercises......Page 114
5.1 BFGS Method......Page 116
5.2.2 Nelder-Mead Downhill Simplex......Page 117
5.3 Trust-Region Method......Page 119
5.4.2 Sequential Quadratic Programming......Page 122
Exercises......Page 124
6.1 KKT Conditions......Page 126
6.2 Convex Optimization Examples......Page 128
6.3 Equality Constrained Optimization......Page 130
6.4 Barrier Functions......Page 132
6.5 Interior-Point Methods......Page 135
6.6 Stochastic and Robust Optimization......Page 136
Exercises......Page 138
7.1.1 Curvature......Page 142
7.1.2 Euler-Lagrange Equation......Page 145
7.2 Variations with Constraints......Page 151
7.3 Variations for Multiple Variables......Page 155
7.4 Optimal Control......Page 156
7.4.1 Control Problem......Page 157
7.4.2 Pontryagin's Principle......Page 158
7.4.3 Multiple Controls......Page 160
7.4.4 Stochastic Optimal Control......Page 161
Exercises......Page 162
8.1 Linear Congruential Algorithms......Page 164
8.2 Uniform Distribution......Page 165
8.3 Other Distributions......Page 167
8.4 Metropolis Algorithms......Page 171
Exercises......Page 172
9.1 Estimating π......Page 174
9.2 Monte Carlo Integration......Page 177
9.3 Importance of Sampling......Page 180
Exercises......Page 182
10.1 Random Process......Page 184
10.2 Random Walk......Page 186
10.2.1 ID Random Walk......Page 187
10.2.2 Random Walk in Higher Dimensions......Page 189
10.3 Lévy Flights......Page 190
10.5 Markov Chain Monte Carlo......Page 192
10.5.1 Metropolis-Hastings Algorithms......Page 195
10.5.2 Random Walk......Page 197
10.6 Markov Chain and Optimisation......Page 198
Exercises......Page 200
PART II METAHEURISTIC ALGORITHMS......Page 202
11.1 Introduction......Page 204
11.2.1 Basic Procedure......Page 205
11.2.2 Choice of Parameters......Page 207
11.3 Implementation......Page 208
Exercises......Page 210
12.1 Annealing and Probability......Page 212
12.2 Choice of Parameters......Page 213
12.4 Implementation......Page 215
Exercises......Page 217
13.1 Behaviour of Ants......Page 220
13.2 Ant Colony Optimization......Page 221
13.3 Double Bridge Problem......Page 223
13.4 Virtual Ant Algorithm......Page 224
Exercises......Page 226
14.1 Behavior of Honey Bees......Page 228
14.2.1 Honey Bee Algorithm......Page 229
14.2.2 Virtual Bee Algorithm......Page 231
14.3 Applications......Page 232
Exercises......Page 233
15.1 Swarm Intelligence......Page 234
15.2 PSO algorithms......Page 235
15.3 Accelerated PSO......Page 236
15.4.1 Multimodal Functions......Page 238
15.4.2 Validation......Page 239
15.5 Constraints......Page 240
Exercises......Page 241
16.1 Music-Based Algorithms......Page 244
16.2 Harmony Search......Page 246
16.3 Implementation......Page 248
Exercises......Page 249
17.1 Behaviour of Fireflies......Page 252
17.2.2 Light Intensity and Attractiveness......Page 253
17.2.4 Two Special Cases......Page 256
17.3.1 Multiple Global Optima......Page 257
17.3.2 Multimodal Functions......Page 258
17.3.3 FA Variants......Page 259
Exercises......Page 260
PART III APPLICATIONS......Page 262
18.1 Pareto Optimality......Page 264
18.2 Weighted Sum Method......Page 268
18.3 Utility Method......Page 270
18.4 Metaheuristic Search......Page 272
18.5 Other Algorithms......Page 273
Exercises......Page 275
19.1 Spring Design......Page 278
19.2 Pressure Vessel......Page 279
19.3 Shape Optimization......Page 280
19.4 Optimization of Eigenvalues and Frequencies......Page 283
19.5 Inverse Finite Element Analysis......Page 287
Exercises......Page 289
Appendix A: Test Problems in Optimization......Page 292
B.l Genetic Algorithms......Page 298
B.2 Simulated Annealing......Page 301
B.3 Particle Swarm Optimization......Page 303
B.4 Harmony Search......Page 304
B.5 Firefly Algorithm......Page 306
B.6 Large Sparse Linear Systems......Page 309
B.7.1 Spring Design......Page 310
B.7.2 Pressure Vessel......Page 312
Appendix C: Glossary......Page 314
Appendix D: Problem Solutions......Page 336
References......Page 364
Index......Page 374