Stochastic Optimization

By: Johannes Schneider, Scott Kirkpatrick

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Hardcover | 1 November 2006

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586 Pages

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General Remarks.- Exact Optimization Algorithms for Simple Problems.- Exact Optimization Algorithms for Complex Problems.- Monte Carlo.- Overview of Optimization Heuristics.- Implementation of Constraints.-Parallelization Strategies.- Construction Heuristics.- Markovian Improvement Heuristics.- Local Search.- Ruin & Recreate.- Simulated Annealing.- Threshold Accepting and Other Algorithms Related to Simulated Annealing.- Changing The Energy Landscape.- Estimation of Expectation Values.- Cooling Techniques.- Estimation of the Calculation Time Needed.- Weakening the Pure Markovian Approach.-Neural Networks.- Genetic Algorithms and Evolution Strategies.- Optimization Algorithms Inspired by Social Animals.- Optimization Algorithms Based on Multi Agent Systems.- Tabu Search.- Histogram Algorithms.- Searching for Backbones.- The Travelling Salesman Problem.- Extensions of the Traveling Salesman Problem.- Application of Construction Heuristics of theTSP.- Local Search Concepts Applied to the TSP.- Next Larger Moves Applied to the TSP.- Ruin and Recreate Applied to the TSP.- Application of Simulated Annealing to the TSP.-Dependencies of the SA-Results on the Moves and the Cooling Process.- Applicaton of Algorithms. Related to Simulated Annealing to the TSP.-Application of Search Space Smoothing to the TSP.-Further Techniques Changing the Energy Landscape of a TSP.- Applicaton of Neural Networks to the TSP. Application of Genetic Algorithms to the TSP.- Social Animal Algorithms Applied to the TSP.- Simulated Trading Applied to the TSP.- Tabu Search Applied to the TSP.- Application of History Algorithms to the TSP.- Application of Searching for Backbones to the TSP.- Simulating Various Types of Government With Searhing for Backbones.- The Constraint Satisfaction Problem.- Construction Heuristics for the CSP.- Random Local Iterative Search Heuristics.- Belief Propagation and Survey Propagation.- Outlook for the Future of the Optimization Business.

Industry Reviews

From the reviews:

"The book is devoted to stochastic global optimization methods. ... The book is primarily addressed to scientists and students from the physical and engineering sciences but may also be useful to a larger community interested in stochastic methods of global optimization." (A. H. Zilinskas, Mathematical Reviews, Issue 2007 i)

"This book provides a rich collection of stochastic optimization algorithms and heuristics that cope with optimization issues. ... In summary, this is a good book on stochastic optimization. It is important book of any engineering library or laboratory. In my opinion, this book may be used as a quick reference for sophisticated scholars, or as an introductory book for students who are interested in an overview of the state-of-the-art mechanisms in this field." (Wei Yen, Computing Reviews, December, 2007)

"This book presents a compendium of Stochastic Optimisation concerned with the use of heuristics mainly including Markov Chain Monte Carlo methods. It is divided into 3 parts. ... 216 references are listed. They cover the main existing results in the theme. I consider that an outstanding feature of the book is its successful synthesis of giving in an 'altogether' curve information needed for being comfortable with the realms of heuristic algorithms. I warmly recommended it for specialists working in optimization." (Carlos Narciso Bouza Herrera, Zentralblatt MATH, Vol. 1116 (18), 2007)

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Optimisation Linear Programming Probability & Statistics Computing & I.T.Computer Science Artificial Intelligence Science Physics

Engineering & Technology Electronics & Communications Engineering Electronics Engineering Technology in General Engineering in General

Theory
Overview of Stochastic Optimization Algorithms
General Remarks	p. 3
Why Optimize Things?	p. 3
Moral Aspects of Optimization	p. 4
How To Think About It	p. 5
Minima, Maxima, and Extrema	p. 6
What Is So Hard About Optimization?	p. 6
Algorithms, Heuristics, Metaheuristics	p. 7
Exact Optimization Algorithms for Simple Problems	p. 9
A Simple Example-Exact Optimization in One Dimension	p. 9
Newton-Raphson Method	p. 10
Descent Methods in More Than One Dimension	p. 12
Conjugate Gradients	p. 13
Exact Optimization Algorithms for Complex Problems	p. 15
Simplex Algorithm	p. 15
Integer Optimization	p. 20
Branch & Bound	p. 21
Branch & Cut	p. 24
Monte Carlo	p. 31
Pseudorandom Numbers	p. 31
Random Number Generation and Random Number Tests	p. 32
Transformation of Random Numbers	p. 37
Example: Calculation of [pi] with MC	p. 42
Overview of Optimization Heuristics	p. 43
Necessity of Heuristics	p. 43
Construction Heuristics	p. 44
Markovian Improvement Heuristics	p. 45
Set-Based Improvement Heuristics	p. 46
Implementation of Constraints	p. 49
Moves, Constraints, Deadlines	p. 49
Incorporation into the Configurations	p. 49
Consideration of Feasible Solutions Only	p. 50
Penalty Functions	p. 50
Parallelization Strategies	p. 53
Parallelization Models and Computer Architectures	p. 53
Running Several Copies	p. 54
Divide et Impera	p. 54
Information Exchange	p. 56
Construction Heuristics	p. 59
General Outline of Construction Heuristics	p. 59
Insertion Heuristics	p. 60
Savings Heuristics	p. 61
More Intelligent Ways of Construction	p. 61
Markovian Improvement Heuristics	p. 63
Constructing a Markov Chain	p. 63
Trivial Acceptance Functions	p. 64
Introduction of a Control Parameter	p. 65
Heat Bath Approach	p. 66
Local Search	p. 69
Classic Local Search Approach	p. 69
Problems of the Local Search Approach	p. 70
Larger Moves	p. 70
Jumping Between Different Move Sizes	p. 71
Ruin & Recreate	p. 73
The Philosophy of Building One's Own Castle	p. 73
Outline of Approach	p. 73
Discussion of Ruin & Recreate	p. 76
Ruin & Recreate as a Self-Contained Optimization Algorithm	p. 77
Simulated Annealing	p. 79
Physical and Historical Background	p. 79
Derivation of Simulated Annealing	p. 81
Thermal Expectation Values	p. 85
Inverse Simulated Annealing	p. 88
Threshold Accepting and Other Algorithms Related to Simulated Annealing	p. 89
Threshold Accepting	p. 89
The Steady-State Equilibrium Characteristics of TA	p. 91
Methods Based on the Tsallis Statistics	p. 96
The Great Deluge Algorithm	p. 100
Changing the Energy Landscape	p. 103
Search Space Smoothing	p. 103
Ant Lion Heuristics and Activation Relaxation Technique	p. 108
Noising or Permutation of System Parts	p. 111
Weight Annealing	p. 112
Estimation of Expectation Values	p. 115
Simple Sampling	p. 115
Biased Sampling	p. 115
Importance Sampling	p. 116
Parallel Sampling	p. 117
Cooling Techniques	p. 119
Standard Cooling Schedules	p. 119
Nonmonotonic Cooling Schedules	p. 122
Ensemble Based Schedules	p. 126
Simulated Tempering and Parallel Tempering	p. 130
Estimation of Calculation Time Needed	p. 135
Exponentially Growing Space Size	p. 135
Polynomial Approach	p. 135
Grest Hypothesis	p. 135
Weakening the Pure Markovian Approach	p. 137
Saving the Best-So-Far Solution and Spinoffs at Good Solutions	p. 137
Record-to-Record Travel	p. 138
Stochastic Tunneling	p. 139
Changing the Cooling Schedule Due to Intermediate Results	p. 139
Neural Networks	p. 143
Biological Motivation	p. 143
Artificial Neural Networks	p. 145
The Hopfield Model	p. 149
Kohonen Networks	p. 154
Genetic Algorithms and Evolution Strategies	p. 157
Charles Darwin's Natural Selection	p. 157
Mutations and Crossovers	p. 158
Application to Optimization Problems	p. 161
Parallel Applications	p. 166
Optimization Algorithms Inspired by Social Animals	p. 169
Inspiration by the Behavior of Animals	p. 169
Ant Colony Optimization	p. 169
Particle Swarm Optimization	p. 171
Fighting and Ranking	p. 172
Optimization Algorithms Based on Multiagent Systems	p. 175
Motivation	p. 175
Simulated Trading	p. 176
Selfish vs. Global Optimization	p. 178
Introduction of a Social Temperature	p. 179
Tabu Search	p. 181
Tabu	p. 181
Use of Memory	p. 182
Aspiration	p. 183
Intensification and Diversification	p. 183
Histogram Algorithms	p. 185
Guided Local Search	p. 185
Multicanonical Algorithm	p. 186
MUCAREM and REMUCA	p. 192
Multicanonical Annealing	p. 192
Searching for Backbones	p. 193
Comparing Different Good Solutions	p. 193
Determining the Backbone	p. 194
Outline of the SFB Algorithm	p. 195
Discussion of the Algorithm	p. 196
Applications
General Remarks	p. 201
Dealing with a Proposed Optimization Problem	p. 201
Programming Languages and Parallelization Libraries	p. 202
Optimization Libraries	p. 204
Difficulty of Comparing Various Algorithms	p. 205
The Traveling Salesman Problem
The Traveling Salesman Problem	p. 211
The Task of the Traveling Salesman	p. 211
Distance Metrics	p. 211
The Dijkstra Algorithm	p. 212
Various Possible Codings	p. 215
Four Approaches to the TSP	p. 218
Benchmark Instances	p. 219
Bounds for the Optimum Solution	p. 223
The Misfit: A Frustration Measure	p. 225
Order Parameters for the TSP	p. 226
Short History of TSP	p. 229
Extensions of Traveling Salesman Problem	p. 233
Temporal Constraints	p. 233
Vehicle Routing Problems	p. 234
Probabilistic Models and Online Optimization	p. 239
Supply Chain Management	p. 240
Application of Construction Heuristics to TSP	p. 243
Nearest Neighbor Heuristic	p. 243
Insertion Heuristics	p. 246
Using Deeper Insight into the Problem	p. 251
The Savings Heuristic	p. 255
Local Search Concepts Applied to TSP	p. 263
Initialization Routine	p. 263
Small Moves	p. 265
Computational Results for Greedy Algorithm	p. 269
Local Search as Afterburner for Construction Heuristics	p. 272
Next Larger Moves Applied to TSP	p. 275
Lin-3-Opts	p. 275
Higher-Order Lin-n-Opts	p. 277
Computational Results for the Greedy Algorithm	p. 283
Combination of Moves of Various Sizes	p. 285
Ruin & Recreate Applied to TSP	p. 287
Application of Ruin & Recreate	p. 287
Analysis of R & R Moves in RW and GRE Modes	p. 290
Ruin & Recreate as Self-Contained Algorithm	p. 294
Discussion of Application Possibilities of Ruin & Recreate	p. 296
Application of Simulated Annealing to TSP	p. 299
Simulated Annealing for the TSP	p. 299
Computational Results for Observables of Interest	p. 302
Computational Results for Acceptance Rates	p. 306
Quality of the Results Achieved with Various Computing Times	p. 310
Dependencies of SA Results on Moves and Cooling Process	p. 315
Results for Various Small Moves	p. 315
Results for Monotonous Cooling Schedules	p. 318
Results for Bouncing	p. 324
Results for Parallel Tempering	p. 334
Application to TSP of Algorithms Related to Simulated Annealing	p. 341
Computational Results for Threshold Accepting	p. 341
Computational Results for Penna Criterion	p. 347
Computational Results for Great Deluge Algorithm	p. 350
Computational Results for Record-to-Record Travel	p. 359
Application of Search Space Smoothing to TSP	p. 367
A Small Toy Problem	p. 367
Gu and Huang Approach	p. 369
Effect of Numerical Precision on Smoothing	p. 383
Smoothing with Finite Numerical Precision Only	p. 386
Further Techniques Changing the Energy Landscape of a TSP	p. 389
The Convex-Concave Approach to Search Space Smoothing	p. 389
Noising the System	p. 397
Weight Annealing	p. 399
Final Remarks on Application of Changing Techniques	p. 403
Application of Neural Networks to TSP	p. 405
Application of a Hopfield Network	p. 405
Computational Results for the Hopfield Network	p. 407
Application of a Kohonen Network	p. 408
Computational Results for a Kohonen Network	p. 409
Application of Genetic Algorithms to TSP	p. 415
Mutations	p. 415
Crossovers	p. 416
Natural Selection	p. 419
Computational Results	p. 420
Social Animal Algorithms Applied to TSP	p. 423
Application of Ant Colony Optimization	p. 423
Computational Results	p. 426
Application of Bird Flock Model	p. 428
Computational Results	p. 429
Simulated Trading Applied to TSP	p. 431
Application of Simulated Trading to the TSP	p. 431
Computational Results	p. 435
Discussion of Simulated Trading	p. 438
Simulated Trading and Working	p. 438
Tabu Search Applied to TSP	p. 441
Definition of a Tabu List	p. 441
Introduction of Short-Term Memory	p. 444
Adding some Aspiration	p. 445
Adding Intensification and Diversification	p. 445
Application of History Algorithms to TSP	p. 449
The Multicanonical Algorithm	p. 449
Multicanonical Annealing	p. 452
Acceptance Simulated Annealing	p. 455
Guided Local Search	p. 464
Application of Searching for Backbones to TSP	p. 471
Definition of a Backbone	p. 471
Application to the Completely Asymmetric TSP	p. 475
Application to Partially Asymmetric TSP	p. 477
Computational Results	p. 478
Simulating Various Types of Government with Searching for Backbones	p. 489
An Aristocratic Approach	p. 489
A Democratic Approach	p. 491
Solution of the PCB442 Problem	p. 492
Can Humans Do This, Too?	p. 496
The Constraint Satisfaction Problem
The Constraint Satisfaction Problem	p. 501
Sources of Constraint Satisfaction Problems	p. 501
Benchmarks and Competitions	p. 503
Randomly Generated Models and Their Complexity	p. 504
Randomly Generated Models and Their Phase Diagrams	p. 506
Mixtures of easy and hard CSPs	p. 510
Construction Heuristics for CSP	p. 513
Application of the Bestinsertion Heuristic to the 3-SAT Problem	p. 513
Assertion, Decimation, and Resolution	p. 517
Analyzable Assertion Protocols	p. 517
Solution Space Structure of XOR-SAT	p. 519
Random Local Iterative Search Heuristics	p. 523
RWalkSAT	p. 523
WalkSAT	p. 524
Simulated Annealing	p. 526
Belief Propagation and Survey Propagation	p. 529
Belief Propagation, Message Passing, and Cavities	p. 529
Message Passing as Side Information for Decimation	p. 531
Belief Propagation and Sudoku	p. 534
Outlook
Future Outlook of Optimization Business	p. 539
P = NP?	p. 539
Quantum Computing	p. 540
DNA Computing	p. 541
How Will the Problems Evolve?	p. 544
Acknowledgments	p. 547
References	p. 551
Index	p. 563
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Stochastic Optimization

At a Glance

Hardcover

Industry Reviews

Shipping

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