Verfügbarkeit: Stochastic optimization | Technische Universität München

Stochastic optimization: 29 tables

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Bibliographische Detailangaben
Beteiligte Personen:	Schneider, Johannes Josef 1971- (VerfasserIn), Kirkpatrick, Scott (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2006
Schriftenreihe:	Scientific computation
Schlagwörter:	Optimisation mathématique Processus stochastiques Mathematical optimization Stochastic processes Stochastische Optimierung Computerarithmetik
Links:	http://deposit.dnb.de/cgi-bin/dokserv?id=2803610&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015733494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Literaturverz. S. 551 - 561
Umfang:	XVI, 565 S. Ill., graph. Darst., Kt.
ISBN:	9783540345596 3540345590

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Datensatz im Suchindex

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adam_text	Contents Part I Theory Overview of Stochastic Optimization Algorithms 0 General Remarks ......................................... 3 0.1 Why Optimize Things? .................................. 3 0.2 Moral Aspects of Optimization ........................... 4 0.3 How To Think About It ................................. 5 0.4 Minima, Maxima, and Extrema .......................... 6 0.5 What Is So Hard About Optimization? .................... 6 0.6 Algorithms, Heuristics, Metaheuristics .................... 7 1 Exact Optimization Algorithms for Simple Problems ..... 9 1.1 A Simple Example — Exact Optimization in One Dimension .. 9 1.2 Newton-Raphson Method ............................... 10 1.3 Descent Methods in More Than One Dimension ............ 12 1.4 Conjugate Gradients .................................... 13 2 Exact Optimization Algorithms for Complex Problems ... 15 2.1 Simplex Algorithm ..................................... 15 2.2 Integer Optimization .................................... 20 2.3 Branch & Bound ....................................... 21 2.4 Branch & Cut .......................................... 24 3 Monte Carlo .............................................. 31 3.1 Pseudorandom Numbers ................................. 31 3.2 Random Number Generation and Random Number Tests .... 32 3.3 Transformation of Random Numbers ...................... 37 3.4 Example: Calculation of π with MC ...................... 42 4 Overview of Optimization Heuristics ...................... 43 4.1 Necessity of Heuristics .................................. 43 4.2 Construction Heuristics ................................. 44 4.3 Markovian Improvement Heuristics ....................... 45 4.4 Set-Based Improvement Heuristics ........................ 46 X Contents 5 Implementation of Constraints ............................ 49 5.1 Moves, Constraints, Deadlines ............................ 49 5.2 Incorporation into the Configurations ..................... 49 5.3 Consideration of Feasible Solutions Only .................. 50 5.4 Penalty Functions ...................................... 50 6 Parallelization Strategies ................................. 53 6.1 Parallelization Models and Computer Architectures ......... 53 6.2 Running Several Copies ................................. 54 6.3 Divide et Impera....................................... 54 6.4 Information Exchange ................................... 56 7 Construction Heuristics ................................... 59 7.1 General Outline of Construction Heuristics ................ 59 7.2 Insertion Heuristics ..................................... 60 7.3 Savings Heuristics ...................................... 61 7.4 More Intelligent Ways of Construction .................... 61 8 Markovian Improvement Heuristics ....................... 63 8.1 Constructing a Markov Chain ............................ 63 8.2 Trivial Acceptance Functions ............................ 64 8.3 Introduction of a Control Parameter ...................... 65 8.4 Heat Bath Approach .................................... 66 9 Local Search .............................................. 69 9.1 Classic Local Search Approach ........................... 69 9.2 Problems of the Local Search Approach ................... 70 9.3 Larger Moves .......................................... 70 9.4 Jumping Between Different Move Sizes .................... 71 10 Ruin L· Recreate ......................................... 73 10.1 The Philosophy of Building One s Own Castle ............. 73 10.2 Outline of Approach .................................... 73 10.3 Discussion of Ruin & Recreate ........................... 76 10.4 Ruin h Recreate as a Self-Contained Optimization Algorithm 77 11 Simulated Annealing ...................................... 79 11.1 Physical and Historical Background ....................... 79 11.2 Derivation of Simulated Annealing ........................ 81 11.3 Thermal Expectation Values ............................. 85 11.4 Inverse Simulated Annealing ............................. 88 12 Threshold Accepting and Other Algorithms Related to Simulated Annealing ................................... 89 12.1 Threshold Accepting .................................... 89 Contents XI 12.2 The Steady-State Equilibrium Characteristics of TA ........ 91 12.3 Methods Based on the Tsallis Statistics ................... 96 12.4 The Great Deluge Algorithm .............................100 13 Changing the Energy Landscape ..........................103 13.1 Search Space Smoothing .................................103 13.2 Ant Lion Heuristics and Activation Relaxation Technique. .. . 108 13.3 Noising or Permutation of System Parts ................... Ill 13.4 Weight Annealing ......................................112 14 Estimation of Expectation Values .........................115 14.1 Simple Sampling .......................................115 14.2 Biased Sampling .......................................115 14.3 Importance Sampling ...................................116 14.4 Parallel Sampling .......................................117 15 Cooling Techniques .......................................119 15.1 Standard Cooling Schedules ..............................119 15.2 Nonmonotonic Cooling Schedules .........................122 15.3 Ensemble Based Schedules ...............................126 15.4 Simulated Tempering and Parallel Tempering ..............130 16 Estimation of Calculation Time Needed ..................135 16.1 Exponentially Growing Space Size ........................135 16.2 Polynomial Approach ...................................135 16.3 Grest Hypothesis .......................................135 17 Weakening the Pure Markovian Approach ................137 17.1 Saving the Best-So-Far Solution and Spinoffs at Good Solutions ...........................137 17.2 Record-to-Record Travel ................................138 17.3 Stochastic Tunneling ....................................139 17.4 Changing the Cooling Schedule Due to Intermediate Results . 139 18 Neural Networks .........................................143 18.1 Biological Motivation ...................................143 18.2 Artificial Neural Networks ...............................145 18.3 The Hopfield Model ....................................149 18.4 Kohonen Networks .....................................154 19 Genetic Algorithms and Evolution Strategies ............. 157 19.1 Charles Darwin s Natural Selection ....................... 157 19.2 Mutations and Crossovers ............................... 158 19.3 Application to Optimization Problems .................... 161 19.4 РагаБеї Applications .................................... 166 XII Contents 20 Optimization Algorithms Inspired by Social Animals ..... 169 20.1 Inspiration by the Behavior of Animals .................... 169 20.2 Ant Colony Optimization ................................ 169 20.3 Particle Swarm Optimization ............................ 171 20.4 Fighting and Ranking ................................... 172 21 Optimization Algorithms Based on Multiagent Systems. .. 175 21.1 Motivation ............................................ 175 21.2 Simulated Trading ...................................... 176 21.3 Selfish vs. Global Optimization ........................... 178 21.4 Introduction of a Social Temperature ..................... 179 22 Tabu Search .............................................. 181 22.1 Tabu ................................................. 181 22.2 Use of Memory ......................................... 182 22.3 Aspiration ............................................. 183 22.4 Intensification and Diversification ......................... 183 23 Histogram Algorithms .................................... 185 23.1 Guided Local Search .................................... 185 23.2 Multicanonical Algorithm ............................... 186 23.3 MUCAREM and REMUCA ............................. 192 23.4 Multicanonical Annealing ................................ 192 24 Searching for Backbones .................................. 193 24.1 Comparing Different Good Solutions ...................... 193 24.2 Determining the Backbone ............................... 194 24.3 Outline of the SFB Algorithm ............................ 195 24.4 Discussion of the Algorithm .............................. 196 Part II Applications 0 General Remarks .........................................201 0.1 Dealing with a Proposed Optimization Problem ............201 0.2 Programming Languages and Parallelization Libraries .......202 0.3 Optimization Libraries ..................................204 0.4 Difficulty of Comparing Various Algorithms ................205 Applications A The Traveling Salesman Problem 1 The Traveling Salesman Problem .........................211 1.1 The Task of the Traveling Salesman ......................211 1.2 Distance Metrics .......................................211 Contents XIII 1.3 The Dijkstra Algorithm .................................212 1.4 Various Possible Codings ................................215 1.5 Four Approaches to the TSP .............................218 1.6 Benchmark Instances ...................................219 1.7 Bounds for the Optimum Solution ........................223 1.8 The Misfit: A Frustration Measure ........................225 1.9 Order Parameters for the TSP ...........................226 1.10 Short History of TSP ...................................229 2 Extensions of Traveling Salesman Problem ................233 2.1 Temporal Constraints ...................................233 2.2 Vehicle Routing Problems ...............................234 2.3 Probabilistic Models and Online Optimization .............239 2.4 Supply Chain Management ..............................240 3 Application of Construction Heuristics to TSP ...........243 3.1 Nearest Neighbor Heuristic ..............................243 3.2 Insertion Heuristics .....................................246 3.3 Using Deeper Insight into the Problem ....................251 3.4 The Savings Heuristic ...................................255 4 Local Search Concepts Applied to TSP ...................263 4.1 Initialization Routine ...................................263 4.2 Small Moves ...........................................265 4.3 Computational Results for Greedy Algorithm ..............269 4.4 Local Search as Afterburner for Construction Heuristics .....272 5 Next Larger Moves Applied to TSP ......................275 5.1 Lin-3-Opts.............................................275 5.2 Higher-Order Lin-ra-Opts ................................277 5.3 Computational Results for the Greedy Algorithm ...........283 5.4 Combination of Moves of Various Sizes ....................285 6 Ruin & Recreate Applied to TSP .........................287 6.1 Application of Ruin & Recreate ..........................287 6.2 Analysis of R & R Moves in RW and GRE Modes ..........290 6.3 Ruin & Recreate as Self-Contained Algorithm ..............294 6.4 Discussion of Application Possibilities of Ruin & Recreate ... 296 7 Application of Simulated Annealing to TSP ..............299 7.1 Simulated Annealing for the TSP .........................299 7.2 Computational Results for Observables of Interest ..........302 7.3 Computational Results for Acceptance Rates ...............306 7.4 Quality of the Results Achieved with Various Computing Times .................................................310 XIV Contents 8 Dependencies of SA Results on Moves and Cooling Process ......................................315 8.1 Results for Various Small Moves ..........................315 8.2 Results for Monotonous Cooling Schedules .................318 8.3 Results for Bouncing ....................................324 8.4 Results for Parallel Tempering ...........................334 9 Application to TSP of Algorithms Related to Simulated Annealing ...................................341 9.1 Computational Results for Threshold Accepting ............341 9.2 Computational Results for Penna Criterion ................347 9.3 Computational Results for Great Deluge Algorithm .........350 9.4 Computational Results for Record-to-Record Travel .........359 10 Application of Search Space Smoothing to TSP ...........367 10.1 A Small Toy Problem ...................................367 10.2 Gu and Huang Approach ................................369 10.3 Effect of Numerical Precision on Smoothing ................383 10.4 Smoothing with Finite Numerical Precision Only ...........386 11 Further Techniques Changing the Energy Landscape of a TSP ..................................................389 11.1 The Convex-Concave Approach to Search Space Smoothing . 389 11.2 Noising the System .....................................397 11.3 Weight Annealing ......................................399 11.4 Final Remarks on Application of Changing Techniques ......403 12 Application of Neural Networks to TSP ..................405 12.1 Application of a Hopfield Network ........................405 12.2 Computational Results for the Hopfield Network ...........407 12.3 Application of a Kohonen Network .......................408 12.4 Computational Results for a Kohonen Network .............409 13 Application of Genetic Algorithms to TSP ................415 13.1 Mutations .............................................415 13.2 Crossovers .............................................416 13.3 Natural Selection .......................................419 13.4 Computational Results ..................................420 14 Social Animal Algorithms Applied to TSP ................423 14.1 Application of Ant Colony Optimization ...................423 14.2 Computational Results ..................................426 14.3 Application of Bird Flock Model .........................428 14.4 Computational Results ..................................429 Contents XV 15 Simulated Trading Applied to TSP .......................431 15.1 Application of Simulated Trading to the TSP ..............431 15.2 Computational Results ..................................435 15.3 Discussion of Simulated Trading ..........................438 15.4 Simulated Trading and Working ..........................438 16 Tabu Search Applied to TSP .............................441 16.1 Definition of a Tabu List ................................441 16.2 Introduction of Short-Term Memory ......................444 16.3 Adding some Aspiration .................................445 16.4 Adding Intensification and Diversification .................445 17 Application of History Algorithms to TSP ................449 17.1 The Multicanonical Algorithm ...........................449 17.2 Multicanonical Annealing ................................452 17.3 Acceptance Simulated Annealing .........................455 17.4 Guided Local Search ....................................464 18 Application of Searching for Backbones to TSP ...........471 18.1 Definition of a Backbone ................................471 18.2 Application to the Completely Asymmetric TSP ............475 18.3 Application to Partially Asymmetric TSP .................477 18.4 Computational Results ..................................478 19 Simulating Various Types of Government with Searching for Backbones .............................489 19.1 An Aristocratic Approach ...............................489 19.2 A Democratic Approach .................................491 19.3 Solution of the PCB442 Problem .........................492 19.4 Can Humans Do This, Too? .............................496 Applications В The Constraint Satisfaction Problem 20 The Constraint Satisfaction Problem .....................501 20.1 Sources of Constraint Satisfaction Problems ................501 20.2 Benchmarks and Competitions ...........................503 20.3 Randomly Generated Models and Their Complexity ........504 20.4 Randomly Generated Models and Their Phase Diagrams .... 506 20.5 Mixtures of easy and hard CSPs ..........................510 XVI Contents 21 Construction Heuristics for CSP ..........................513 21.1 Application of the Bestinsertion Heuristic to the 3-SAT Problem ...............................................513 21.2 Assertion, Decimation, and Resolution ....................517 21.3 Analyzable Assertion Protocols ...........................517 21.4 Solution Space Structure of XOR-SAT ....................519 22 Random Local Iterative Search Heuristics ................523 22.1 RWalkSAT ............................................523 22.2 WalkSAT ..............................................524 22.3 Simulated Annealing ....................................526 23 Belief Propagation and Survey Propagation ...............529 23.1 Belief Propagation, Message Passing, and Cavities ..........529 23.2 Message Passing as Side Information for Decimation ........531 23.3 Belief Propagation and Sudoku ...........................534 Part III Outlook 24 Future Outlook of Optimization Business .................539 24.1 V = ΛίΡ? .............................................539 24.2 Quantum Computing ...................................540 24.3 DNA Computing .......................................541 24.4 How Will the Problems Evolve? ..........................544 Acknowledgments ............................................547 References ....................................................551 Index .........................................................563
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series2	Scientific computation
spellingShingle	Schneider, Johannes Josef 1971- Kirkpatrick, Scott Stochastic optimization 29 tables Optimisation mathématique Processus stochastiques Mathematical optimization Stochastic processes Stochastische Optimierung (DE-588)4057625-5 gnd Computerarithmetik (DE-588)4135485-0 gnd
subject_GND	(DE-588)4057625-5 (DE-588)4135485-0
title	Stochastic optimization 29 tables
title_auth	Stochastic optimization 29 tables
title_exact_search	Stochastic optimization 29 tables
title_full	Stochastic optimization 29 tables Johannes J. Schneider ; Scott Kirkpatrick
title_fullStr	Stochastic optimization 29 tables Johannes J. Schneider ; Scott Kirkpatrick
title_full_unstemmed	Stochastic optimization 29 tables Johannes J. Schneider ; Scott Kirkpatrick
title_short	Stochastic optimization
title_sort	stochastic optimization 29 tables
title_sub	29 tables
topic	Optimisation mathématique Processus stochastiques Mathematical optimization Stochastic processes Stochastische Optimierung (DE-588)4057625-5 gnd Computerarithmetik (DE-588)4135485-0 gnd
topic_facet	Optimisation mathématique Processus stochastiques Mathematical optimization Stochastic processes Stochastische Optimierung Computerarithmetik
url	http://deposit.dnb.de/cgi-bin/dokserv?id=2803610&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015733494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT schneiderjohannesjosef stochasticoptimization29tables AT kirkpatrickscott stochasticoptimization29tables

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