Stochastic optimization /

Stochastic optimization /

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Bibliographic Details
Author / Creator:Schneider, Johannes J. (Johannes Josef)
Imprint:Berlin : Springer, 2006.
Description:xvi, 565 p. : ill. (some col.) ; 25 cm.
Language:English
Series:Scientific computation, 1434-8322
Subject:
Mathematical optimization.
Stochastic processes.
Mathematical optimization.
Stochastic processes.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/6244449
Hidden Bibliographic Details
Other authors / contributors:Kirkpatrick, Scott.
ISBN:9783540345596 (hd.bd.)
3540345590 (hd.bd.)
Notes:Includes bibliographical references (p.[551]-561) and index.
Standard no.:9783540345596
Table of Contents:
  • Part I. Theory
  • Overview of Stochastic Optimization Algorithms
  • 0. General Remarks
  • 0.1. Why Optimize Things?
  • 0.2. Moral Aspects of Optimization
  • 0.3. How To Think About It
  • 0.4. Minima, Maxima, and Extrema
  • 0.5. What Is So Hard About Optimization?
  • 0.6. Algorithms, Heuristics, Metaheuristics
  • 1. Exact Optimization Algorithms for Simple Problems
  • 1.1. A Simple Example-Exact Optimization in One Dimension
  • 1.2. Newton-Raphson Method
  • 1.3. Descent Methods in More Than One Dimension
  • 1.4. Conjugate Gradients
  • 2. Exact Optimization Algorithms for Complex Problems
  • 2.1. Simplex Algorithm
  • 2.2. Integer Optimization
  • 2.3. Branch & Bound
  • 2.4. Branch & Cut
  • 3. Monte Carlo
  • 3.1. Pseudorandom Numbers
  • 3.2. Random Number Generation and Random Number Tests
  • 3.3. Transformation of Random Numbers
  • 3.4. Example: Calculation of [pi] with MC
  • 4. Overview of Optimization Heuristics
  • 4.1. Necessity of Heuristics
  • 4.2. Construction Heuristics
  • 4.3. Markovian Improvement Heuristics
  • 4.4. Set-Based Improvement Heuristics
  • 5. Implementation of Constraints
  • 5.1. Moves, Constraints, Deadlines
  • 5.2. Incorporation into the Configurations
  • 5.3. Consideration of Feasible Solutions Only
  • 5.4. Penalty Functions
  • 6. Parallelization Strategies
  • 6.1. Parallelization Models and Computer Architectures
  • 6.2. Running Several Copies
  • 6.3. Divide et Impera
  • 6.4. Information Exchange
  • 7. Construction Heuristics
  • 7.1. General Outline of Construction Heuristics
  • 7.2. Insertion Heuristics
  • 7.3. Savings Heuristics
  • 7.4. More Intelligent Ways of Construction
  • 8. Markovian Improvement Heuristics
  • 8.1. Constructing a Markov Chain
  • 8.2. Trivial Acceptance Functions
  • 8.3. Introduction of a Control Parameter
  • 8.4. Heat Bath Approach
  • 9. Local Search
  • 9.1. Classic Local Search Approach
  • 9.2. Problems of the Local Search Approach
  • 9.3. Larger Moves
  • 9.4. Jumping Between Different Move Sizes
  • 10. Ruin & Recreate
  • 10.1. The Philosophy of Building One's Own Castle
  • 10.2. Outline of Approach
  • 10.3. Discussion of Ruin & Recreate
  • 10.4. Ruin & Recreate as a Self-Contained Optimization Algorithm
  • 11. Simulated Annealing
  • 11.1. Physical and Historical Background
  • 11.2. Derivation of Simulated Annealing
  • 11.3. Thermal Expectation Values
  • 11.4. Inverse Simulated Annealing
  • 12. Threshold Accepting and Other Algorithms Related to Simulated Annealing
  • 12.1. Threshold Accepting
  • 12.2. The Steady-State Equilibrium Characteristics of TA
  • 12.3. Methods Based on the Tsallis Statistics
  • 12.4. The Great Deluge Algorithm
  • 13. Changing the Energy Landscape
  • 13.1. Search Space Smoothing
  • 13.2. Ant Lion Heuristics and Activation Relaxation Technique
  • 13.3. Noising or Permutation of System Parts
  • 13.4. Weight Annealing
  • 14. Estimation of Expectation Values
  • 14.1. Simple Sampling
  • 14.2. Biased Sampling
  • 14.3. Importance Sampling
  • 14.4. Parallel Sampling
  • 15. Cooling Techniques
  • 15.1. Standard Cooling Schedules
  • 15.2. Nonmonotonic Cooling Schedules
  • 15.3. Ensemble Based Schedules
  • 15.4. Simulated Tempering and Parallel Tempering
  • 16. Estimation of Calculation Time Needed
  • 16.1. Exponentially Growing Space Size
  • 16.2. Polynomial Approach
  • 16.3. Grest Hypothesis
  • 17. Weakening the Pure Markovian Approach
  • 17.1. Saving the Best-So-Far Solution and Spinoffs at Good Solutions
  • 17.2. Record-to-Record Travel
  • 17.3. Stochastic Tunneling
  • 17.4. Changing the Cooling Schedule Due to Intermediate Results
  • 18. Neural Networks
  • 18.1. Biological Motivation
  • 18.2. Artificial Neural Networks
  • 18.3. The Hopfield Model
  • 18.4. Kohonen Networks
  • 19. Genetic Algorithms and Evolution Strategies
  • 19.1. Charles Darwin's Natural Selection
  • 19.2. Mutations and Crossovers
  • 19.3. Application to Optimization Problems
  • 19.4. Parallel Applications
  • 20. Optimization Algorithms Inspired by Social Animals
  • 20.1. Inspiration by the Behavior of Animals
  • 20.2. Ant Colony Optimization
  • 20.3. Particle Swarm Optimization
  • 20.4. Fighting and Ranking
  • 21. Optimization Algorithms Based on Multiagent Systems
  • 21.1. Motivation
  • 21.2. Simulated Trading
  • 21.3. Selfish vs. Global Optimization
  • 21.4. Introduction of a Social Temperature
  • 22. Tabu Search
  • 22.1. Tabu
  • 22.2. Use of Memory
  • 22.3. Aspiration
  • 22.4. Intensification and Diversification
  • 23. Histogram Algorithms
  • 23.1. Guided Local Search
  • 23.2. Multicanonical Algorithm
  • 23.3. MUCAREM and REMUCA
  • 23.4. Multicanonical Annealing
  • 24. Searching for Backbones
  • 24.1. Comparing Different Good Solutions
  • 24.2. Determining the Backbone
  • 24.3. Outline of the SFB Algorithm
  • 24.4. Discussion of the Algorithm
  • Part II. Applications
  • 0. General Remarks
  • 0.1. Dealing with a Proposed Optimization Problem
  • 0.2. Programming Languages and Parallelization Libraries
  • 0.3. Optimization Libraries
  • 0.4. Difficulty of Comparing Various Algorithms
  • Applications A. The Traveling Salesman Problem
  • 1. The Traveling Salesman Problem
  • 1.1. The Task of the Traveling Salesman
  • 1.2. Distance Metrics
  • 1.3. The Dijkstra Algorithm
  • 1.4. Various Possible Codings
  • 1.5. Four Approaches to the TSP
  • 1.6. Benchmark Instances
  • 1.7. Bounds for the Optimum Solution
  • 1.8. The Misfit: A Frustration Measure
  • 1.9. Order Parameters for the TSP
  • 1.10. Short History of TSP
  • 2. Extensions of Traveling Salesman Problem
  • 2.1. Temporal Constraints
  • 2.2. Vehicle Routing Problems
  • 2.3. Probabilistic Models and Online Optimization
  • 2.4. Supply Chain Management
  • 3. Application of Construction Heuristics to TSP
  • 3.1. Nearest Neighbor Heuristic
  • 3.2. Insertion Heuristics
  • 3.3. Using Deeper Insight into the Problem
  • 3.4. The Savings Heuristic
  • 4. Local Search Concepts Applied to TSP
  • 4.1. Initialization Routine
  • 4.2. Small Moves
  • 4.3. Computational Results for Greedy Algorithm
  • 4.4. Local Search as Afterburner for Construction Heuristics
  • 5. Next Larger Moves Applied to TSP
  • 5.1. Lin-3-Opts
  • 5.2. Higher-Order Lin-n-Opts
  • 5.3. Computational Results for the Greedy Algorithm
  • 5.4. Combination of Moves of Various Sizes
  • 6. Ruin & Recreate Applied to TSP
  • 6.1. Application of Ruin & Recreate
  • 6.2. Analysis of R & R Moves in RW and GRE Modes
  • 6.3. Ruin & Recreate as Self-Contained Algorithm
  • 6.4. Discussion of Application Possibilities of Ruin & Recreate
  • 7. Application of Simulated Annealing to TSP
  • 7.1. Simulated Annealing for the TSP
  • 7.2. Computational Results for Observables of Interest
  • 7.3. Computational Results for Acceptance Rates
  • 7.4. Quality of the Results Achieved with Various Computing Times
  • 8. Dependencies of SA Results on Moves and Cooling Process
  • 8.1. Results for Various Small Moves
  • 8.2. Results for Monotonous Cooling Schedules
  • 8.3. Results for Bouncing
  • 8.4. Results for Parallel Tempering
  • 9. Application to TSP of Algorithms Related to Simulated Annealing
  • 9.1. Computational Results for Threshold Accepting
  • 9.2. Computational Results for Penna Criterion
  • 9.3. Computational Results for Great Deluge Algorithm
  • 9.4. Computational Results for Record-to-Record Travel
  • 10. Application of Search Space Smoothing to TSP
  • 10.1. A Small Toy Problem
  • 10.2. Gu and Huang Approach
  • 10.3. Effect of Numerical Precision on Smoothing
  • 10.4. Smoothing with Finite Numerical Precision Only
  • 11. Further Techniques Changing the Energy Landscape of a TSP
  • 11.1. The Convex-Concave Approach to Search Space Smoothing
  • 11.2. Noising the System
  • 11.3. Weight Annealing
  • 11.4. Final Remarks on Application of Changing Techniques
  • 12. Application of Neural Networks to TSP
  • 12.1. Application of a Hopfield Network
  • 12.2. Computational Results for the Hopfield Network
  • 12.3. Application of a Kohonen Network
  • 12.4. Computational Results for a Kohonen Network
  • 13. Application of Genetic Algorithms to TSP
  • 13.1. Mutations
  • 13.2. Crossovers
  • 13.3. Natural Selection
  • 13.4. Computational Results
  • 14. Social Animal Algorithms Applied to TSP
  • 14.1. Application of Ant Colony Optimization
  • 14.2. Computational Results
  • 14.3. Application of Bird Flock Model
  • 14.4. Computational Results
  • 15. Simulated Trading Applied to TSP
  • 15.1. Application of Simulated Trading to the TSP
  • 15.2. Computational Results
  • 15.3. Discussion of Simulated Trading
  • 15.4. Simulated Trading and Working
  • 16. Tabu Search Applied to TSP
  • 16.1. Definition of a Tabu List
  • 16.2. Introduction of Short-Term Memory
  • 16.3. Adding some Aspiration
  • 16.4. Adding Intensification and Diversification
  • 17. Application of History Algorithms to TSP
  • 17.1. The Multicanonical Algorithm
  • 17.2. Multicanonical Annealing
  • 17.3. Acceptance Simulated Annealing
  • 17.4. Guided Local Search
  • 18. Application of Searching for Backbones to TSP
  • 18.1. Definition of a Backbone
  • 18.2. Application to the Completely Asymmetric TSP
  • 18.3. Application to Partially Asymmetric TSP
  • 18.4. Computational Results
  • 19. Simulating Various Types of Government with Searching for Backbones
  • 19.1. An Aristocratic Approach
  • 19.2. A Democratic Approach
  • 19.3. Solution of the PCB442 Problem
  • 19.4. Can Humans Do This, Too?
  • Applications B. The Constraint Satisfaction Problem
  • 20. The Constraint Satisfaction Problem
  • 20.1. Sources of Constraint Satisfaction Problems
  • 20.2. Benchmarks and Competitions
  • 20.3. Randomly Generated Models and Their Complexity
  • 20.4. Randomly Generated Models and Their Phase Diagrams
  • 20.5. Mixtures of easy and hard CSPs
  • 21. Construction Heuristics for CSP
  • 21.1. Application of the Bestinsertion Heuristic to the 3-SAT Problem
  • 21.2. Assertion, Decimation, and Resolution
  • 21.3. Analyzable Assertion Protocols
  • 21.4. Solution Space Structure of XOR-SAT
  • 22. Random Local Iterative Search Heuristics
  • 22.1. RWalkSAT
  • 22.2. WalkSAT
  • 22.3. Simulated Annealing
  • 23. Belief Propagation and Survey Propagation
  • 23.1. Belief Propagation, Message Passing, and Cavities
  • 23.2. Message Passing as Side Information for Decimation
  • 23.3. Belief Propagation and Sudoku
  • Part III. Outlook
  • 24. Future Outlook of Optimization Business
  • 24.1. P = NP?
  • 24.2. Quantum Computing
  • 24.3. DNA Computing
  • 24.4. How Will the Problems Evolve?
  • Acknowledgments
  • References
  • Index

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