Fast sequential Monte Carlo methods for counting and optimization / Reuven Rubinstein, Ad Ridder, Radislav Vaisman.

Format:

Book

Author/Creator:

Rubinstein, Reuven Y.

Contributor:

Ridder, Ad, 1955-

Vaisman, Radislav.

Series:

Wiley Series in Probability and Statistics

Wiley series in probability and statistics

Language:

English

Subjects (All):

Mathematical optimization.

Monte Carlo method.

Physical Description:

1 online resource (208 p.)

Edition:

1st edition

Place of Publication:

Hoboken, New Jersey : John Wiley & Sons, Inc., [2014]

Language Note:

English

System Details:

text file

Summary:

A comprehensive account of the theory and application of Monte Carlo methods Based on years of research in efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization, Fast Sequential Monte Carlo Methods for Counting and Optimization is a complete illustration of fast sequential Monte Carlo techniques. The book provides an accessible overview of current work in the field of Monte Carlo methods, specifically sequential Monte Carlo techniques, for solving abstract counting and optimization problems.

Contents:

Cover; Title Page; Contents; Preface; Chapter 1 Introduction to Monte Carlo Methods; Chapter 2 Cross-Entropy Method; 2.1. Introduction; 2.2. Estimation of Rare-Event Probabilities; 2.3. Cross-Entrophy Method for Optimization; 2.3.1. The Multidimensional 0/1 Knapsack Problem; 2.3.2. Mastermind Game; 2.3.3. Markov Decision Process and Reinforcement Learning; 2.4. Continuous Optimization; 2.5. Noisy Optimization; 2.5.1. Stopping Criterion; Chapter 3 Minimum Cross-Entropy Method; 3.1. Introduction; 3.2. Classic MinxEnt Method; 3.3. Rare Events and MinxEnt; 3.4. Indicator MinxEnt Method

3.4.1. Connection between CE and IME3.5. IME Method for Combinatorial Optimization; 3.5.1. Unconstrained Combinatorial Optimization; 3.5.2. Constrained Combinatorial Optimization: The Penalty Function Approach; Chapter 4 Splitting Method for Counting and Optimization; 4.1. Background; 4.2. Quick Glance at the Splitting Method; 4.3. Splitting Algorithm with Fixed Levels; 4.4. Adaptive Splitting Algorithm; 4.5. Sampling Uniformly on Discrete Regions; 4.6. Splitting Algorithm for Combinatorial Optimization; 4.7. Enhanced Splitting Method for Counting; 4.7.1. Counting with the Direct Estimator

4.7.2. Counting with the Capture-Recapture Method4.8. Application of Splitting to Reliability Models; 4.8.1. Introduction; 4.8.2. Static Graph Reliability Problem; 4.8.3. BMC Algorithm for Computing S(Y); 4.8.4. Gibbs Sampler; 4.9. Numerical Results with the Splitting Algorithms; 4.9.1. Counting; 4.9.2. Combinatorial Optimization; 4.9.3. Reliability Models; 4.10. Appendix: Gibbs Sampler; Chapter 5 Stochastic Enumeration Method; 5.1. Introduction; 5.2. OSLA Method and Its Extensions; 5.2.1. Extension of OSLA: nSLA Method; 5.2.2. Extension of OSLA for SAW: Multiple Trajectories; 5.3. SE Method

5.3.1. SE Algorithm5.4. Applications of SE; 5.4.1. Counting the Number of Trajectories in a Network; 5.4.2. SE for Probabilities Estimation; 5.4.3. Counting the Number of Perfect Matchings in a Graph; 5.4.4. Counting SAT; 5.5. Numerical Results; 5.5.1. Counting SAW; 5.5.2. Counting the Number of Trajectories in a Network; 5.5.3. Counting the Number of Perfect Matchings in a Graph; 5.5.4. Counting SAT; 5.5.5. Comparison of SE with Splitting and SampleSearch; Appendix A Additional Topics; A.1. Combinatorial Problems; A.1.1. Counting; A.1.2. Combinatorial Optimization; A.2. Information

A.2.1. Shannon EntropyA.2.2. Kullback-Leibler Cross-Entropy; A.3. Efficiency of Estimators; A.3.1. Complexity; A.3.2. Complexity of Randomized Algorithms; Bibliography; Abbreviations and Acronyms; List of Symbols; Index; Series Page

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781118612354

1118612353

9781118612323

1118612329

9781118612316

1118612310

OCLC:

843010592