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 IME -- 3.5. 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 Method -- 4.8. 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 Algorithm -- 5.4. 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 Entropy -- A.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.