A Set of Examples of Global and Discrete Optimization: Applications of Bayesian Heuristic Approach

ISBN-13: 9781461371144 / Angielski / Miękka / 2013 / 322 str.

Jonas Mockus

Opis

This book shows how the Bayesian Approach (BA) improves well- known heuristics by randomizing and optimizing their parameters. That is the Bayesian Heuristic Approach (BHA). The ten in-depth examples are designed to teach Operations Research using Internet. Each example is a simple representation of some impor- tant family of real-life problems. The accompanying software can be run by remote Internet users. The supporting web-sites include software for Java, C++, and other lan- guages. A theoretical setting is described in which one can discuss a Bayesian adaptive choice of heuristics for discrete and global optimization prob- lems. The techniques are evaluated in the spirit of the average rather than the worst case analysis. In this context, "heuristics" are understood to be an expert opinion defining how to solve a family of problems of dis- crete or global optimization. The term "Bayesian Heuristic Approach" means that one defines a set of heuristics and fixes some prior distribu- tion on the results obtained. By applying BHA one is looking for the heuristic that reduces the average deviation from the global optimum. The theoretical discussions serve as an introduction to examples that are the main part of the book. All the examples are interconnected. Dif- ferent examples illustrate different points of the general subject. How- ever, one can consider each example separately, too.

Spis treści

Preface. Part I: About the Bayesian Approach. 1. General Ideas. 2. Explaining BHA by Knapsack Example. Part II: Software for Global Optimization. 3. Introduction. 4. Fortran. 5. Turbo C. 6. C++. 7. Java 1.0. 8. Java 1.2. Part III: Examples of Models. 9. Nash Equilibrium. 10. Walras Equilibrium. 11. Inspection Model. 12. Differential Game. 13. Investment Problem. 14. Exchange Rate Prediction. 15. Call Centers. 16. Optimal Scheduling. 17. Sequential Decisions. References. Index.