A Set of Examples of Global and Discrete Optimization

1. Front Matter

   Pages i-xiii

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2. About the Bayesian Approach

   1. Front Matter

      Pages 1-1

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   2. General Ideas of Bayesian Heuristic Approach

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      Pages 3-9

   3. Explaining Bayesian Heuristic Approach by Example of Knapsack Problem

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      Pages 11-29

3. Software for Global Optimization

   1. Front Matter

      Pages 31-31

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   2. Introduction to Software

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      Pages 33-43

   3. Portable Fortran Version (GMF)

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      Pages 45-53

   4. Turbo C Version (TCGM)

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      Pages 55-61

   5. C++ Version (GMC)

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      Pages 63-73

   6. Java JDK1.0 Version (GMJ0)

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      Pages 75-83

   7. Java JDK1.1 and JDK1.2 Versions, GMJ1 and GMJ2

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      Pages 85-112

4. Examples of Models

   1. Front Matter

      Pages 113-113

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   2. Competition Model with Fixed Resource Prices, Nash Equilibrium

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      Pages 115-121

   3. Competition Model with Free Resource Prices, Walras Equilibrium

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      Pages 123-142

   4. Inspection Model

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      Pages 143-149

   5. “Duel” Problem, Differential Game Model

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      Pages 151-172

   6. “Portfolio” Problem, Optimal Investment of Resources

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      Pages 173-186

   7. Exchange Rate Prediction, Time Series Model

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      Pages 187-243

   8. Call Center Model

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      Pages 245-273

   9. Optimal Scheduling

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      Pages 275-289

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.

• Optimization Methods
• global optimization
• operations research
• optimization
• scheduling
• combinatorics

• Institute of Mathematics and Informatics, Kaunas Technological University, Lithuania

  Jonas Mockus

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