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

Authors: Jonas Mockus



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.

Table of contents (17 chapters)

Front Matter

About the Bayesian Approach
• Front Matter
• General Ideas of Bayesian Heuristic Approach
• Explaining Bayesian Heuristic Approach by Example of Knapsack Problem

Software for Global Optimization
• Front Matter
• Introduction to Software
• Portable Fortran Version (GMF)
• Turbo C Version (TCGM)
• C++ Version (GMC)
• Java JDK1.0 Version (GMJ0)
• Java JDK1.1 and JDK1.2 Versions, GMJ1 and GMJ2

Examples of Models
• Front Matter
• Competition Model with Fixed Resource Prices, Nash Equilibrium
• Competition Model with Free Resource Prices, Walras Equilibrium
• Inspection Model
• “Duel” Problem, Differential Game Model
• “Portfolio” Problem, Optimal Investment of Resources
• Exchange Rate Prediction, Time Series Model
• Call Center Model
• Optimal Scheduling
• Sequential Statistical Decisions Model, “Bride Problem”

Back Matter