# A Set of Examples of Global and Discrete Optimization

## Applications of Bayesian Heuristic Approach

• Jonas Mockus
Book

Part of the Applied Optimization book series (APOP, volume 41)

1. Front Matter
Pages i-xiii
2. ### About the Bayesian Approach

1. Front Matter
Pages 1-1
2. Jonas Mockus
Pages 3-9
3. Jonas Mockus
Pages 11-29
3. ### Software for Global Optimization

1. Front Matter
Pages 31-31
2. Jonas Mockus
Pages 33-43
3. Jonas Mockus
Pages 45-53
4. Jonas Mockus
Pages 55-61
5. Jonas Mockus
Pages 63-73
6. Jonas Mockus
Pages 75-83
7. Jonas Mockus
Pages 85-112
4. ### Examples of Models

1. Front Matter
Pages 113-113
2. Jonas Mockus
Pages 115-121
3. Jonas Mockus
Pages 123-142
4. Jonas Mockus
Pages 143-149
5. Jonas Mockus
Pages 151-172
6. Jonas Mockus
Pages 173-186
7. Jonas Mockus
Pages 187-243
8. Jonas Mockus
Pages 245-273
9. Jonas Mockus
Pages 275-289

### Introduction

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.

### Keywords

Optimization Methods global optimization operations research optimization scheduling

#### Authors and affiliations

• Jonas Mockus
• 1
1. 1.Institute of Mathematics and InformaticsKaunas Technological UniversityLithuania

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4615-4671-9
• Copyright Information Springer-Verlag US 2000
• Publisher Name Springer, Boston, MA
• eBook Packages
• Print ISBN 978-1-4613-7114-4
• Online ISBN 978-1-4615-4671-9
• Series Print ISSN 1384-6485