Discrete Optimization with Interval Data

Minmax Regret and Fuzzy Approach

• Authors
Book

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 228)

1. Front Matter
2. Minmax Regret Combinatorial Optimization Problems with Interval Data

1. Front Matter
Pages 1-1
Pages 3-16
Pages 17-30
Pages 31-38
Pages 39-50
Pages 51-60
Pages 61-79
Pages 81-112
Pages 113-120
Pages 121-135
Pages 137-153
Pages 155-157
3. Minmax Regret Sequencing Problems with Interval Data

1. Front Matter
Pages 159-159
Pages 161-165
Pages 167-173
Pages 175-182
Pages 183-195
Pages 197-198
Pages 199-207
4. Back Matter

Introduction

In operations research applications we are often faced with the problem of incomplete or uncertain data. This book considers solving combinatorial optimization problems with imprecise data modeled by intervals and fuzzy intervals. It focuses on some basic and traditional problems, such as minimum spanning tree, shortest path, minimum assignment, minimum cut and various sequencing problems. The interval based approach has become very popular in the recent decade. Decision makers are often interested in hedging against the risk of poor (worst case) system performance. This is particularly important for decisions that are encountered only once. In order to compute a solution that behaves reasonably under any likely input data, the maximal regret criterion is widely used. Under this criterion we seek a solution that minimizes the largest deviation from optimum over all possible realizations of the input data.

The minmax regret approach to discrete optimization with interval data has attracted considerable attention in the recent decade. This book summarizes the state of the art in the area and addresses some open problems. Furthermore, it contains a chapter devoted to the extension of the framework to the case when fuzzy intervals are applied to model uncertain data. The fuzzy intervals allow a more sophisticated uncertainty evaluation in the setting of possibility theory.

This book is a valuable source of information for all operations research practitioners who are interested in modern approaches to problem solving. Apart from the description of the theoretical framework, it also presents some algorithms that can be applied to solve problems that arise in practice.

Keywords

Fuzziness Fuzzy Operations Research Robust optimization minmax algorithm algorithms combinatorial optimization minmax optimization

Bibliographic information

• DOI https://doi.org/10.1007/978-3-540-78484-5
• Copyright Information Springer-Verlag Berlin Heidelberg 2008
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Engineering Engineering (R0)
• Print ISBN 978-3-540-78483-8
• Online ISBN 978-3-540-78484-5
• Series Print ISSN 1434-9922
• Series Online ISSN 1860-0808
• Buy this book on publisher's site