# The Quadratic Assignment Problem

## Theory and Algorithms

• Eranda Çela
Book

Part of the Combinatorial Optimization book series (COOP, volume 1)

1. Front Matter
Pages i-xv
2. Eranda Çela
Pages 1-25
3. Eranda Çela
Pages 27-71
4. Eranda Çela
Pages 73-106
5. Eranda Çela
Pages 107-157
6. Eranda Çela
Pages 159-194
7. Eranda Çela
Pages 195-222
8. Eranda Çela
Pages 223-249
9. Back Matter
Pages 251-287

### Introduction

The quadratic assignment problem (QAP) was introduced in 1957 by Koopmans and Beckmann to model a plant location problem. Since then the QAP has been object of numerous investigations by mathematicians, computers scientists, ope- tions researchers and practitioners. Nowadays the QAP is widely considered as a classical combinatorial optimization problem which is (still) attractive from many points of view. In our opinion there are at last three main reasons which make the QAP a popular problem in combinatorial optimization. First, the number of re- life problems which are mathematically modeled by QAPs has been continuously increasing and the variety of the fields they belong to is astonishing. To recall just a restricted number among the applications of the QAP let us mention placement problems, scheduling, manufacturing, VLSI design, statistical data analysis, and parallel and distributed computing. Secondly, a number of other well known c- binatorial optimization problems can be formulated as QAPs. Typical examples are the traveling salesman problem and a large number of optimization problems in graphs such as the maximum clique problem, the graph partitioning problem and the minimum feedback arc set problem. Finally, from a computational point of view the QAP is a very difficult problem. The QAP is not only NP-hard and - hard to approximate, but it is also practically intractable: it is generally considered as impossible to solve (to optimality) QAP instances of size larger than 20 within reasonable time limits.

### Keywords

Approximation Facility Location Notation STATISTICA algorithms combinatorial optimization complexity constant graphs optimization scheduling

#### Authors and affiliations

• Eranda Çela
• 1
1. 1.Institute of MathematicsTechnical University GrazGrazAustria

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-2787-6
• Copyright Information Springer-Verlag US 1998
• Publisher Name Springer, Boston, MA
• eBook Packages
• Print ISBN 978-1-4419-4786-4
• Online ISBN 978-1-4757-2787-6
• Series Print ISSN 1388-3011
• Buy this book on publisher's site
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