The Quadratic Assignment Problem: Theory and Algorithms

✍ Scribed by Eranda Çela (auth.)

• Publisher: Springer US
• Year: 1998
• Tongue: English
• Leaves: 295
• Series: Combinatorial Optimization 1
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xv
Problem Statement and Complexity Aspects....Pages 1-25
Exact Algorithms and Lower Bounds....Pages 27-71
Heuristics and Asymptotic Behavior....Pages 73-106
QAPS on Specially Structured Matrices....Pages 107-157
Two More Restricted Versions of the QAP....Pages 159-194
QAPS Arising as Optimization Problems in Graphs....Pages 195-222
On the Biquadratic Assignment Problem (BIQAP)....Pages 223-249
Back Matter....Pages 251-287

✦ Subjects

Optimization; Algorithms; Theory of Computation; Discrete Mathematics in Computer Science; Combinatorics