The Quadratic Assignment Problem

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.

Texte du rabat

The quadratic assignment problem (QAP) is a classical combinatorial optimization problem with numerous applications in facility location, scheduling, manufacturing, VLSI design, statistical data analysis, etc. The QAP is an extremely hard problem from both theoretical and practical points of view: 1) The QAP is NP-hard to solve to optimality and to approximate within a constant approximation ratio, and 2) QAP instances of size larger than 22 are still considered intractable. Hence, the QAP is in effect a problem that has yet to be solved. This volume presents a general overview of the most studied aspects of the QAP, as well as outlining a number of research directions which currently seem to be promising. The book gives a systematic presentation of various results scattered in the literature, such as: bounding techniques and exact solution methods, linearisations, heuristic approaches and computational complexity. Some more recent research directions discussed in detail in the book are the asymptotic behaviour of the QAP and restricted versions of the problem: in particular, polynomially solvable and provably hard cases of the QAP. Audience: This volume will be of interest to researchers and students interested in the quadratic assignment problem and to practitioners who face the QAP and wish to better understand this problem in its inherent complexity.

Résumé
`... will be primarily of interest to researchers in the field of mathematics for operational research. Practitioners wanting to read the book, however, will find all the necessary references in order to understand the mathematical terminology. The book can also be recommended to young researchers and to PhD students seeking challenging problems.'
Journal of the Operational Research Society, 50:5 (1999)

Contenu
1 Problem Statement and Complexity Aspects.- 2 Exact Algorithms and Lower Bounds.- 3 Heuristics and Asymptotic Behavior.- 4 QAPS on Specially Structured Matrices.- 5 Two More Restricted Versions of the QAP.- 6 QAPS Arising as Optimization Problems in Graphs.- 7 On the Biquadratic Assignment Problem (BIQAP).- References.- Notation Index.