The Quadratic Assignment Problem

Theory and Algorithms
1. Auflage 1997
ISBN: 978-0-7923-4878-8
Verlag: Springer

Buch, Englisch, Band 1, 287 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1350 g

Reihe: Combinatorial Optimization

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.

Zielgruppe

Research

Autoren/Hrsg.

Cela, E.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Mathematik | Informatik Mathematik Operations Research Graphentheorie

Inhaltsverzeichnis

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.