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Author ร{135}ela, Eranda. author The Quadratic Assignment Problem [electronic resource] : Theory and Algorithms / by Eranda ร{135}ela Boston, MA : Springer US : Imprint: Springer, 1998 http://dx.doi.org/10.1007/978-1-4757-2787-6 XV, 287 p. online resource

SUMMARY

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

CONTENT

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

Mathematics Computers Computer science -- Mathematics Algorithms Mathematical optimization Combinatorics Mathematics Optimization Algorithms Theory of Computation Discrete Mathematics in Computer Science Combinatorics

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