Mauricio G. C. Resende
Abstract
In the NP-complete quadratic assignment problem (QAP), n facilities are to be assigned to n sites at minimum cost. The contribution of assigning facility i to site k and facility j to site l to the total cost is fij dkl, where fij is the flow between facilities i and j, and dkl is the distance between sites k and l. Only very small (n≤20) instances of the QAP have been solved exactly, and heuristics are therefore used to produce approximate solutions. This article describes a set of Fortran subroutines to find approximate solutions to dense quadratic assignment problems, having at least one symmetric flow or distance matrix. A greedy, randomized, adaptive search procedure (GRASP) is used to produce the solutions. The design and implementation of the code are described in detail, and extensive computational experiments are reported, illustrating solution quality as a function of running time.
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Index Terms
- Algorithm 754: Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP
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Reviews
Sven-Ake Gustafson
The authors describe computer software that can be used for the treatment of large-scale quadratic assignment problems where n facilities are to be assigned to n sites at minimum cost. This problem is NP-hard, and only very small instances ( n?20 ) have been solved exactly. Therefore, heuristics are used to produce approximate solutions. In the introductory section, the problem and the solution method are described. The second section is devoted to the design of the program packet, and the third section describes its use. In s<__?__Pub Caret>ection 4, a comprehensive set of runs on test problems is reported. Here the efficiency and speed of the programs are studied. The last section contains the conclusions. The paper is clear and well organized, and the reference list is adequate. This paper is suitable for specialists who need to solve assignment problems.
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