The Quadratic Assignment Problem

Rainer E. Burkard (), Eranda Çela (), Panos M. Pardalos () and Leonidas S. Pitsoulis ()
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Rainer E. Burkard: Technical University Graz, Institute of Mathematics
Eranda Çela: Technical University Graz, Institute of Mathematics
Panos M. Pardalos: University of Florida, Center for Applied Optimization, Industrial and Systems Engineering Department
Leonidas S. Pitsoulis: University of Florida, Center for Applied Optimization, Industrial and Systems Engineering Department

A chapter in Handbook of Combinatorial Optimization, 1998, pp 1713-1809 from Springer

Abstract: Abstract The quadratic assignment problem (QAP) was introduced by Koopmans and Beckmann in 1957 as a mathematical model for the location of a set of indivisible economical activities [113]. Consider the problem of allocating a set of facilities to a set of locations, with the cost being a function of the distance and flow between the facilities, plus costs associated with a facility being placed at a certain location. The objective is to assign each facility to a location such that the total cost is minimized. Specifically, we are given three n x n input matrices with real elements F = (f ij ), D = (d kl ) and B = (b ik ), where f ij is the flow between the facility i and facility j, d kl is the distance between the location k and location l, and b ik is the cost of placing facility i at location k. The Koopmans-Beckmann version of the QAP can be formulated as follows: Let n be the number of facilities and locations and denote by N the set N = {1, 2,..., n}.

Keywords: Tabu Search; Travel Salesman Problem; Travel Salesman Problem; Master Problem; Greedy Randomize Adaptive Search Procedure (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4613-0303-9_27

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