Handbook of Combinatorial Optimization pp 1713-1809 | Cite as

# The Quadratic Assignment Problem

## 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## Preview

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