A Genetic Local Search Approach to the Quadratic Assignment Problem.

Abstract

Augmenting genetic algorithms with local search heuristics is a promising approach to the solution of combinatorial optimization problems. In this paper, a genetic local search approach to the quadratic assignment problem (QAP) is presented. New genetic operators for realizing the approach are described, and its performance is tested on various QAP instances containing between 30 and 256 facilities/locations. The results indicate that the proposed algorithm is able to arrive at high quality solutions in a relatively short time limit: for the largest publicly known problem instance, a new best solution could be found. 1 INTRODUCTION In the quadratic assignment problem (QAP), n facilities have to be assigned to n locations at minimum cost. Given a set \\Pi(n) of all permutations of f1; 2; : : : ; ng and two n \\Theta n matrices A = (a ij ) and B = (b ij ), the task is to minimize the quantity C(ß) = n X i=1 n X j=1 a ij b ß(i)ß(j) ; ß 2 \\Pi(n): (1) Matrix A can be interpreted as a ...