Tabu Search and Hybrid Genetic Algorithms for Quadratic Assignment Problems

Abstract

In this chapter experience with solving quadratic assignment problems is reported. The results reported in this chapter are the best results for heuristic solutions of the quadratic assignment problem available to date and can serve as bench mark results for future researchers who propose new approaches for solving quadratic assignment problems. The most effective method to date for solving quadratic assignment problems heuristically is the hybrid genetic algorithm. The offspring produced by the genetic algorithms are improved by tabu search before considering them for inclusion into the population. Six different tabu searches are described and are embedded in a special genetic algorithm whose merging process is the most effective for heuristically solving quadratic assignment problems. The most successful merging process (the crossover operator) used in the genetic algorithm is described. This specific merging process exploits the special structure of quadratic assignment problems and is especially effective when the distance matrix consists of “real” distances rather than random values. A short cut suggested by Taillard (1995) is described. This short cut reduces the time required for the evaluation of all O(n2) values of the objective function by all pair-wise exchanges of facilities from O(n4) to O(n2) (i.e. O(1) per pair exchange) where n is the number of facilities. Grey pattern problems are quadratic assignment problems with a special structure. For these problems a special merging process and a special tabu search are developed (Drezner, 2006). Several improvement schemes for genetic algorithms (or hybrid genetic algorithms) are described and discussed. These include: gender specific genetic algorithms, distance based approach to selecting parents in genetic algorithms, a distance based rule for removing population members, and compounded genetic algorithms. These improvement schemes can help researchers who work on other problems as well to improve the performance of their genetic or hybrid genetic algorithms. The chapter concludes with summary tables of computational experiments with various techniques. These include the best known results for 32 “pure” quadratic assignment problems and 127 grey pattern quadratic assignment problems. All pure quadratic assignment problems have between 36 and 150 facilities. Smaller problems, with a few