A · Local Search Algorithm for the Quadra . Tic Assignment Problem

In this paper, we present a new local search algorithm for solving the Quadratic Assignment Problem based on the Kernighan.Lin heuristic for the. Graph Partitioning Problem. We also prove that finding a local optimum for the Quadratic Assignment Problem, with the neighborhood.structure defined in the algorithm, is PLi·complete. The greatest advantages of the algorithm are its simplicity and sPfed in generating high quality solutions. Tlie algorithm has been implemented alnd tested on an IBM 3090 computer with a variety of test" problems of dimensions up to 100, including many test problems available in the literature and a newi set of test problems with known optimal permuta.tions. Subject classifications: analysis of algorithms: computational com· plexity, suboptimal algorithms; facilities/equipment planning: discrete location. Other key words: combinatorial optimization, graph partitioning, poly· nomial·time local search. Introduction. The Quadratic Assignment Problem(QAP) belongs to a class of corn binatorial optimization problems that have many practical applications but are computationally difficult to solve. Given a set N = {l, 2, ... , n} and n x n matrices F = (Iij) and D = (d,ill ), the problem is to find a permutation p of the set N that mInImIZeS n n C(p) = L Lfijdp(i)p(j).