Experimental Analyses of the Life Span Method for the Quadratic Assignment Problem Katsuki FUJISAWA Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo, Japan Mikio KUBO Department of Information Engineering and Logistics, Tokyo University of Mercantile Marine, Etsujima, Koutou-ku, Tokyo, Japan Abstract In this paper, we report an application of the life span method (LSM), a variant of tabu search introduced by the authors, to the quadratic assignment problem which has applications on facility location and backboard wiring, etc. We discuss how to adapt the LSM to the quadratic assignment problem and compare the performance with previous heuristics. The main purpose of this paper is to perform experimental analyses composed of optimizing the various parameters and to estimate the performance not only in the best case but the average behavior. Key words: life span method, tabu search, combinatorial optimization, approximate algorithms, experimental analysis, quadratic assignment problem. 1 Introduction The Quadratic Assignment Problem (QAP) is a combinatorial optimization problem having many applications including facility location, ordering of data on a disk, backboard wiring, machine scheduling, analyzing chemical, the location of departments (or offices), etc. [9]. In the context of facility location, a set of n facilities is to be assigned to an equal number of locations. The QAP is defined as follows: Definition 1 (Quadratic Assignment Problem: QAP) Given a set V = {1, ··· ,n} and n × n symmetric matrices F =(f ij ) and D =(d kℓ ), find a permutation π : V →{1, ··· ,n} which minimizes the cost function c(π)=  i  j f ij d π(i)π(j ) . 1