Local Search and Metaheuristics for the Quadratic Assignment Problem Thomas St ¨ utzle Intellectics Group, Department of Computer Science Darmstadt University of Technology email: stuetzle@informatik.tu-darmstadt.de WWW: www.intellektik.informatik.tu-darmstadt.de/˜tom Marco Dorigo IRIDIA, Universit´ e Libre de Bruxelles email: mdorigo@ulb.ac.be WWW: iridia.ulb.ac.be/˜mdorigo 1 Introduction The quadratic assignment problem (QAP) is an important problem in theory and practice. It was , which was introduced by Koopmans and Beckmann in 1957 [28] and is a model for many practical problems like backboard wiring [53], campus and hospital layout [15, 17], typewriter keyboard design [9], scheduling [23] and many others [16, 29] can be formulated as QAPs. Intuitively, the QAP can best be described as the problem of assigning a set of facilities to a set of locations with given distances between the locations and given flows between the facilities. The goal then is to place the facilities on locations in such a way that the sum of the product between flows and distances is minimal. More formally, given facilities and locations, two matrices and , where is the distance between locations and and is the flow between facilities and , the QAP can be stated as follows: (1) where is the set of all permutations (corresponding to the assignments) of the set of inte- gers , and gives the location of facility in the current solution . Here describes the cost contribution of simultaneously assigning facility to location and facility to location . A more general form of the QAP was introduced by Lawler [31], but here we will focus on the above given 1