. Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment problem. We focus our attention on recent developments. 1. Introduction Given a set N = f1; 2; : : : ; ng and n \Theta n matrices F = (f ij ) and D = (d kl ), the quadratic assignment problem (QAP) can be stated as follows: min p2\Pi N n X i=1 n X j=1 f ij d p(i)p(j) + n X i=1 c ip(i) ; where \Pi N is the set of all permutations of N . One of the major applications of the QAP is in location theory where the matrix F = (f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = (d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [62, 67, 137]. The cost of simultaneously assigning facility i to locat...

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadratic assignment problem, and discusses the relationship between the QAP and other well known combinatorial optimization problems, e.g. the traveling salesman problem, the graph partitioning problem, etc. The paper will appear in the Handbook of Combinatorial Optimization to be published by Kluwer Academic Publishers, P. Pardalos and D.-Z. Du, eds.

In this paper, a fitness landscape analysis for several instances of the quadratic assignment problem (QAP) is performed and the results are used to classify problem instances according to their hardness for local search heuristics and meta-heuristics based on local search. The local properties of the tness landscape are studied by performing an autocorrelation analysis, while the global structure is investigated by employing a fitness distance correlation analysis. It is shown that epistasis, as expressed by the dominance of the flow and distance matrices of a QAP instance, the landscape ruggedness in terms of the correlation length of a landscape, and the correlation between fitness and distance of local optima in the landscape together are useful for predicting the performance of memetic algorithms - evolutionary algorithms incorporating local search - to a certain extent. Thus, based on these properties a favorable choice of recombination and/or mutation operators can be found.

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 ...

A memetic algorithm (MA), i.e. an evolutionary algorithm making use of local search, for the quadratic assignment problem is presented. A new recombination operator for realizing the approach is described, and the behavior of the MA is investigated on a set of problem instances containing between 25 and 100 facilities/locations. The results indicate that the proposed MA is able to produce high quality solutions quickly. A comparison of the MA with some of the currently best alternative approaches -- reactive tabu search, robust tabu search and the fast ant colony system -- demonstrates that the MA outperforms its competitors on all studied problem instances of practical interest. 1 Introduction The problem of assigning a set of facilities (with given flows between them) to a set of locations (with given distances between them) in such a way that the sum of the product between flows and distances is minimized is known as the facilities location problem [1] or the quadratic assignment ...

Scope and Purpose-Heuristic search procedures that aspire to find global optima usually require some type of diversification strategy in order to overcome their myopic perspective of the solution space. Traditionally, randomization has been used to accomplish this diversification. In this paper, we prt:sent a deterministic approach to diversification that has proved to be much more powerful than silnple randomization. This approach uses the solution method, solution history, and the problem structUJ:e to move the search into unexplored regions of the solution space. We believe that the concepts presented here can form the foundation for effective diversification strategies for many types of optimization problems. Abstract-Diversification strategies can be used to enhance general heuristic search procedures such as tabu search, genetic algorithms, and simulated annealing. These strategies are especially relevant to searches that, starting from a particular point, explore a solution path until new exploitable regions are inaccessible, and a new starting point becomes necessary. To date, no one has studied the effect of applying diversification methods independently of other metastrategic components, to identify their power and limitations. In this paper we develop diversification strategies and apply them to the quadratic assignment problem (QAP). We show that these strategies alone succeed in finding high quality solutions to reasonably large (~AP instances reported in the literature. We also describe how our diversification strategies can be e'isily incorporated within general solution frameworks. 1.

An efficient algorithm for the approximate solution of the maximum cardinality stable set problem is presented. The algorithm is based on a variant of tabu search which we call the life span method. Numerical experiments on random and benchmark instances show that our algorithm dominates all the algorithms given in the literature both in accuracy of solutions and in speed. We also investigate how to tune up our implementation and to optimize the parameters via extensive numerical experiments. Key words: maximum stable set problem, maximum clique problem, approximate algorithm, experimental analyses, tabu search, life span method. 1 Introduction Let G = (V; E) be an undirected graph, where V is the set of vertices and E is the set of edges. A stable set of G is a subset of V such that no two vertices of the subset are pairwise adjacent. The Maximum Stable Set Problem (MSSP) is to find a stable set of maximum cardinality in G. A clique is a subset of V such that all the vertices are pa...

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadratic assignment problem, and discusses the relationship between the QAP and other well known combinatorial optimization problems, e.g. the traveling salesman problem, the graph partitioning problem, etc. The paper will appear in the Handbook of Combinatorial Optimization to be published