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The Quadratic Assignment Problem
 TO APPEAR IN THE HANDBOOK OF COMBINATORIAL OPTIMIZATION
"... 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, an ..."
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Cited by 182 (3 self)
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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 Quadratic Assignment Problem: A Survey and Recent Developments
 In Proceedings of the DIMACS Workshop on Quadratic Assignment Problems, volume 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1994
"... . 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 probl ..."
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Cited by 114 (16 self)
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. 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...
Fitness Landscape Analysis and Memetic Algorithms for the Quadratic Assignment Problem
, 1999
"... 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 metaheuristics based on local search. The local properties of t ..."
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Cited by 84 (9 self)
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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 metaheuristics 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.
A Genetic Local Search Approach to the Quadratic Assignment Problem
 in Proceedings of the 7th International Conference on Genetic Algorithms
, 1997
"... 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 descr ..."
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Cited by 47 (9 self)
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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 Comparison of Memetic Algorithms, Tabu Search, and Ant Colonies for the Quadratic Assignment Problem
 Proc. Congress on Evolutionary Computation, IEEE
, 1999
"... 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 ..."
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Cited by 38 (4 self)
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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 ...
A study of diversification strategies for the quadratic assignment problem
 Computers and Operations Research
, 1994
"... Scope and PurposeHeuristic 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 ..."
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Cited by 13 (2 self)
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Scope and PurposeHeuristic 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. AbstractDiversification 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.
FACOPT: A user friendly FACility layout OPTimization system
 Innovative Systems Design and Engineering www.iiste.org ISSN 22221727 (Paper) ISSN 22222871 (Online) Vol.4, No.6, 2013  Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications
, 2003
"... Various effective algorithms have been proposed for facility layout. However many of them are not flexible enough to handle intricacies such as unequal department sizes. Others do not provide userfriendly interfaces. Thus there is a need for userfriendly software incorporating effective and flexib ..."
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Cited by 8 (0 self)
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Various effective algorithms have been proposed for facility layout. However many of them are not flexible enough to handle intricacies such as unequal department sizes. Others do not provide userfriendly interfaces. Thus there is a need for userfriendly software incorporating effective and flexible algorithms. In this research we present FACOPT, a heuristic approach that is effective and user friendly. The software has the ability use two of the more recent and effective search algorithms in facility layout. The computational experience with each algorithm is reported. FACOPT has a Visual BASIC interface and runs in a Windows environment for ease of use.
An efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems
 European Journal of Operational Research
, 2011
"... ar ..."
A GAACOLocal Search Hybrid Algorithm for Solving Quadratic Assignment Problem
"... In recent decades, many metaheuristics, including genetic algorithm (GA), ant colony optimization (ACO) and various local search (LS) procedures have been developed for solving a variety of NPhard combinatorial optimization problems. Depending on the complexity of the optimization problem, a meta ..."
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Cited by 2 (0 self)
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In recent decades, many metaheuristics, including genetic algorithm (GA), ant colony optimization (ACO) and various local search (LS) procedures have been developed for solving a variety of NPhard combinatorial optimization problems. Depending on the complexity of the optimization problem, a metaheuristic method that may have proven to be successful in the past might not work as well. Hence it is becoming a common practice to hybridize metaheuristics and local heuristics with the aim of improving the overall performance. In this paper, we propose a novel adaptive GAACOLS hybrid algorithm for solving quadratic assignment problem (QAP). Empirical study on a diverse set of QAP benchmark problems shows that the proposed adaptive GAACOLS converges to good solutions efficiently. The results obtained were compared to the recent stateoftheart algorithm for QAP, and our algorithm showed obvious improvement.
Experimental analyses of the life span method for the quadratic assignment porblem
 The Institute of Statistical Mathematics Cooperative Research Report
, 1995
"... 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 an ..."
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Cited by 1 (1 self)
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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