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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.
Greedy Randomized Adaptive Search Procedures For The Steiner Problem In Graphs
 QUADRATIC ASSIGNMENT AND RELATED PROBLEMS, VOLUME 16 OF DIMACS SERIES ON DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1999
"... We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions ..."
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Cited by 121 (30 self)
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We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions on a variety of test problems are reported. On the majority of instances from the ORLibrary, a set of standard test problems, the GRASP produced optimal solutions. On those that optimal solutions were not found, the GRASP found good quality approximate solutions.
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...
A Genetic Approach to the Quadratic Assignment Problem
, 1992
"... The Quadratic Assignment Problem (QAP) is a wellknown combinatorial optimization problem with a wide variety of practical applications. Although many heuristics and semienumerative procedures for QAP have been proposed, no dominant algorithm has emerged. In this paper, we describe a Genetic Algori ..."
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Cited by 72 (7 self)
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The Quadratic Assignment Problem (QAP) is a wellknown combinatorial optimization problem with a wide variety of practical applications. Although many heuristics and semienumerative procedures for QAP have been proposed, no dominant algorithm has emerged. In this paper, we describe a Genetic Algorithm (GA) approach to QAP. Genetic algorithms are a class of randomized parallel search heuristics which emulate biological natural selection on a population of feasible solutions. We present computational results which show that this GA approach finds solutions competitive with those of the best previouslyknown heuristics, and argue that genetic algorithms provide a particularly robust method for QAP and its more complex extensions.
Selected Topics on Assignment Problems
, 1999
"... We survey recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignment problems, in particular lower bounds, special cases and asymptotic results, biquadratic and co ..."
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Cited by 34 (1 self)
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We survey recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignment problems, in particular lower bounds, special cases and asymptotic results, biquadratic and communication assignment problems.
ChemicalReactionInspired Metaheuristic for Optimization
, 2009
"... Abstract — We encounter optimization problems in our daily lives and in various research domains. Some of them are so hard that we can, at best, approximate the best solutions with (meta)heuristic methods. However, the huge number of optimization problems and the small number of generally acknowled ..."
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Cited by 18 (9 self)
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Abstract — We encounter optimization problems in our daily lives and in various research domains. Some of them are so hard that we can, at best, approximate the best solutions with (meta)heuristic methods. However, the huge number of optimization problems and the small number of generally acknowledged methods mean that more metaheuristics are needed to fill the gap. We propose a new metaheuristic, called Chemical Reaction Optimization (CRO), to solve optimization problems. It mimics the interactions of molecules in a chemical reaction to reach a low energy stable state. Simulation results show that CRO is very competitive with the few existing successful metaheuristics, outperforming them in some cases. Moreover, with the NoFreeLunch theorem, CRO must have equal performance as the others on the average but it can outperform all other metaheuristics when matched to the right problem type. Therefore, it provides a new approach for solving optimization problems. CRO may potentially solve those problems which may not be solvable with the few generally acknowledged approaches. Index Terms—Optimization methods, chemical reaction, metaheuristics, natureinspired algorithms. O
MultiStart Tabu Search and Diversification Strategies for the Quadratic Assignment Problem
, 2006
"... The quadratic assignment problem (QAP) is a well known combinatorial optimization problem most commonly used to model the facilitylocation problem. The widely acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this study, we introduce several mul ..."
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Cited by 15 (1 self)
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The quadratic assignment problem (QAP) is a well known combinatorial optimization problem most commonly used to model the facilitylocation problem. The widely acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this study, we introduce several multistart tabu search variants and show the benefit of utilizing strategic diversification within the tabu search framework for the QAP. Computational results for a set of problems obtained from QAPLIB demonstrate the ability of our TS multistart variants to improve on the classic tabu search approach that is one of the principal and most widely used methods for the QAP. We also show that our new procedures are highly competitive with the best recently introduced methods from the literature, including more complex hybrid approaches that incorporate a classic tabu search method as a subroutine.
A Modified Simulated Annealing Algorithm for the Quadratic Assignment Problem
, 2003
"... Abstract. The quadratic assignment problem (QAP) is one of the wellknown combinatorial optimization problems and is known for its various applications. In this paper, we propose a modified simulated annealing algorithm for the QAP – MSAQAP. The novelty of the proposed algorithm is an advanced for ..."
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Cited by 10 (0 self)
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Abstract. The quadratic assignment problem (QAP) is one of the wellknown combinatorial optimization problems and is known for its various applications. In this paper, we propose a modified simulated annealing algorithm for the QAP – MSAQAP. The novelty of the proposed algorithm is an advanced formula of calculation of the initial and final temperatures, as well as an original cooling schedule with oscillation, i.e., periodical decreasing and increasing of the temperature. In addition, in order to improve the results obtained, the simulated annealing algorithm is combined with a tabu search approach based algorithm. We tested our algorithm on a number of instances from the library of the QAP instances – QAPLIB. The results obtained from the experiments show that the proposed algorithm appears to be superior to earlier versions of the simulated annealing for the QAP. The power of MSAQAP is also corroborated by the fact that the new best known solution was found for the one of the largest QAP instances – THO150. Key words: heuristics, local search, simulated annealing, quadratic assignment problem. 1.
Parallel Hybrid MetaHeuristics: Application to the Quadratic Assignment Problem
 IN PROCEEDINGS OF THE PARALLEL OPTIMIZATION COLLOQUIUM
, 1996
"... Metaheuristics are search techniques that can be applied to a broad range of combinatorial optimization problems. Each metaheuristic explores and exploits the search space in its own way. No heuristic can be better than any heuristic on a wide spectrum of problems. To make the search more efficie ..."
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Cited by 8 (1 self)
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Metaheuristics are search techniques that can be applied to a broad range of combinatorial optimization problems. Each metaheuristic explores and exploits the search space in its own way. No heuristic can be better than any heuristic on a wide spectrum of problems. To make the search more efficient and robust, hybridization of heuristics should be used. In this paper, we present an ongoing research on parallel hybrid heuristics. The Quadratic Assignement Problem is used as a testbed problem. We present the performance of different metaheuristics and their hybridization on standard problems taken from the QAPLIB library.