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24
Solving Large Quadratic Assignment Problems on Computational Grids
, 2000
"... The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computat ..."
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Cited by 67 (6 self)
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The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms. In this article we describe a novel approach to solve QAPs using a stateoftheart branchandbound algorithm running on a federation of geographically distributed resources known as a computational grid. Solution of QAPs of unprecedented complexity, including the nug30, kra30b, and tho30 instances, is reported.
A Scatter Search Based Approach for the Quadratic Assignment Problem
, 1997
"... In this report, we are mainly interested in Scatter Search which is an evolutionary heuristic, proposed two decades ago, that uses linear combination of a population subset to create new solutions. A special operator is used to ensure their feasibility and to improve their quality. We propose hereaf ..."
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Cited by 38 (2 self)
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In this report, we are mainly interested in Scatter Search which is an evolutionary heuristic, proposed two decades ago, that uses linear combination of a population subset to create new solutions. A special operator is used to ensure their feasibility and to improve their quality. We propose hereafter a Scatter Search approach to the Quadratic Assignment Problem (QAP) problem. The basic method is extended with intensification and diversification stages and we present a procedure to generate good scattered initial solutions.
A New Bound for the Quadratic Assignment Problem Based on Convex Quadratic Programming
 MATHEMATICAL PROGRAMMING
, 1999
"... We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the wellknown projected eigenvalue bound, and appears to be comp ..."
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Cited by 31 (3 self)
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We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the wellknown projected eigenvalue bound, and appears to be competitive with existing bounds in the tradeoff between bound quality and computational effort.
Solving Large Quadratic Assignment Problems in Parallel.
 Computational Optimization and Applications
, 1994
"... . Quadratic Assignment problems are in practice among the most difficult to solve in the class of NPcomplete problems. The only successful approach hitherto has been BranchandBound based algorithms, but such algorithms are crucially dependent on good bound functions to limit the size of the space ..."
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Cited by 23 (6 self)
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. Quadratic Assignment problems are in practice among the most difficult to solve in the class of NPcomplete problems. The only successful approach hitherto has been BranchandBound based algorithms, but such algorithms are crucially dependent on good bound functions to limit the size of the space searched. Much work has been done to identify such functions for the QAP, but with limited success. Parallel processing has also been used in order to increase the size of problems solvable to optimality. The systems used have, however, often been systems with relatively few, but very powerful vector processors, and have hence not been ideally suited for computations essentially involving nonvectorizable computations on integers. In this paper we investigate the combination of one of the best bound functions for a Branchand Bound algorithm (the GilmoreLawler bound) and various testing, variable binding and recalculation of bounds between branchings when used in a parallel BranchandBo...
On the Best Search Strategy in Parallel BranchandBound  BestFirstSearch vs. Lazy DepthFirstSearch.
 Annals of Operations Research
, 1996
"... or because pruning and evaluation tests are more effective in DFS due to the presence of better incumbents. 1 Introduction. One of the key issues of searchbased algorithms in general and B&Balgorithms in particular is the search strategy employed: In which order should the unexplored parts of t ..."
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Cited by 19 (4 self)
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or because pruning and evaluation tests are more effective in DFS due to the presence of better incumbents. 1 Introduction. One of the key issues of searchbased algorithms in general and B&Balgorithms in particular is the search strategy employed: In which order should the unexplored parts of the solution space be searched? Different search strategies have different properties regarding time efficiency and memory consumption, both when considered in a sequential and a parallel setting. Supported by the EU HCM project SCOOP and the Danish NSF project EPOS M. Perregaard and J. Clausen / Search Strategies in Parallel Branch and Bound 2 In parallel B&B one often regards the BestFirstSearch strategy (BeFS) and the DepthFirstSearch strategy (DFS) to be two of the prime candidates  BeFS due to expectations of efficiency and theoretical properties regarding anomalies, and DFS for reasons of space efficiency. However BeFS requires that the bou
Solving Quadratic Assignment Problems Using Convex Quadratic Programming Relaxations
, 2000
"... ..."
A Dual Framework for Lower Bounds of the Quadratic Assignment Problem Based on Linearization
, 1997
"... A dual framework allowing the comparison of various bounds for the quadratic assignment problem (QAP) based on linearization, e.g. the bounds of Adams and Johnson, Carraresi and Malucelli, and Hahn and Grant, is presented. We discuss the differences of these bounds and propose a new and more general ..."
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Cited by 13 (0 self)
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A dual framework allowing the comparison of various bounds for the quadratic assignment problem (QAP) based on linearization, e.g. the bounds of Adams and Johnson, Carraresi and Malucelli, and Hahn and Grant, is presented. We discuss the differences of these bounds and propose a new and more general bounding procedure based on the dual of the linearization of Adams and Johnson. The new procedure has been applied to problems of dimension up to n = 72, and the computational results indicate that the new bound competes well with existing linearization bounds and yields a good trade off between computation time and bound quality.
Solving largescale QAP problems in parallel with the search library ZRAM
 Journal of Parallel and Distributed Computing
, 1998
"... Program libraries are one tool to make the cooperation between specialists from various elds successful: the separation of applicationspeci c knowledge from applicationindependent tasks ensures portability, maintenance, extensibility, and exibility. The current paper demonstrates the success in com ..."
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Cited by 12 (1 self)
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Program libraries are one tool to make the cooperation between specialists from various elds successful: the separation of applicationspeci c knowledge from applicationindependent tasks ensures portability, maintenance, extensibility, and exibility. The current paper demonstrates the success in combining problemspeci c knowledge for the quadratic assignment problem (QAP) with the raw computing power o ered by contemporary parallel hardware by using the library of parallel search algorithms ZRAM. Solutions of previously unsolved large standard testinstances of the QAP are presented. 1
Tree Elaboration Strategies In Branch and Bound Algorithms For Solving the Quadratic Assignment Problem
, 1999
"... This paper presents a new strategy for selecting nodes in a branchandbound algorithm for solving exactly the Quadratic Assignment Problem (QAP). It was developed when it was learned that older strategies failed on the larger size problems. The strategy is a variation of polytomic depthfirst searc ..."
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Cited by 10 (3 self)
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This paper presents a new strategy for selecting nodes in a branchandbound algorithm for solving exactly the Quadratic Assignment Problem (QAP). It was developed when it was learned that older strategies failed on the larger size problems. The strategy is a variation of polytomic depthfirst search of Mautor and Roucairol which extends a node by all assignments of an unassigned facility to unassigned locations based upon the counting of 'forbidden' locations. A forbidden location is one where the addition of the corresponding leader (linear cost) element would increase the lower bound beyond the upper bound. We learned that this fortuitous situation never occurs near the root on Nugent problems larger than 15. One has to make better estimates of the bound if the strategy is to work. We have, therefore, designed and implemented an increasingly improved set of bound calculations. The better of these bound calculations to be utilized near the root and the less accurate (poorer bounds) utilized further into the tree. The result is an effective and powerful technique for shortening the run times of problem instances in the range of size 16 to 25. Run times were decreased generally by five or sixtoone and the number of nodes evaluated was decreased as much as 10toone. Later improvements in our strategy produced a better than 3to1 reduction in runtime so that overall improvement in run time was as high as 20to1 as compared to our earlier results. At the end of our paper, we compare the performance of the four most successful algorithms for exact solution of the QAP.
On the quality of local search for the Quadratic Assignment Problem
, 1997
"... Local search is widely used to solve approximately NPcomplete combinatorial optimization problems. But, few is known about quality of obtained local minima, for a given neighborhood. We concentrate on one of the most difficult optimization problems, the Quadratic Assignment Problem, and we give an ..."
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Cited by 9 (3 self)
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Local search is widely used to solve approximately NPcomplete combinatorial optimization problems. But, few is known about quality of obtained local minima, for a given neighborhood. We concentrate on one of the most difficult optimization problems, the Quadratic Assignment Problem, and we give an upper bound for the quality of solutions obtained with deepest local search. Moreover, other recently established results on the Traveling Salesman Problem, the Graph Bipartitioning Problem and the Maximum Independent Set Problem can be deduced as particular cases. Keywords: local search, quadratic assignment problem, maximum independent set. 1 Introduction Local search (respectively deepest descent local search) works in an iterative fashion by successively replacing the current solution by a better (respectively the best) one in the neighborhood of the current solution. It terminates when a locally optimal solution is attained, i.e. when no further improvement is possible. In [JPY88] a ne...