Solving large quadratic assignment problems on computational grids

Anstreicher, Kurt M.; Brixius, Nathan W.; Goux, Jean-Pierre; Linderoth, Jeff

doi:10.1007/s101070100255

Cited by 192 publications

(122 citation statements)

References 37 publications

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“…Brüngger et al (1998) set up such an estimator in their solver to predict the running time when tackling large-scale quadratic assignment problems (QAP) by parallel computation. Anstreicher et al (2002) also used Knuth's procedure for estimating the solution time of a specialized branch-and-bound algorithm for QAP. They reported excellent results of the basic, unbiased method for instances of size less than 24 but pointed out that the quality of the estimation rapidly deteriorates as the size of the problems increased.…”

Section: Earlier Workmentioning

confidence: 99%

Early Estimates of the Size of Branch-and-Bound Trees

Cornujols

Karamanov

2006

INFORMS Journal on Computing

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This paper intends to show that the time needed to solve mixed integer programming problems by branch and bound can be roughly predicted early in the solution process. We construct a procedure that can be implemented as part of an MIP solver. It is based on analyzing the partial tree resulting from running the algorithm for a short period of time, and predicting the shape of the whole tree. The procedure is tested on instances from the literature. This work was inspired by the practical applicability of such a result.

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Section: Earlier Workmentioning

confidence: 99%

Early Estimates of the Size of Branch-and-Bound Trees

Cornujols

Karamanov

2006

INFORMS Journal on Computing

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Section: Experiments and Resultsmentioning

confidence: 99%

“…This instance is the largest QAPLIB instance ever solved to proven optimality, Had20 -the optimal solution was found by Brüngger et al solved using the branch and bound algorithm based on the Hungarian method [44], Kra32 -the optimal solution was found using the B&B algorithm by Anstreicher et al [45], Lipa50a, Lipa90a -asymmetric instances produced by the generator with the known optimal solutions [46]. The optimal solution was found using the hybrid genetic algorithm by Ji et al [47], Nug20, Nug30 -Anstreicher and Brixius [45] found the optimal solution to n = 30 using a parallel B&B algorithm running on one thousand computers within a week, Rou20 -instance produced by the generator with the known optimal solutions [22]. The optimal solution was found using B&B algorithm in [22], Scr20 -the optimal solution of this problem was found by Mautor using the B&B algorithm [39], Sko42, Sko90, Sko100a -the best solution was obtained using the robust tabu search algorithm and the genetic algorithm (Sko100a) [40], Ste36a -the best solution was found using the tabu search algorithm by Skorin and Karpov [40], Tai30a, Tai50a, Tai100a -the best solution to the first instance was found by robust tabu search by Taillard [41] and for the second and third one by iterated tabu search by Misevicius [48], Tai100b, Tai150b -the best solution for both instances was found by Taillard, the first one using the robust tabu search [41] and the second one by GA [49], Tai64c, Tai256c -the best solution for the first instance was found using the B&B algorithm by Fischetti [43] and the second one using ant-system by Stützle [50], Tho40 -the best solution was found by the simulation annealing algorithm by Bölte [51], Wil50, Wil100 -the best solution was found by the simulation annealing algorithm by Bölte [51] and the genetic hybrids algorithm by Fleurent et al [52].…”

Section: Experiments and Resultsmentioning

confidence: 99%

A comparison of nature inspired algorithms for the quadratic assignment problem

Chmiel

Kadłuczka

Kwiecień

et al. 2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. This paper presents an application of the ant algorithm and bees algorithm in optimization of QAP problem as an example of NPhard optimization problem. The experiments with two types of algorithms: the bees algorithm and the ant algorithm were performed for the test instances of the quadratic assignment problem from QAPLIB, designed by Burkard, Karisch and Rendl. On the basis of the experiments results, an influence of particular elements of algorithms, including neighbourhood size and neighbourhood search method, will be determined. The QAP is an NP-hard problem and this difficulty is not restricted only to finding the optimal solution. Sahni and Gonzalez [4] proved that even finding an ɛ-approximation solution for QAP is a hard problem in this sense that the existence of a ɛ-approximation algorithm implies P = NP.Finding an optimal solution to QAP is a difficult task not only in case of looking for the best solution among all the feasible ones. It might appear that finding an optimal solution in the subset of the feasible solutions can be easier. For QAP it was proven that finding an optimal solution in case of the local search is a difficult problem too. Johnson and Papadimitriou in [6] created the base for the complexity theory in the local search case, where a special structure of neighbourhood is introduced. They define the PLS-problems (polynomial-time local search problem) as a set for which a locally optimal solution can be found in polynomial time. Next, they introduce a PLS-complete decision problem as an analogy of NP-complete one, which are the most difficult problems in PLS.Murthy, Pardalos and Li [7] proposed a neighbourhood structure for QAP problem and proved that the corresponding local search problem is PLS-complete. The proposed structure is similar to that proposed by Kernighan and Lin [8] for the graph partitioning problem called K-L type neighbourhood structure N K-L . As the problem of finding QAP optimal solution in N K-L (called (QAP, N K-L )) is PLS-complete, then in the

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“…Na tentativa de completar a bibliografia até os dias de hoje, indicamos ainda alguns trabalhos mais recentes que, em geral, tratam de procedimentos e técnicas de resolução do PQA ou discutem as dificuldades por ele apresentadas, apontando a tendência mais atual das pesquisas, [GTD99], [AQB99], [RAB00], [AZ02], [ABLG02] e [Mi03]. …”

Section: Introductionunclassified

Ordenações parciais nos conjuntos das soluções dos problemas de alocação linear e quadrático

Rangel

Abreu

2003

Pesqui. Oper.

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ResumoO Problema Quadrático de Alocação, PQA, pode ser abordado através de uma relaxação na forma do Problema de Alocação Linear, PAL. Introduzimos um poset (conjunto parcialmente ordenado) no conjunto das soluções lineares que nos permite comparar também os custos das soluções do problema quadrático, sem o conhecimento prévio das matrizes que definem seus exemplares. Construímos um algoritmo polinomial capaz de determinar pares de permutações livremente comparáveis, conceito apresentado neste trabalho. Provamos um teorema que garante que os custos associados a tais permutações preservam a ordem dada pelo número de inversões das mesmas. Associando soluções do problema a permutações, testes empíricos são apresentados, visando a validação do número de inversões como um parâmetro de referência para a qualidade das soluções. Este trabalho é uma extensão do artigo [RA01] publicado nos anais do XXXIII SBPO, em CD-ROM, 1277-1287, Sobrapo, ILTC, 2001.Palavras-chave: ordenação parcial; problema quadrático de alocação; problema de alocação linear. AbstractWe present an approach to Quadratic Assignment Problem, QAP, via a linear relaxation, through the use of the Linear Assignment Problem, LAP. We define one ordering an LAP-solution-set that makes us compare QAP costs. From here, this poset, partial ordering set, considers coordinates of instances as free variables. We have managed to build a capable algorithm to determine freely comparable permutation pairs. A theorem shows that the order mentioned above is compatible to the one that involves inversion numbers of permutations. We can apply linear and quadratic solutions to permutations and empiric tests are presented to show that the inversion numbers can be used to measure the quality of QAP-solutions. This work is an extension of the article [RA01] published in

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Solving large quadratic assignment problems on computational grids

Cited by 192 publications

References 37 publications

Early Estimates of the Size of Branch-and-Bound Trees

Early Estimates of the Size of Branch-and-Bound Trees

A comparison of nature inspired algorithms for the quadratic assignment problem

Ordenações parciais nos conjuntos das soluções dos problemas de alocação linear e quadrático

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