Solving Large-Scale QAP Problems in Parallel with the Search Library ZRAM

Brüngger, Adrian; Marzetta, Ambros; Clausen, Jens; Perregaard, Michael

doi:10.1006/jpdc.1998.1434

Cited by 20 publications

(5 citation statements)

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“…One conclusion was that Knuth's estimator can be used for comparison purpose even when it outputs imprecise predictions. 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.…”

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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“…However, until recently many successful branch-and-bound algorithms for QAP were based on GLB or closely related bounds; see for example Refs. [2,5,7,15,17].…”

Section: Gilmore-lawler Boundmentioning

confidence: 98%

Gilmore-Lawler bound of quadratic assignment problem

Xia

2008

Front. Math. China

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The Gilmore-Lawler bound (GLB) is one of the well-known lower bound of quadratic assignment problem (QAP). Checking whether GLB is tight is an NP-complete problem. In this article, based on Xia and Yuan linearization technique, we provide an upper bound of the complexity of this problem, which makes it pseudo-polynomial solvable. We also pseudopolynomially solve a class of QAP whose GLB is equal to the optimal objective function value, which was shown to remain NP-hard.Keywords Quadratic assignment problem (QAP), Gilmore-Lawler bound, computational complexity, NP-hard MSC 68Q17, 90C11, 90C27

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“…The best known objective value for the 1-norm version of SWP, 9526, was rst obtained in 1990 using a tabu search algorithm 40], and has been subsequently rediscovered many times. One permutation (assignment of components to locations) attaining this value is: (12,19,30,11,2,3,22,20,10,21,5,4,13,15,31,32,28,29,24,14,17,18,16,9,8,7,6,23,33,34,35,25,27,26,1,36). Note that in this assignment the two dummy components (numbers 35 and 36) are placed in corners of the grid that are diagonally opposite one another.…”

Section: Quadratic Assignment Problemsmentioning

confidence: 99%