Joining forces in solving large-scale quadratic assignment problems in parallel

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

doi:10.1109/ipps.1997.580936

Cited by 22 publications

(10 citation statements)

References 10 publications

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“…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].…”

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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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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“…An analytical comparison of different heuristic and meta-heuristic algorithms are presented in [37], [38], [39], [40]. Even parallel solutions to QAP are reported [26], [41].…”

Section: A Generalized Placement Problemmentioning

confidence: 99%

Towards Quick Solutions for Generalized Placement Problem

Srinivasan

Kamakoti

Bhattacharya

2011

2011 International Symposium on Electronic System Design

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The problem of placement is well known in Computer Aided Design (CAD) of VLSI Chips, DNA Microarrays and Microfluidic biochips. Because of the similarity of the placement problem across diverse domains a generalization of the same is reported in the literature. The generalized placement problem is an instance of the classical Quadratic Assignment Problem (QAP). In this paper, we present a new randomization based heuristic algorithm for QAP. The key to success of the proposed technique is a novel probability distribution that is employed by the heuristics to generate the necessary randomization. We show through simulation results that the proposed algorithm finds competitive solutions comparable with one of the best heuristics reported in literature, while consuming significantly smaller amount of CPU time.

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“…As formulated, the proposed zoning model is a combinatorial problem of quadratic assignment belonging to the NP-hard class (Nemhauser and Wolsey, 1988). The solution of this kind of problem by exact methods is computationally feasible only for small problems (Bruenegger et al 1996). Even when mapped on a scale of hectares, protected natural areas are composed of at least tens and not uncommonly tens of thousands of land units to be assigned.…”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

A mathematical model for zoning of protected natural areas

Verdiell¹,

Sabatini²,

Maciel³

et al. 2005

Int Trans Operational Res

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When formulated in mathematical terms, the problem of zoning a protected natural area subject to both box and spatial constraints results in a combinatorial optimization problem belonging to the NP‐hard class. This fact and the usual dimension of the problem (regularly in the tens of thousands order) suggest the need to apply a heuristic approach. In this contribution we describe a quantitative method for zoning protected natural areas based on a simulated annealing algorithm. Building upon previous work by Bos (1993), we introduce three main innovations (a quadratic function of distance between land units, a non‐symmetric matrix of compatibilities among uses, and a spatial connection constraint) that make the approach applicable for ecological purposes. When applied to solving small‐size simulated problems, the results were indistinguishable from those obtained via an exact, enumerative method. A coarse‐scale zoning of Talampaya National Park (Argentina) rendered maps remarkably similar to those produced by subject area experts using a non‐quantitative consensus‐seeking approach. Results are encouraging and show particular potential for the periodical update of zoning of protected natural areas. Such a capability is crucial for application in developing countries where both human and financial resources are usually scarce but still critical for updating zoning and management plans.

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Joining forces in solving large-scale quadratic assignment problems in parallel

Cited by 22 publications

References 10 publications

A comparison of nature inspired algorithms for the quadratic assignment problem

A comparison of nature inspired algorithms for the quadratic assignment problem

Towards Quick Solutions for Generalized Placement Problem

A mathematical model for zoning of protected natural areas

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