On the Applicability of Lower Bounds for Solving RectilinearQuadratic Assignment Problems in Parallel

Authors:
Jens Clausen;Stefan E. Karisch;Michael Perregaard;Franz Rendl
Affiliations:
Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen, Denmark;Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen, Denmark;Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen, Denmark;Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria
Venue:
Computational Optimization and Applications
Year:
1998

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Abstract

The quadratic assignment problem (QAP) belongs tothe hard core of NP-hard optimization problems. After almostforty years of research only relatively small instances can besolved to optimality. The reason is that the quality of the lowerbounds available for exact methods is not sufficient. Recently,lower bounds based on decomposition were proposed for the so calledrectilinear QAP that proved to be the strongest for a large classof problem instances. We investigate the strength of these boundswhen applied not only at the root node of a search tree but as thebound function used in a Branch-and-Bound code solving large scale QAPs.