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Lower bounds for the quadratic assignment problem via triangle decompositions

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Abstract

We consider transformations of the (metric) Quadratic Assignment Problem (QAP) that exploit the metric structure of a given instance. We show in particular how the structural properties of rectangular grids can be used to improve a given lower bound. Our work is motivated by previous research of Palubetskes (1988), and it extends a bounding approach proposed by Chakrapani and Skorin-Kapov (1993). Our computational results indicate that the present approach is practical; it has been applied to problems of dimension up ton = 150. Moreover, the new approach yields by far the best lower bounds on most of the instances of metric QAPs that we considered.

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Authors and Affiliations

  1. Institut für Mathematik (501B), Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    Stefan E. Karisch & Franz Rendl

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  1. Stefan E. Karisch
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  2. Franz Rendl
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The authors gratefully acknowledge financial support by the Christian Doppler Laboratorium für Diskrete Optimierung.

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Karisch, S.E., Rendl, F. Lower bounds for the quadratic assignment problem via triangle decompositions. Mathematical Programming 71, 137–151 (1995). https://doi.org/10.1007/BF01585995

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  • DOI: https://doi.org/10.1007/BF01585995

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