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Bounds for the quadratic assignment problem using the bundle method

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Abstract

Semidefinite programming (SDP) has recently turned out to be a very powerful tool for approximating some NP-hard problems. The nature of the quadratic assignment problem (QAP) suggests SDP as a way to derive tractable relaxations. We recall some SDP relaxations of QAP and solve them approximately using a dynamic version of the bundle method. The computational results demonstrate the efficiency of the approach. Our bounds are currently among the strongest ones available for QAP. We investigate their potential for branch and bound settings by looking also at the bounds in the first levels of the branching tree.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Klagenfurt, Universitätsstraße 65-67, 9020, Klagenfurt, Austria

    Franz Rendl

  2. Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, 3010, Australia

    Renata Sotirov

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  1. Franz Rendl
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  2. Renata Sotirov
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Correspondence to Franz Rendl.

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Rendl, F., Sotirov, R. Bounds for the quadratic assignment problem using the bundle method. Math. Program. 109, 505–524 (2007). https://doi.org/10.1007/s10107-006-0038-8

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  • DOI: https://doi.org/10.1007/s10107-006-0038-8

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