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A Cutting Planes Algorithm Based Upon a Semidefinite Relaxation for the Quadratic Assignment Problem

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Algorithms – ESA 2005 (ESA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3669))

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Abstract

We present a cutting planes algorithm for the Quadratic Assignment Problem based upon a semidefinite relaxation, and we report experiments for classical instances. Our lower bound is compared with the ones obtained by linear and semidefinite approaches. Our tests show that the cuts we use (originally proposed for a linear approach) allow to improve significantly on the bounds obtained by the other approaches. Moreover, this is achieved within a moderate additional computing effort, and even in a shorter total time sometimes. Indeed, thanks to the strong tailing off effect of the SDP solver we have used (SB), we obtain in a reasonable time an approximate solution which is suitable to generate efficient cutting planes which speed up the convergence of SB.

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Authors and Affiliations

  1. CEDRIC, CNAM-Institut d’Informatique d’Entreprise, 18 allée Jean Rostand, 91025 cedex, Evry, France

    Alain Faye & Frédéric Roupin

Authors
  1. Alain Faye
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  2. Frédéric Roupin
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Editors and Affiliations

  1. BRICS, MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Gerth Stølting Brodal

  2. University of Rome “La Sapienza”, Rome, Italy

    Stefano Leonardi

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© 2005 Springer-Verlag Berlin Heidelberg

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Faye, A., Roupin, F. (2005). A Cutting Planes Algorithm Based Upon a Semidefinite Relaxation for the Quadratic Assignment Problem. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_75

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  • DOI: https://doi.org/10.1007/11561071_75

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29118-3

  • Online ISBN: 978-3-540-31951-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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