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International Symposium on Combinatorial Optimization

ISCO 2016: Combinatorial Optimization pp 414–425Cite as

A Novel SDP Relaxation for the Quadratic Assignment Problem Using Cut Pseudo Bases

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

Abstract

The quadratic assignment problem (QAP) is one of the hardest combinatorial optimization problems. Its range of applications is wide, including facility location, keyboard layout, and various other domains. The key success factor of specialized branch-and-bound frameworks for minimizing QAPs is an efficient implementation of a strong lower bound. In this paper, we propose a lower-bound-preserving transformation of a QAP to a different quadratic problem that allows for small and efficiently solvable SDP relaxations. This transformation is self-tightening in a branch-and-bound process.

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Notes

  1. 1.

    The Frobenius product \(A \bullet B := tr( A^T B) = \sum _{i,j} a_{ij} b_{ij}\) is the standard inner product on the space of \(n \times n\) matrices used in semi-definite programming.

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Authors and Affiliations

  1. Max Planck Institute for Informatics, Saarbrücken, Germany

    Maximilian John & Andreas Karrenbauer

Authors
  1. Maximilian John
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  2. Andreas Karrenbauer
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Correspondence to Maximilian John .

Editor information

Editors and Affiliations

  1. University of Salerno , Fisciano, Italy

    Raffaele Cerulli

  2. Kyoto University , Kyoto, Japan

    Satoru Fujishige

  3. LAMSADE, Université Paris-Dauphine , Paris , France

    A. Ridha Mahjoub

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John, M., Karrenbauer, A. (2016). A Novel SDP Relaxation for the Quadratic Assignment Problem Using Cut Pseudo Bases. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_36

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  • DOI: https://doi.org/10.1007/978-3-319-45587-7_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45586-0

  • Online ISBN: 978-3-319-45587-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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