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Exploiting group symmetry in semidefinite programming relaxations of the quadratic assignment problem

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  • Klerk, E. de

    (Tilburg University)

  • Sotirov, R.

    (Tilburg University)

Abstract

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard, S.E. Karisch, F. Rendl. QAPLIB — a quadratic assignment problem library. Journal on Global Optimization, 10: 291–403, 1997]. AMS classification: 90C22, 20Cxx, 70-08.

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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-3125772.

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Date of creation: 2010
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Publication status: Published in Mathematical Programming (2010) v.122, p.225-246
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-3125772

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Web page: http://www.tilburguniversity.edu/

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  1. Rendl, F. & Sotirov, R., 2007. "Bounds for the quadratic assignment problem using the bundle method," Open Access publications from Tilburg University urn:nbn:nl:ui:12-192934, Tilburg University.
  2. Ivanov, I.D. & Klerk, E. de, 2007. "Parallel Implementation of a Semidefinite Programming Solver based on CSDP in a distributed memory cluster," Discussion Paper 2007-20, Tilburg University, Center for Economic Research.
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Cited by:
  1. Klerk, E. de & Pasechnik, D.V. & Sotirov, R., 2007. "On Semidefinite Programming Relaxations of the Travelling Salesman Problem (Replaced by DP 2008-96)," Discussion Paper 2007-101, Tilburg University, Center for Economic Research.
  2. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3736413, Tilburg University.
  3. de Klerk, Etienne & -Nagy, Marianna E. & Sotirov, Renata & Truetsch, Uwe, 2014. "Symmetry in RLT-type relaxations for the quadratic assignment and standard quadratic optimization problems," European Journal of Operational Research, Elsevier, vol. 233(3), pages 488-499.
  4. Nyberg, Axel & Westerlund, Tapio, 2012. "A new exact discrete linear reformulation of the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 220(2), pages 314-319.
  5. Klerk, E. de & Pasechnik, D.V. & Sotirov, R., 2008. "On Semidefinite Programming Relaxations of the Traveling Salesman Problem (revision of DP 2007-101)," Discussion Paper 2008-96, Tilburg University, Center for Economic Research.

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