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Solving the maximum vertex weight clique problem via binary quadratic programming

Author

Listed:
  • Yang Wang

    (Northwestern Polytechnical University)

  • Jin-Kao Hao

    (Université d’Angers
    Institut Universitaire de France)

  • Fred Glover

    (OptTek Systems, Inc)

  • Zhipeng Lü

    (Huazhong University of Science and Technology)

  • Qinghua Wu

    (Huazhong University of Science and Technology)

Abstract

In recent years, the general binary quadratic programming (BQP) model has been widely applied to solve a number of combinatorial optimization problems. In this paper, we recast the maximum vertex weight clique problem (MVWCP) into this model which is then solved by a probabilistic tabu search algorithm designed for the BQP. Experimental results on 80 challenging DIMACS-W and 40 BHOSLIB-W benchmark instances demonstrate that this general approach is viable for solving the MVWCP problem.

Suggested Citation

  • Yang Wang & Jin-Kao Hao & Fred Glover & Zhipeng Lü & Qinghua Wu, 2016. "Solving the maximum vertex weight clique problem via binary quadratic programming," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 531-549, August.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:2:d:10.1007_s10878-016-9990-2
    DOI: 10.1007/s10878-016-9990-2
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    References listed on IDEAS

    as
    1. Wu, Qinghua & Hao, Jin-Kao, 2015. "A review on algorithms for maximum clique problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 693-709.
    2. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    3. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    4. Qinghua Wu & Jin-Kao Hao & Fred Glover, 2012. "Multi-neighborhood tabu search for the maximum weight clique problem," Annals of Operations Research, Springer, vol. 196(1), pages 611-634, July.
    5. Alidaee, Bahram & Kochenberger, Gary & Lewis, Karen & Lewis, Mark & Wang, Haibo, 2008. "A new approach for modeling and solving set packing problems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 504-512, April.
    6. Fred Glover, 1989. "Tabu Search---Part I," INFORMS Journal on Computing, INFORMS, vol. 1(3), pages 190-206, August.
    7. Alidaee, Bahram & Glover, Fred & Kochenberger, Gary & Wang, Haibo, 2007. "Solving the maximum edge weight clique problem via unconstrained quadratic programming," European Journal of Operational Research, Elsevier, vol. 181(2), pages 592-597, September.
    8. Steffen Rebennack & Marcus Oswald & Dirk Oliver Theis & Hanna Seitz & Gerhard Reinelt & Panos M. Pardalos, 2011. "A Branch and Cut solver for the maximum stable set problem," Journal of Combinatorial Optimization, Springer, vol. 21(4), pages 434-457, May.
    9. Wu, Yu-Liang & Huang, Wenqi & Lau, Siu-chung & Wong, C. K. & Young, Gilbert H., 2002. "An effective quasi-human based heuristic for solving the rectangle packing problem," European Journal of Operational Research, Elsevier, vol. 141(2), pages 341-358, September.
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    Cited by:

    1. Zhou, Yi & Hao, Jin-Kao & Goëffon, Adrien, 2017. "PUSH: A generalized operator for the Maximum Vertex Weight Clique Problem," European Journal of Operational Research, Elsevier, vol. 257(1), pages 41-54.

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