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PUSH: A generalized operator for the Maximum Vertex Weight Clique Problem

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  • Zhou, Yi
  • Hao, Jin-Kao
  • Goëffon, Adrien

Abstract

The Maximum Vertex Weight Clique Problem (MVWCP) is an important generalization of the well-known NP-hard Maximum Clique Problem. In this paper, we introduce a generalized move operator called PUSH, which generalizes the conventional ADD and SWAP operators commonly used in the literature and can be integrated in a local search algorithm for MVWCP. The PUSH operator also offers opportunities to define new search operators by considering dedicated candidate push sets. To demonstrate the usefulness of the proposed operator, we implement two simple tabu search algorithms which use PUSH to explore different candidate push sets. The computational results on 142 benchmark instances from different sources (DIMACS, BHOSLIB, and Winner Determination Problem) indicate that these algorithms compete favorably with the leading MVWCP algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:1:p:41-54
    DOI: 10.1016/j.ejor.2016.07.056
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. Dijkhuizen, G. & Faigle, U., 1993. "A cutting-plane approach to the edge-weighted maximal clique problem," European Journal of Operational Research, Elsevier, vol. 69(1), pages 121-130, August.
    5. 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.
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    Cited by:

    1. Li, Chu-Min & Liu, Yanli & Jiang, Hua & Manyà, Felip & Li, Yu, 2018. "A new upper bound for the maximum weight clique problem," European Journal of Operational Research, Elsevier, vol. 270(1), pages 66-77.
    2. Zhou, Yi & Rossi, André & Hao, Jin-Kao, 2018. "Towards effective exact methods for the Maximum Balanced Biclique Problem in bipartite graphs," European Journal of Operational Research, Elsevier, vol. 269(3), pages 834-843.

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