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Multi-neighborhood tabu search for the maximum weight clique problem

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  • Qinghua Wu
  • Jin-Kao Hao
  • Fred Glover

Abstract

Given an undirected graph G=(V,E) with vertex set V={1,…,n} and edge set E⊆V×V. Let w:V→Z + be a weighting function that assigns to each vertex i∈V a positive integer. The maximum weight clique problem (MWCP) is to determine a clique of maximum weight. This paper introduces a tabu search heuristic whose key features include a combined neighborhood and a dedicated tabu mechanism using a randomized restart strategy for diversification. The proposed algorithm is evaluated on a total of 136 benchmark instances from different sources (DIMACS, BHOSLIB and set packing). Computational results disclose that our new tabu search algorithm outperforms the leading algorithm for the maximum weight clique problem, and in addition rivals the performance of the best methods for the unweighted version of the problem without being specialized to exploit this problem class. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:611-634:10.1007/s10479-012-1124-3
    DOI: 10.1007/s10479-012-1124-3
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    References listed on IDEAS

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    1. Delorme, Xavier & Gandibleux, Xavier & Rodriguez, Joaquin, 2004. "GRASP for set packing problems," European Journal of Operational Research, Elsevier, vol. 153(3), pages 564-580, March.
    2. 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.
    3. Kwon, Roy H., 2005. "Data dependent worst case bounds for weighted set packing," European Journal of Operational Research, Elsevier, vol. 167(1), pages 68-76, November.
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    Citations

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    Cited by:

    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. Xinyun Wu & Shengfeng Yan & Xin Wan & Zhipeng Lü, 2016. "Multi-neighborhood based iterated tabu search for routing and wavelength assignment problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 445-468, August.
    3. 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.
    4. Alex Gliesch & Marcus Ritt, 2022. "A new heuristic for finding verifiable k-vertex-critical subgraphs," Journal of Heuristics, Springer, vol. 28(1), pages 61-91, February.
    5. Yi Chu & Boxiao Liu & Shaowei Cai & Chuan Luo & Haihang You, 2020. "An efficient local search algorithm for solving maximum edge weight clique problem in large graphs," Journal of Combinatorial Optimization, Springer, vol. 39(4), pages 933-954, May.
    6. 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.
    7. Pierre Hansen & Nenad Mladenović & Raca Todosijević & Saïd Hanafi, 2017. "Variable neighborhood search: basics and variants," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 423-454, September.
    8. Oleksandra Yezerska & Sergiy Butenko & Vladimir L. Boginski, 2018. "Detecting robust cliques in graphs subject to uncertain edge failures," Annals of Operations Research, Springer, vol. 262(1), pages 109-132, March.
    9. Bruno Nogueira & Rian G. S. Pinheiro, 2020. "A GPU based local search algorithm for the unweighted and weighted maximum s-plex problems," Annals of Operations Research, Springer, vol. 284(1), pages 367-400, January.

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