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An adaptive multistart tabu search approach to solve the maximum clique problem

Author

Listed:
  • Qinghua Wu

    (Université d’Angers)

  • Jin-Kao Hao

    (Université d’Angers)

Abstract

Given an undirected graph G=(V,E) with vertex set V={1,…,n} and edge set E⊆V×V. The maximum clique problem is to determine in G a clique (i.e., a complete subgraph) of maximum cardinality. This paper presents an effective algorithm for the maximum clique problem. The proposed multistart tabu search algorithm integrates a constrained neighborhood, a dynamic tabu tenure mechanism and a long term memory based restart strategy. Our proposed algorithm is evaluated on the whole set of 80 DIMACS challenge benchmarks and compared with five state-of-the-art algorithms. Computational results show that our proposed algorithm attains the largest known clique for 79 benchmarks.

Suggested Citation

  • Qinghua Wu & Jin-Kao Hao, 2013. "An adaptive multistart tabu search approach to solve the maximum clique problem," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 86-108, July.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-011-9437-8
    DOI: 10.1007/s10878-011-9437-8
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    References listed on IDEAS

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    1. Wayne Pullan, 2006. "Phased local search for the maximum clique problem," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 303-323, November.
    2. Stanislav Busygin & Sergiy Butenko & Panos M. Pardalos, 2002. "A Heuristic for the Maximum Independent Set Problem Based on Optimization of a Quadratic Over a Sphere," Journal of Combinatorial Optimization, Springer, vol. 6(3), pages 287-297, September.
    3. Valmir C. Barbosa & Luciana C. D. Campos, 2004. "A Novel Evolutionary Formulation of the Maximum Independent Set Problem," Journal of Combinatorial Optimization, Springer, vol. 8(4), pages 419-437, December.
    4. 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.
    5. Philippe Galinier & Jin-Kao Hao, 1999. "Hybrid Evolutionary Algorithms for Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 379-397, December.
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    Cited by:

    1. MohammadAmin Fazli & Azin Ghazimatin & Jafar Habibi & Hamid Haghshenas, 2016. "Team selection for prediction tasks," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 743-757, February.
    2. Furini, Fabio & Ljubić, Ivana & San Segundo, Pablo & Zhao, Yanlu, 2021. "A branch-and-cut algorithm for the Edge Interdiction Clique Problem," European Journal of Operational Research, Elsevier, vol. 294(1), pages 54-69.
    3. 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.
    4. San Segundo, Pablo & Furini, Fabio & Álvarez, David & Pardalos, Panos M., 2023. "CliSAT: A new exact algorithm for hard maximum clique problems," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1008-1025.
    5. Yi Zhou & Jin-Kao Hao & Adrien Goëffon, 2016. "A three-phased local search approach for the clique partitioning problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 469-491, August.
    6. San Segundo, Pablo & Coniglio, Stefano & Furini, Fabio & Ljubić, Ivana, 2019. "A new branch-and-bound algorithm for the maximum edge-weighted clique problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 76-90.
    7. Zhou, Qing & Benlic, Una & Wu, Qinghua, 2020. "An opposition-based memetic algorithm for the maximum quasi-clique problem," European Journal of Operational Research, Elsevier, vol. 286(1), pages 63-83.
    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. Daniel Porumbel & Jin-Kao Hao, 2020. "Distance-guided local search," Journal of Heuristics, Springer, vol. 26(5), pages 711-741, October.

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