IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v26y2013i1d10.1007_s10878-011-9437-8.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-011-9437-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-011-9437-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Wayne Pullan, 2006. "Phased local search for the maximum clique problem," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 303-323, November.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2020. "A Lagrangian Bound on the Clique Number and an Exact Algorithm for the Maximum Edge Weight Clique Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 747-762, July.
    4. Nicolas Zufferey & Olivier Labarthe & David Schindl, 2012. "Heuristics for a project management problem with incompatibility and assignment costs," Computational Optimization and Applications, Springer, vol. 51(3), pages 1231-1252, April.
    5. Xiao-Feng Xie & Jiming Liu, 2009. "Graph coloring by multiagent fusion search," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 99-123, August.
    6. Chen, Liang & Chen, Sheng-Jie & Chen, Wei-Kun & Dai, Yu-Hong & Quan, Tao & Chen, Juan, 2023. "Efficient presolving methods for solving maximal covering and partial set covering location problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 73-87.
    7. Raja Marappan & Gopalakrishnan Sethumadhavan, 2020. "Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem," Mathematics, MDPI, vol. 8(3), pages 1-20, February.
    8. David Bergman & Andre A. Cire & Willem-Jan van Hoeve & J. N. Hooker, 2014. "Optimization Bounds from Binary Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 253-268, May.
    9. M Plumettaz & D Schindl & N Zufferey, 2010. "Ant Local Search and its efficient adaptation to graph colouring," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 819-826, May.
    10. Mabrouk, Bchira Ben & Hasni, Hamadi & Mahjoub, Zaher, 2009. "On a parallel genetic-tabu search based algorithm for solving the graph colouring problem," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1192-1201, September.
    11. Laurent Moalic & Alexandre Gondran, 2018. "Variations on memetic algorithms for graph coloring problems," Journal of Heuristics, Springer, vol. 24(1), pages 1-24, February.
    12. Li, Mingjie & Hao, Jin-Kao & Wu, Qinghua, 2024. "A flow based formulation and a reinforcement learning based strategic oscillation for cross-dock door assignment," European Journal of Operational Research, Elsevier, vol. 312(2), pages 473-492.
    13. C A Glass & A Prügel-Bennett, 2005. "A polynomially searchable exponential neighbourhood for graph colouring," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 324-330, March.
    14. Zhiqiang Zhang & Zhongwen Li & Xiaobing Qiao & Weijun Wang, 2019. "An Efficient Memetic Algorithm for the Minimum Load Coloring Problem," Mathematics, MDPI, vol. 7(5), pages 1-20, May.
    15. Valmir C. Barbosa & Carlos A.G. Assis & Josina O. Do Nascimento, 2004. "Two Novel Evolutionary Formulations of the Graph Coloring Problem," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 41-63, March.
    16. Enrico Malaguti & Michele Monaci & Paolo Toth, 2008. "A Metaheuristic Approach for the Vertex Coloring Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 302-316, May.
    17. Nasirian, Farzaneh & Mahdavi Pajouh, Foad & Balasundaram, Balabhaskar, 2020. "Detecting a most closeness-central clique in complex networks," European Journal of Operational Research, Elsevier, vol. 283(2), pages 461-475.
    18. Renatha Capua & Yuri Frota & Luiz Satoru Ochi & Thibaut Vidal, 2018. "A study on exponential-size neighborhoods for the bin packing problem with conflicts," Journal of Heuristics, Springer, vol. 24(4), pages 667-695, August.
    19. 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.
    20. Hertz, Alain & Widmer, Marino, 2003. "Guidelines for the use of meta-heuristics in combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 151(2), pages 247-252, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-011-9437-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.