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

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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.

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Notes

  1. The source code of AMTS is available at: http://www.info.univ-angers.fr/pub/hao/amts.html.

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Acknowledgement

We are grateful to the referees for their comments and questions which helped us to improve the paper. This work was partially supported by the Region of “Pays de la Loire” (France) within the Radapop and LigeRO Projects.

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  1. LERIA, Université d’Angers, 2 Boulevard Lavoisier, 49045, Angers Cedex 01, France

    Qinghua Wu & Jin-Kao Hao

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  1. Qinghua Wu
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  2. Jin-Kao Hao
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Correspondence to Jin-Kao Hao.

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Wu, Q., Hao, JK. An adaptive multistart tabu search approach to solve the maximum clique problem. J Comb Optim 26, 86–108 (2013). https://doi.org/10.1007/s10878-011-9437-8

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