Journal of Combinatorial Optimization

, Volume 26, Issue 1, pp 86–108

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



Given an undirected graph G=(V,E) with vertex set V={1,…,n} and edge set EV×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.


Tabu search Maximum clique Constrained neighborhood Informed restart Combinatorial optimization 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.LERIAUniversité d’AngersAngers Cedex 01France

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