Annals of Operations Research

, Volume 196, Issue 1, pp 611–634 | Cite as

Multi-neighborhood tabu search for the maximum weight clique problem

  • Qinghua Wu
  • Jin-Kao Hao
  • Fred Glover


Given an undirected graph G=(V,E) with vertex set V={1,…,n} and edge set EV×V. Let w:VZ + be a weighting function that assigns to each vertex iV 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.


Multi-neighborhood search Maximum weight clique Maximum clique Tabu search Heuristics 



We are grateful to the referees for their suggestions. The work is partially supported by the “Pays de la Loire” Region (France) within the RaDaPop (2009-2013) and LigeRO (2010-2013) projects.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.LERIAUniversité d’AngersAngers Cedex 01France
  2. 2.OptTek Systems, Inc.BoulderUSA

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