A Scatter Search Algorithm for the Maximum Clique Problem

  • Luís Cavique
  • César Rego
  • Isabel Themido
Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 15)


The objective of the Maximum Clique Problem (MCP) is to find the largest complete subgraph in a given graph. The problem is known as NP-hard and we have developed a heuristic algorithm based on a Scatter Search (SS) framework to find a lower bound for this maximization problem. The proposed algorithm was developed with two search features: a guidance search and a local search feature. For the first feature a Scatter Search algorithm was chosen with the purpose of extensively exploring regions with strategically combined solutions. The new solutions obtained in the combination phase are thereafter improved by a neighborhood search procedure based on tabu search for implementing the second feature. The computational results obtained with DIMACS clique benchmark instances show that the proposed algorithm finds solutions comparable to the ones provided by some of the most competitive algorithms for the MCP.


Tabu Search Tabu List Trial Solution Tabu Search Algorithm Scatter Search 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Luís Cavique
    • 1
  • César Rego
    • 2
  • Isabel Themido
    • 3
  1. 1.Escola Superior de Comunicação SocialInstituto Politécnico de LisboaPortugal
  2. 2.Hearin Center for Enterprise Science, School of Business AdministrationUniversity of Mississippi UniversityUSA
  3. 3.CESUR, Instituto Superior TécnicoUniversidade Técnica de LisboaPortugal

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