A hybrid heuristic for the maximum clique problem

Authors:
Alok Singh;Ashok Kumar Gupta
Affiliations:
J. K. Institute of Applied Physics and Technology, Faculty of Science, University of Allahabad, Allahabad, India 211002;J. K. Institute of Applied Physics and Technology, Faculty of Science, University of Allahabad, Allahabad, India 211002
Venue:
Journal of Heuristics
Year:
2006

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Abstract

In this paper we present a heuristic based steady-state genetic algorithm for the maximum clique problem. The steady-state genetic algorithm generates cliques, which are then extended into maximal cliques by the heuristic. We compare our algorithm with three best evolutionary approaches and the overall best approach, which is non-evolutionary, for the maximum clique problem and find that our algorithm outperforms all the three evolutionary approaches in terms of best and average clique sizes found on majority of DIMACS benchmark instances. However, the obtained results are much inferior to those obtained with the best approach for the maximum clique problem.