A Scatter Search Algorithm for the Maximum Clique Problem
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.
KeywordsTabu Search Tabu List Trial Solution Tabu Search Algorithm Scatter Search
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- L. Cavique, C. Rego, and I. Themido. Estruturas de Vizinhanga e Algoritmos de Procura Local para o Problema da Clique Máxima. To appear in: Revista de Investigação Operacional. Google Scholar
- V.-D. Cung, T. Mautor, P. Michelon, and A. Tavares. A Scatter Search Based Approach for the Quadratic Assignment Problem. In: Proceedings of IEEE International Conference on Evolutionary Computation, pages 165–169, 1997.Google Scholar
- F. Glover. Scatter Search and Path Relinking. In: New Ideas in Optimization, D. Corne, M. Dorigo, and F. Glover, editors, pages 297–316, McGraw Hill, 1999.Google Scholar
- A. Jagota. Efficient Approximating Max-Clique in a Holpfield-Style Network. In: IEEE, International Joint Conference on Neural Networks, vol. 2, pages 248–253, Baltimore, 1992.Google Scholar
- A. Jagota, L. Sanchis, and R. Ganesan. Approximately Solving Maximum Clique using Neural Network Related Heuristics. DIM ACS Series on Discrete Mathematics and Theoretical Computer Science, 26:169–203, 1996.Google Scholar
- D.S. Johnson and M.A. Trick (editors). Clique, Coloring and Satisfiability. DIM ACS Series on Discrete Mathematics and Theoretical Computer Science, 26, 1996.Google Scholar
- M. Laguna. Scatter Search. Research Report, University of Colorado, Boulder, 1999.Google Scholar
- H. Lourengo, J. Paixão, and R. Portugal. Meta-Heuristics for the BusDriver Scheduling Problem. Economic Working Papers Series 304, Universitat Pompeu Fabra, Barcelone, 1999.Google Scholar
- C. Rego and P. Leão. A Scatter Search Tutorial for Graph-Based Permutation Problems. Research Paper HCES-10–00, Hearin Center for Enterprise Science, University of Mississippi, 2000.Google Scholar