Searching for Maximum Cliques with Ant Colony Optimization
In this paper, we investigate the capabilities of Ant Colony Optimization (ACO) for solving the maximum clique problem. We describe Ant-Clique, an algorithm that successively generates maximal cliques through the repeated addition of vertices into partial cliques. ACO is used to choose, at each step, the vertex to add. We illustrate the behaviour of this algorithm on two representative benchmark instances and we study the impact of pheromone on the solution process. We also experimentally compare Ant-Clique with GLS, a Genetic Local Search approach, and we show that Ant-Clique finds larger cliques, on average, on a majority of DIMACS benchmark instances, even though it does not reach the best known results on some instances.
Unable to display preview. Download preview PDF.
- 2.I. Bomze, M. Budinich, P. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4. Kluwer Academic Publishers, Boston, MA, 1999.Google Scholar
- 3.M. Dorigo. Optimization, Learning and Natural Algorithms (in Italian). PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy, 1992.Google Scholar
- 6.E. Marchiori. Genetic, iterated and multistart local search for the maximum clique problem. In Applications of Evolutionary Computing, Proceedings of EvoWorkshops2002: EvoCOP, EvoIASP, EvoSTim, volume 2279, pages 112–121. Springer-Verlag, 2002.Google Scholar
- 8.C. Solnon. Boosting ACO with a preprocessing step. In Applications of Evolutionary Computing, Proceedings of EvoWorkshops2002: EvoCOP, EvoIASP, EvoSTim, volume 2279, pages 161–170. Springer-Verlag, 2002.Google Scholar