An ant system for the maximum independent set problem

Early applications of Ant Colony Optimization (ACO) have been mainly concerned with solving ordering problems (e.g., the Traveling Salesperson Problem). More recently, promising results were obtained for solving the Multiple Knapsack Problem by introducing a modification of the standard Ant System algorithm. In this paper we extend our study on the applicability of the ACO approach to subset problems. The computational study involves its applicability for solving the Maximum Independent Set Problem (MISP). The set of instances tested were either randomly generated by specific methods or taken from the so-called DIMACS benchmark graphs. The reported results which are comparable with different state-of-the-art algorithms show the potential of the ACO approach for solving the MISP.

[1]  Béla Bollobás,et al.  Random Graphs , 1985 .

[2]  Marco Dorigo,et al.  Swarm intelligence: from natural to artificial systems , 1999 .

[3]  Charu C. Aggarwal,et al.  Optimized Crossover for the Independent Set Problem , 1997, Oper. Res..

[4]  Z. Michalewicz,et al.  A new version of ant system for subset problems , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[5]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[6]  Marcello Pelillo,et al.  Annealed replication: a new heuristic for the maximum clique problem , 2002, Discret. Appl. Math..

[7]  Celso C. Ribeiro,et al.  Greedy Randomized Adaptive Search Procedures , 2003, Handbook of Metaheuristics.

[8]  Thomas Bäck,et al.  An evolutionary heuristic for the maximum independent set problem , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[9]  Luca Maria Gambardella,et al.  Ant Algorithms for Discrete Optimization , 1999, Artificial Life.

[10]  Shumeet Baluja,et al.  A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning , 1994 .

[11]  C. Rossi,et al.  A replicator equations-based evolutionary algorithm for the maximum clique problem , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[12]  Panos M. Pardalos,et al.  A continuous based heuristic for the maximum clique problem , 1993, Cliques, Coloring, and Satisfiability.

[13]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[14]  Vittorio Maniezzo,et al.  The Ant System Applied to the Quadratic Assignment Problem , 1999, IEEE Trans. Knowl. Data Eng..

[15]  Mauricio G. C. Resende,et al.  A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set , 1994, Oper. Res..

[16]  Elena Marchiori.  A simple heuristic based genetic algorithm for the maximum clique problem , 1998, SAC '98.