An Experimental Investigation of Iterated Local Search for Coloring Graphs
Graph coloring is a well known problem from graph theory that, when attacking it with local search algorithms, is typically treated as a series of constraint satisfaction problems: for a given number of colors k one has to find a feasible coloring; once such a coloring is found, the number of colors is decreased and the local search starts again. Here we explore the application of Iterated Local Search on the graph coloring problem. Iterated Local Search is a simple and powerful metaheuristic that has shown very good results for a variety of optimization problems. In our research we investigated several perturbation schemes and present computational results on a widely used set of benchmarks problems, a sub-set of those available from the DIMACS benchmark suite. Our results suggest that Iterated Local Search is particularly promising on hard, structured graphs.
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- 11.H.R. Lourenço, O. Martin, and T. Stützle. Iterated local search. In F. Glover and G. Kochenberger, editors, Handbook of Metaheuristics. Kluwer Academic Publishers, Boston, MA, USA, 2002. to appear.Google Scholar
- 12.J.C. Culberson. Iterated greedy graph coloring and the difficulty landscape. Technical Report 92–07, Department of Computing Science, The University of Alberta, Edmonton, Alberta, Canada, June 1992.Google Scholar
- 14.R. Dorne and J.K. Hao. Tabu search for graph coloring, t-colorings and set t-colorings. In I.H. Osman S. Voss, S. Martello and C. Roucairol, editors, Meta-heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 77–92. Kluwer Academic Publishers, Boston, MA, USA, 1999.Google Scholar
- 16.L. Davis. Order-based genetic algorithms and the graph coloring problem. In Handbook of Genetic Algorithms, pages 72–90. Van Nostrand Reinhold; New York, 1991.Google Scholar
- 19.C. Fleurent and J. Ferland. Object-oriented implementation of heuristic search methods for graph coloring, maximum clique and satisfiability. In D.S. Johnson and M.A. Trick, editors, Cliques, Coloring, and Satisfiability: SecondDIMACS Implementation Challenge, volume 26, pages 619–652. American Mathematical Society, 1996.Google Scholar
- 20.D.S. Johnson and L.A. McGeoch. The travelling salesman problem: A case study in local optimization. In E.H.L. Aarts and J.K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215–310. John Wiley & Sons, Chichester, UK, 1997.Google Scholar
- 21.O. Martin and S.W. Otto. Partitoning of unstructured meshes for load balancing. Concurrency: Practice and Experience, 7:303–314, 1995.Google Scholar
- 22.H.H. Hoos and T. Stützle. Evaluating Las Vegas algorithms-pitfalls and remedies. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), pages 238–245. Morgan Kaufmann, San Francisco, 1998.Google Scholar