Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M.W. Carter. A survey of pratical applications of examination timetabling algorithms. Operations Research, 34(2):193–202, 1986.
D.J. Castelino, S. Hurley, and N.M. Stephens. A tabu search algorithm for frequency assignment. Annals of Operations Research, 63:301–320, 1996.
M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, CA, USA, 1979.
A. Mehrotra and M. Trick. A column generation approach for graph coloring. INFORMS Journal On Computing, 8(4):344–354, 1996.
D. Brélaz. New methods to color the vertices of a graph. Communications of the ACM, 22(4):251–256, 1979.
C. Fleurent and J. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437–464, 1996.
P. Galinier and J.K. Hao. Hybrid evolutionary algorithms for graph coloring. Journal of Combinatorial Optimization, 3(4):379–397, 1999.
A. Hertz and D. de Werra. Using tabu search techniques for graph coloring. Computing, 39:345–351, 1987.
D.S. Johnson, C.R. Aragon, L.A. McGeoch, and C. Schevon. Optimization by simulated annealing: An experimental evaluation: Part II, graph coloring and number partitioning. Operations Research, 39(3):378–406, 1991.
F.T. Leighton. Agraph coloring algorithm for large scheduling problems. Journal of Research of the National Bureau of Standards, 85:489–506, 1979.
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.
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.
S. Minton, M.D. Johnston, A.B. Philips, and P. Laird. Minimizing conflicts: A heuristic repair method for constraint satisfaction and scheduling problems. Artificial Intelligence, 52:161–205, 1992.
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.
M. Chams, A. Hertz, and D. De Werra. Some experiments with simulated annealing for coloring graphs. European Journal of Operational Research, 32:260–266, 1987.
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.
A.E. Eiben, J.K. Hauw, and J.I. Van Hemert. Graph coloring with adaptive evolutionary algorithms. Journal of Heuristics, 4:25–46, 1998.
M. Laguna and R. Martí. A GRASP for coloring sparse graphs. Computational Optimization and Applications, 19(2):165–178, 2001.
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.
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.
O. Martin and S.W. Otto. Partitoning of unstructured meshes for load balancing. Concurrency: Practice and Experience, 7:303–314, 1995.
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.
H.H. Hoos and T. Stützle. Characterising the behaviour of stochastic local search. Artificial Intelligence, 112:213–232, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Paquete, L., Stützle, T. (2002). An Experimental Investigation of Iterated Local Search for Coloring Graphs. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds) Applications of Evolutionary Computing. EvoWorkshops 2002. Lecture Notes in Computer Science, vol 2279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46004-7_13
Download citation
DOI: https://doi.org/10.1007/3-540-46004-7_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43432-0
Online ISBN: 978-3-540-46004-6
eBook Packages: Springer Book Archive