An Experimental Investigation of Iterated Local Search for Coloring Graphs

  • Luis Paquete
  • Thomas Stützle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2279)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.W. Carter. A survey of pratical applications of examination timetabling algorithms. Operations Research, 34(2):193–202, 1986.MathSciNetGoogle Scholar
  2. 2.
    D.J. Castelino, S. Hurley, and N.M. Stephens. A tabu search algorithm for frequency assignment. Annals of Operations Research, 63:301–320, 1996.zbMATHCrossRefGoogle Scholar
  3. 3.
    M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, CA, USA, 1979.zbMATHGoogle Scholar
  4. 4.
    A. Mehrotra and M. Trick. A column generation approach for graph coloring. INFORMS Journal On Computing, 8(4):344–354, 1996.zbMATHGoogle Scholar
  5. 5.
    D. Brélaz. New methods to color the vertices of a graph. Communications of the ACM, 22(4):251–256, 1979.zbMATHCrossRefGoogle Scholar
  6. 6.
    C. Fleurent and J. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437–464, 1996.zbMATHCrossRefGoogle Scholar
  7. 7.
    P. Galinier and J.K. Hao. Hybrid evolutionary algorithms for graph coloring. Journal of Combinatorial Optimization, 3(4):379–397, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    A. Hertz and D. de Werra. Using tabu search techniques for graph coloring. Computing, 39:345–351, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    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.zbMATHCrossRefGoogle Scholar
  10. 10.
    F.T. Leighton. Agraph coloring algorithm for large scheduling problems. Journal of Research of the National Bureau of Standards, 85:489–506, 1979.MathSciNetGoogle Scholar
  11. 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. 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
  13. 13.
    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.CrossRefMathSciNetGoogle Scholar
  14. 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
  15. 15.
    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.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 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
  17. 17.
    A.E. Eiben, J.K. Hauw, and J.I. Van Hemert. Graph coloring with adaptive evolutionary algorithms. Journal of Heuristics, 4:25–46, 1998.zbMATHCrossRefGoogle Scholar
  18. 18.
    M. Laguna and R. Martí. A GRASP for coloring sparse graphs. Computational Optimization and Applications, 19(2):165–178, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  19. 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. 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. 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. 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
  23. 23.
    H.H. Hoos and T. Stützle. Characterising the behaviour of stochastic local search. Artificial Intelligence, 112:213–232, 1999.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Luis Paquete
    • 1
  • Thomas Stützle
    • 1
  1. 1.Computer Science Department, Intellectics GroupDarmstadt University of TechnologyDarmstadtGermany

Personalised recommendations