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Ant Local Search and its efficient adaptation to graph colouring

Author

Listed:
  • M Plumettaz

    (Columbia University)

  • D Schindl

    (Geneva School of Business Administration (HEG))

  • N Zufferey

    (University of Geneva)

Abstract

In this paper, we propose a new kind of ant algorithm called Ant Local Search. In most ant algorithms, the role of each ant is to build a solution in a constructive way. In contrast, we propose to consider each ant as a local search, where at each step and in concordance with all ant algorithms, each ant modifies the current solution by the use of the greedy force and the trail systems. We also propose ways to reduce the computational effort associated with each ant decision. Such a new and general ant methodology is then applied to the well-known k-colouring problem, which is NP-hard. Computational experiments give evidence that our algorithm is competitive with the best colouring methods.

Suggested Citation

  • M Plumettaz & D Schindl & N Zufferey, 2010. "Ant Local Search and its efficient adaptation to graph colouring," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 819-826, May.
    • Handle: RePEc:pal:jorsoc:v:61:y:2010:i:5:d:10.1057_jors.2009.27
    DOI: 10.1057/jors.2009.27
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    References listed on IDEAS

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    1. David S. Johnson & Cecilia R. Aragon & Lyle A. McGeoch & Catherine Schevon, 1991. "Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning," Operations Research, INFORMS, vol. 39(3), pages 378-406, June.
    2. Enrico Malaguti & Michele Monaci & Paolo Toth, 2008. "A Metaheuristic Approach for the Vertex Coloring Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 302-316, May.
    3. Anuj Mehrotra & Michael A. Trick, 1996. "A Column Generation Approach for Graph Coloring," INFORMS Journal on Computing, INFORMS, vol. 8(4), pages 344-354, November.
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    5. Chams, M. & Hertz, A. & de Werra, D., 1987. "Some experiments with simulated annealing for coloring graphs," European Journal of Operational Research, Elsevier, vol. 32(2), pages 260-266, November.
    6. C A Glass & A Prügel-Bennett, 2005. "A polynomially searchable exponential neighbourhood for graph colouring," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 324-330, March.
    7. Philippe Galinier & Jin-Kao Hao, 1999. "Hybrid Evolutionary Algorithms for Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 379-397, December.
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    Cited by:

    1. Simon Thevenin & Nicolas Zufferey & Marino Widmer, 2016. "Order acceptance and scheduling with earliness and tardiness penalties," Journal of Heuristics, Springer, vol. 22(6), pages 849-890, December.
    2. Nicolas Zufferey & Olivier Labarthe & David Schindl, 2012. "Heuristics for a project management problem with incompatibility and assignment costs," Computational Optimization and Applications, Springer, vol. 51(3), pages 1231-1252, April.
    3. Ivo Blöchliger & Nicolas Zufferey, 2013. "Multi-coloring and job-scheduling with assignment and incompatibility costs," Annals of Operations Research, Springer, vol. 211(1), pages 83-101, December.

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