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Two Novel Evolutionary Formulations of the Graph Coloring Problem

Author

Listed:
  • Valmir C. Barbosa

    (Universidade Federal do Rio de Janeiro)

  • Carlos A.G. Assis

    (Universidade Federal do Rio de Janeiro)

  • Josina O. Do Nascimento

    (Universidade Federal do Rio de Janeiro
    Observatório Nacional)

Abstract

We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The second formulation, unlike the first one, does not tackle one graph at a time, but rather aims at evolving a “program” to color all graphs belonging to a class whose members all have the same number of nodes and other common attributes. The heuristics that result from these formulations have been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and have been found to be competitive when compared to the several other heuristics that have also been tested on those graphs.

Suggested Citation

  • Valmir C. Barbosa & Carlos A.G. Assis & Josina O. Do Nascimento, 2004. "Two Novel Evolutionary Formulations of the Graph Coloring Problem," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 41-63, March.
    • Handle: RePEc:spr:jcomop:v:8:y:2004:i:1:d:10.1023_b:joco.0000021937.26468.b2
    DOI: 10.1023/B:JOCO.0000021937.26468.b2
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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. de Werra, D., 1985. "An introduction to timetabling," European Journal of Operational Research, Elsevier, vol. 19(2), pages 151-162, February.
    3. 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. Valmir C Barbosa, 2010. "Network Conduciveness with Application to the Graph-Coloring and Independent-Set Optimization Transitions," PLOS ONE, Public Library of Science, vol. 5(7), pages 1-9, July.
    2. Xiao-Feng Xie & Jiming Liu, 2009. "Graph coloring by multiagent fusion search," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 99-123, August.
    3. Barbosa, Valmir C. & Ferreira, Rubens G., 2004. "On the phase transitions of graph coloring and independent sets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 401-423.
    4. Bernard Gendron & Alain Hertz & Patrick St-Louis, 2007. "On edge orienting methods for graph coloring," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 163-178, February.

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