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Variations on memetic algorithms for graph coloring problems

Author

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  • Laurent Moalic

    (Univ. Bourgogne Franche-Comté)

  • Alexandre Gondran

    (French Civil Aviation University)

Abstract

Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem. The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm. This paper presents a new memetic algorithm based on one of the most effective algorithms: the hybrid evolutionary algorithm (HEA) from Galinier and Hao (J Comb Optim 3(4): 379–397, 1999). The proposed algorithm, denoted HEAD—for HEA in Duet—works with a population of only two individuals. Moreover, a new way of managing diversity is brought by HEAD. These two main differences greatly improve the results, both in terms of solution quality and computational time. HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for $${ }$$ , 81-colorings for $${ }$$ and even 47-colorings for $${ }$$ and 82-colorings for $${ }$$ .

Suggested Citation

  • Laurent Moalic & Alexandre Gondran, 2018. "Variations on memetic algorithms for graph coloring problems," Journal of Heuristics, Springer, vol. 24(1), pages 1-24, February.
    • Handle: RePEc:spr:joheur:v:24:y:2018:i:1:d:10.1007_s10732-017-9354-9
    DOI: 10.1007/s10732-017-9354-9
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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. Nicolas Barnier & Pascal Brisset, 2004. "Graph Coloring for Air Traffic Flow Management," Annals of Operations Research, Springer, vol. 130(1), pages 163-178, August.
    3. Olawale Titiloye & Alan Crispin, 2012. "Parameter Tuning Patterns for Random Graph Coloring with Quantum Annealing," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-9, November.
    4. 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:

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    3. Melo, Rafael A. & Queiroz, Michell F. & Santos, Marcio C., 2021. "A matheuristic approach for the b-coloring problem using integer programming and a multi-start multi-greedy randomized metaheuristic," European Journal of Operational Research, Elsevier, vol. 295(1), pages 66-81.

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