IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v8y2004i1d10.1023_bjoco.0000021937.26468.b2.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:JOCO.0000021937.26468.b2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/B:JOCO.0000021937.26468.b2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Caramia, Massimiliano & Dell'Olmo, Paolo, 2008. "Embedding a novel objective function in a two-phased local search for robust vertex coloring," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1358-1380, September.
    2. Vincenzo Cutello & Giuseppe Nicosia & Mario Pavone, 2007. "An immune algorithm with stochastic aging and kullback entropy for the chromatic number problem," Journal of Combinatorial Optimization, Springer, vol. 14(1), pages 9-33, July.
    3. Iztok Fister & Marjan Mernik & Bogdan Filipič, 2013. "Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm," Computational Optimization and Applications, Springer, vol. 54(3), pages 741-770, April.
    4. 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.
    5. Severino F. Galán, 2017. "Simple decentralized graph coloring," Computational Optimization and Applications, Springer, vol. 66(1), pages 163-185, January.
    6. Jagota, Arun, 1996. "An adaptive, multiple restarts neural network algorithm for graph coloring," European Journal of Operational Research, Elsevier, vol. 93(2), pages 257-270, September.
    7. Xiao-Feng Xie & Jiming Liu, 2009. "Graph coloring by multiagent fusion search," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 99-123, August.
    8. 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.
    9. Massimiliano Caramia & Paolo Dell'Olmo, 2001. "Iterative coloring extension of a maximum clique," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(6), pages 518-550, September.
    10. 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.
    11. Bradley Hardy & Rhyd Lewis & Jonathan Thompson, 2018. "Tackling the edge dynamic graph colouring problem with and without future adjacency information," Journal of Heuristics, Springer, vol. 24(3), pages 321-343, June.
    12. Celia A. Glass & Adam Prügel-Bennett, 2003. "Genetic Algorithm for Graph Coloring: Exploration of Galinier and Hao's Algorithm," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 229-236, September.
    13. Avanthay, Cedric & Hertz, Alain & Zufferey, Nicolas, 2003. "A variable neighborhood search for graph coloring," European Journal of Operational Research, Elsevier, vol. 151(2), pages 379-388, December.
    14. 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.
    15. Philippe Galinier & Zied Boujbel & Michael Coutinho Fernandes, 2011. "An efficient memetic algorithm for the graph partitioning problem," Annals of Operations Research, Springer, vol. 191(1), pages 1-22, November.
    16. 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.
    17. Laurent Moalic & Alexandre Gondran, 2018. "Variations on memetic algorithms for graph coloring problems," Journal of Heuristics, Springer, vol. 24(1), pages 1-24, February.
    18. S. Butenko & P. Festa & P. M. Pardalos, 2001. "On the Chromatic Number of Graphs," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 69-83, April.
    19. Lü, Zhipeng & Hao, Jin-Kao, 2010. "A memetic algorithm for graph coloring," European Journal of Operational Research, Elsevier, vol. 203(1), pages 241-250, May.
    20. Drexl, Andreas & Juretzka, Jan & Salewski, Frank, 1993. "Academic course scheduling under workload and changeover constraints," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 337, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:8:y:2004:i:1:d:10.1023_b:joco.0000021937.26468.b2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.