IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v203y2010i1p241-250.html
   My bibliography  Save this article

A memetic algorithm for graph coloring

Author

Listed:
  • Lü, Zhipeng
  • Hao, Jin-Kao

Abstract

Given an undirected graph G=(V,E) with a set V of vertices and a set E of edges, the graph coloring problem consists of partitioning all vertices into k independent sets and the number of used colors k is minimized. This paper presents a memetic algorithm (denoted by MACOL) for solving the problem of graph coloring. The proposed MACOL algorithm integrates several distinguished features such as an adaptive multi-parent crossover (AMPaX) operator and a distance-and-quality based replacement criterion for pool updating. The proposed algorithm is evaluated on the DIMACS challenge benchmarks and computational results show that the proposed MACOL algorithm achieves highly competitive results, compared with 11 state-of-the-art algorithms. The influence of some ingredients of MACOL on its performance is also analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:203:y:2010:i:1:p:241-250
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00517-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Smith, D. H. & Hurley, S. & Thiel, S. U., 1998. "Improving heuristics for the frequency assignment problem," European Journal of Operational Research, Elsevier, vol. 107(1), pages 76-86, May.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Philippe Galinier & Jin-Kao Hao, 1999. "Hybrid Evolutionary Algorithms for Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 379-397, December.
    7. Burke, Edmund K. & McCollum, Barry & Meisels, Amnon & Petrovic, Sanja & Qu, Rong, 2007. "A graph-based hyper-heuristic for educational timetabling problems," European Journal of Operational Research, Elsevier, vol. 176(1), pages 177-192, January.
    8. C A Glass, 2002. "Bag rationalisation for a food manufacturer," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(5), pages 544-551, May.
    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. 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.
    2. Raja Marappan & Gopalakrishnan Sethumadhavan, 2020. "Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem," Mathematics, MDPI, vol. 8(3), pages 1-20, February.
    3. Qin, Hu & Zhang, Zizhen & Qi, Zhuxuan & Lim, Andrew, 2014. "The freight consolidation and containerization problem," European Journal of Operational Research, Elsevier, vol. 234(1), pages 37-48.
    4. Casado, Silvia & Laguna, Manuel & Pacheco, Joaquín & Puche, Julio C., 2020. "Grouping products for the optimization of production processes: A case in the steel manufacturing industry," European Journal of Operational Research, Elsevier, vol. 286(1), pages 190-202.
    5. 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.
    6. Geng Lin & Wenxing Zhu & M. Montaz Ali, 2016. "An effective discrete dynamic convexized method for solving the winner determination problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 563-593, August.
    7. Yupeng Zhou & Jinshu Li & Yang Liu & Shuai Lv & Yong Lai & Jianan Wang, 2020. "Improved Memetic Algorithm for Solving the Minimum Weight Vertex Independent Dominating Set," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    8. Zhou, Yangming & Wang, Gezi & Hao, Jin-Kao & Geng, Na & Jiang, Zhibin, 2023. "A fast tri-individual memetic search approach for the distance-based critical node problem," European Journal of Operational Research, Elsevier, vol. 308(2), pages 540-554.
    9. Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2010. "A hybrid metaheuristic approach to solving the UBQP problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1254-1262, December.
    10. Bo Peng & Yuan Zhang & Yuvraj Gajpal & Xiding Chen, 2019. "A Memetic Algorithm for the Green Vehicle Routing Problem," Sustainability, MDPI, vol. 11(21), pages 1-20, October.
    11. Ferrarini, Luca & Gualandi, Stefano, 2022. "Total Coloring and Total Matching: Polyhedra and Facets," European Journal of Operational Research, Elsevier, vol. 303(1), pages 129-142.
    12. 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.

    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. 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.
    2. Severino F. Galán, 2017. "Simple decentralized graph coloring," Computational Optimization and Applications, Springer, vol. 66(1), pages 163-185, January.
    3. 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.
    4. 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.
    5. Renatha Capua & Yuri Frota & Luiz Satoru Ochi & Thibaut Vidal, 2018. "A study on exponential-size neighborhoods for the bin packing problem with conflicts," Journal of Heuristics, Springer, vol. 24(4), pages 667-695, August.
    6. 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.
    7. 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.
    8. 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.
    9. Mabrouk, Bchira Ben & Hasni, Hamadi & Mahjoub, Zaher, 2009. "On a parallel genetic-tabu search based algorithm for solving the graph colouring problem," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1192-1201, September.
    10. Alex Gliesch & Marcus Ritt, 2022. "A new heuristic for finding verifiable k-vertex-critical subgraphs," Journal of Heuristics, Springer, vol. 28(1), pages 61-91, February.
    11. Xiao-Feng Xie & Jiming Liu, 2009. "Graph coloring by multiagent fusion search," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 99-123, August.
    12. Pirlot, Marc, 1996. "General local search methods," European Journal of Operational Research, Elsevier, vol. 92(3), pages 493-511, August.
    13. 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.
    14. 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.
    15. 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.
    16. Hawa, Asyl L. & Lewis, Rhyd & Thompson, Jonathan M., 2022. "Exact and approximate methods for the score-constrained packing problem," European Journal of Operational Research, Elsevier, vol. 302(3), pages 847-859.
    17. B Suman & P Kumar, 2006. "A survey of simulated annealing as a tool for single and multiobjective optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(10), pages 1143-1160, October.
    18. 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.
    19. 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.
    20. 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.

    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:eee:ejores:v:203:y:2010:i:1:p:241-250. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.