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A memetic algorithm for graph coloring

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  • 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
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    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. 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.
    4. 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.
    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. 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.
    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.
    8. 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.
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    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Zhou, Yangming & Qu, Chenhui & Wu, Qinghua & Kou, Yawen & Jiang, Zhibin & Zhou, MengChu, 2024. "A bilevel hybrid iterated search approach to soft-clustered capacitated arc routing problems," Transportation Research Part B: Methodological, Elsevier, vol. 184(C).
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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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