Abstract
We present a hybrid evolutionary algorithm for the graph coloring problem (Evocol). Evocol is based on two simple-but-effective ideas. First, we use an enhanced crossover that collects the best color classes out of more than two parents; the best color classes are selected using a ranking based on both class fitness and class size. We also introduce a simple method of using distances to assure the population diversity: at each operation that inserts an individual into the population or that eliminates an individual from the population, Evocol tries to maintain the distances between the remaining individuals as large as possible. The results of Evocol match the best-known results from the literature on almost all difficult DIMACS instances (a new solution is also reported for a very large graph). Evocol obtains these performances with a success rate of at least 50%.
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References
Blöchliger, I., Zufferey, N.: A graph coloring heuristic using partial solutions and a reactive tabu scheme. Computers and Operations Research 35(3), 960–975 (2008)
Costa, D., Hertz, A., Dubuis, C.: Embedding a sequential procedure within an evolutionary algorithm for coloring problems in graphs. Journal of Heuristics 1(1), 105–128 (1995)
Day, W.H.E.: The complexity of computing metric distances between partitions. Mathematical Social Sciences 1, 269–287 (1981)
Dorne, R., Hao, J.K.: A new genetic local search algorithm for graph coloring. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 745–754. Springer, Heidelberg (1998)
Eiben, A.E., Raué, P.E., Ruttkay, Z.: Genetic algorithms with multi-parent recombination. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 78–87. Springer, Heidelberg (1994)
Fleurent, C., Ferland, J.A.: Genetic and hybrid algorithms for graph coloring. Annals of Operations Research 63(3), 437–461 (1996)
Galinier, P., Hao, J.K.: Hybrid Evolutionary Algorithms for Graph Coloring. Journal of Combinatorial Optimization 3(4), 379–397 (1999)
Galinier, P., Hertz, A., Zufferey, N.: An adaptive memory algorithm for the k-coloring problem. Discrete Applied Mathematics 156(2), 267–279 (2008)
Glass, C.A., Pruegel-Bennett, A.: A polynomially searchable exponential neighbourhood for graph colouring. Journal of the Operational Research Society 56(3), 324–330 (2005)
Gusfield, D.: Partition-distance: A problem and class of perfect graphs arising in clustering. Information Processing Letters 82(3), 159–164 (2002)
Hertz, A., Plumettaz, A., Zufferey, N.: Variable space search for graph coloring. Discrete Applied Mathematics 156(13), 2551–2560 (2008)
Hertz, A., Werra, D.: Using tabu search techniques for graph coloring. Computing 39(4), 345–351 (1987)
Johnson, D.S., Trick, M.: Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge. DIMACS series in Discrete Mathematics and Theoretical Computer Science, vol. 26. American Mathematical Society, Providence (1996)
Malaguti, E., Monaci, M., Toth, P.: A Metaheuristic Approach for the Vertex Coloring Problem. INFORMS Journal on Computing 20(2), 302 (2008)
Morgenstern, C.: Distributed coloration neighborhood search. In: [13], pp. 335–358
Sörensen, K., Sevaux, M.: MA|PM: Memetic algorithms with population management. Computers and Operations Research 33(5), 1214–1225 (2006)
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Porumbel, D.C., Hao, JK., Kuntz, P. (2009). Diversity Control and Multi-Parent Recombination for Evolutionary Graph Coloring Algorithms. In: Cotta, C., Cowling, P. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2009. Lecture Notes in Computer Science, vol 5482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01009-5_11
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DOI: https://doi.org/10.1007/978-3-642-01009-5_11
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