Abstract
In this paper, we present a first scatter search approach for the Graph Coloring Problem (GCP). The evolutionary strategy scatter search operates on a set of configurations by combining two or more elements. New configurations are improved before replacing others according to their quality (fitness), and sometimes, to their diversity. Scatter search has been applied recently to some combinatorial optimization problems with promising results. Nevertheless, it seems that no attempt of scatter search has been published for the GCP. This paper presents such an investigation and reports experimental results on some wellstudied DIMACS graphs.
This work was partially supported by the Sino-French Joint Laboratory in Computer Science, Control and Applied Mathematics (LIAMA) and the Sino-French Advanced Research Programme (PRA).
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References
Brélaz., D.: New methods to color the vertices of a graph. Commun. ACM 22(4) (1979) 251–256
Culberson, J.: Bibliography on graph coloring. Available on the wold wide web at http://liinwww.ira.uka.de/bibliography/Theory/graph.coloring.html (2000)
Dorne, R., Hao, J.K.: Tabu search for graph coloring, T-colorings and set Tcolorings. In Voss, S., Martello, S., Osman, I.H., Roucairol, C. (editors) Metaheuristics: advances and trends in local search paradigms for optimization Kluwer Academic Publishers (1998) 77–92
Dorne, R., Hao, J.K.: A new genetic local search algorithm for graph coloring. Lecture Notes in Computer Science 1498 Springer-Verlag (1998) 745–754
Dubois, N., de Werra, D.: EPCOT: an efficient procedure for coloring optimally with tabu search. Computers Math. Appl. 25(10/11) (1993) 35–45
Ferland, J.A., Fleurent, C.: Object-oriented implementation of heuristic search methods for graph coloring, maximum clique, and satisfiability. In [19] (1996) 619–652
Funabiki, N., Higashino, T.: A minimal-state processing search algorithm for graph colorings problems. IEICE Trans. Fundamentals E83-A(7) (2000) 1420–1430
Galinier, P., Hao, J.K.: Hybrid evolutionary algorithms for graph coloring. J. Combin. Optim. 3(4) (1999) 379–397
Gamst, A.: Some lower bounds for a class of frequency assignment problems. IEEE Trans. Veh. Tech. 35(1) (1986) 8–14
Glover, F.: A template for scatter search and path relinking. In Hao, J.K., Lutton, E., Ronald, E., Schoenauer, M., Snyers, D. (editors) Artificial evolution. Lecture Notes in Computer Science 1363 Springer-Verlag (1998) 13–54
Glover, F.: Tutorial on surrogate constraint approaches for optimization in graphs. Tech. Report (February 2001)
Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers (1997)
Glover, F., Laguna, M., Martí, R.: Fundamentals of scatter search and path relinking. Control and Cybernetics 39(3) (2000) 653–684
Glover, F., Laguna, M., Martí, R.: Scatter search. In Ghosh, A., Tsutsui, S. (editors) Theory and applications of evolutionary computation: recent trends Springer-Verlag (to appear)
Halldórsson, M.M.: A still better performance guarantee for approximate graph coloring. Inform. Process. Lett. 45 (1993) 19–23
Hertz, A., de Werra, D.: Using tabu search techniques for graph coloring. Computing 39 (1987) 345–351
Jagota, A.: An adaptive, multiple restarts neural network algorithm for graph coloring. European J. Oper. Res. 93 (1996) 257–270
Johnson, D.S., Aragon, C.R., McGeoch, L.A., Schevon, C.: Optimization by simulated annealing: an experimental evaluation. II. Graph coloring and number partitioning. Oper. Res. 39(3) (1991) 378–406
Johnson, D.S., Trick., M.A. (editors): Cliques, coloring, and satisfiability: 2nd DIMACS implementation challenge, 1993. DIMACS Series in Discr. Math. and Theoretical Comput. Sci. 26 American Math. Soc. (1996)
Karp, R.M.: Reducibility among combinatorial problems. In Miller, R.E., Thatcher, J.W. (editors) Complexity of computer computations Plenum Press, New York (1972) 85–103
Laguna, M.: Scatter search. In Pardalos, P.M., Resende, M.G.C. (editors) Handbook of applied optimization Oxford Academic Press (to appear)
Laguna, M., Armento, V.A.: Lessons from applying and experimenting with scatter search. Tech. Report (March 2001)
Laguna, M., Martí, R.: Experimental testing of advanced scatter search designs for global optimization of multimodal functions. Tech. Report (August 2000)
Leighton, F.T.: A graph coloring algorithm for large scheduling problems. J. Res. Nat. Bur. Stand. 84 (1979) 489–506
Lund, C., Yannakakis, M.: On the hardness of approximating minimization problems. Proc. 25th Annual ACM Symp. Theory of Comput. (1993) 286–293
Morgenstern, C.A.: Distributed coloration neighborhood search. In [19] (1996) 335–357
Rego, C.: Integrating advanced principles of tabu search for the vehicle routing problem. Working paper, Faculty of Sciences, University of Lisbon (1999)
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Hamiez, JP., Hao, JK. (2002). Scatter Search for Graph Coloring. In: Collet, P., Fonlupt, C., Hao, JK., Lutton, E., Schoenauer, M. (eds) Artificial Evolution. EA 2001. Lecture Notes in Computer Science, vol 2310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46033-0_14
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DOI: https://doi.org/10.1007/3-540-46033-0_14
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