Abstract
In this paper, we propose a new neighborhood structure based on the improvement graph for solving the Robust Graph Coloring Problem, an interesting extension of classical graph coloring. Different from the traditional neighborhood where the color of only one vertex is modified, the new neighborhood involves several vertices. In addition, the questions of how to select the modified vertices and how to modify them are modelled by an improvement graph and solved by a Dynamic Programming method. The experimental results clearly show that our new improvement graph based k-exchange cycle neighborhood improves the accuracy significantly, especially for large scale heuristic search.
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References
Barthelemy, J.P., Guenoche, A.: Trees and Proximity Representations. John Wiley Sons, New York (1991)
Brelaz, D.: New methods to color vertices of a graph. Communications of ACM 22, 251–256 (1979)
Chaitin, G.J.: Register allocation and spilling via graph coloring. In: SIGPLAN 1982 Symposium on Compiler Construction, Boston, Mass, June, vol. 17, pp. 98–105 (1982)
Chams, M., Hertz, A., de Werra, D.: Some experiments with simulated annealing for coloring graphs. European Journal of Operational Research 32, 260–266 (1987)
Costa, D., Hertz, A., Dubuis, O.: Embedding a sequential procedure within an evolutionary algorithm for coloring problems. Journal of Heuristics 1, 105–128 (1995)
Dorne, R., Hao, J.K.: Meta-heuristics: Advances and Trends in Local Search Paradigms for Optimization. In: Chapter 6: Tabu search for graph coloring T-colorings and set T-colorings, pp. 77–92. Kluwer Academic, Dordrecht (1998)
Galinier, P., Hao, J.K.: Hybrid evolutionary algorithm for graph coloring. Journal of Combinatorial Optimization 3, 379–397 (1999)
Gamst, A.: Some lower bounds for a class of frequency assignment problems. IEEE Transactions of Vehicular Technology 35(1), 8–14 (1986)
Garey, M.R., Johnson, D.S.: Computer and Intractability. Freeman, San Francisco (1979)
Halldorsson, M.M.: A still better performance guarantee for approximate graph coloring. Technical Report 91-35, DIMACS, New Brunswick, NJ (1990)
Johnson, D.S., Aragon, C.R., McGeoch, L.A., Schevon, C.: Optimization by simulated annealing: an experimental evaluation; part ii, graph coloring and number partitioning. Operations Research 39(3), 378–406 (1991)
Johnson, D.S., Trick, M.A.: Proceedings of the 2nd DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26. American Mathematical Society, Providence (1996)
Joslin, D.E., Clements, D.P.: Spueaky wheel optimization. In: the National Conference on Artificial Intelligence, AAAI-1998, Edmonton, Alberta, Canada (1998)
Kong, Y., Wang, F., Lim, A., Guo, S.S.: A New Hybrid Genetic Algorithm for the Robust Graph Coloring Problem. In: Proceeding of Australian Conference on Artificial Intelligence 2003, pp. 125–136 (2003)
Korte, B., Vygen, J.: Combinatorial Optimization, 2nd edn. Springer-Verlag, Heidelberg (2002)
Kubale, M., Jackowski, B.: A generalized implicit enumeration algorithm for graph coloring. Communications of the ACM 28, 412–418 (1985)
Opsut, R.J., Roberts, F.S.: On the fleet maintenance, Mobile radio frequency, task assignment and traffic phasing problems. In: The Theory and Applications of Graphs, pp. 479–492. John Wiley Sons, New York (1981)
Pardalos, P.M., Mavridou, T., Xue, J.: The Graph Coloring Problems: A Bibliographic Survey. In: Handbook of Combinatorial Optimization, vol. 2, pp. 331–395. Kluwer Academic Publishers, Dordrecht (1998)
Yanez, J., Ramirez, J.: The robust coloring problem. European Journal of Operational Research 148(3), 546–558 (2003)
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Guo, S., Kong, Y., Lim, A., Wang, F. (2004). A New Neighborhood Based on Improvement Graph for Robust Graph Coloring Problem. In: Webb, G.I., Yu, X. (eds) AI 2004: Advances in Artificial Intelligence. AI 2004. Lecture Notes in Computer Science(), vol 3339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30549-1_55
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DOI: https://doi.org/10.1007/978-3-540-30549-1_55
Publisher Name: Springer, Berlin, Heidelberg
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