Abstract
The evaluation or fitness function is a key component of any heuristic search algorithm. This paper introduces a new evaluation function for the well-known graph K-coloring problem. This function takes into account not only the number of conflicting vertices, but also inherent information related to the structure of the graph. To assess the effectiveness of this new evaluation function, we carry out a number of experiments using a set of DIMACS benchmark graphs. Based on statistic data obtained with a parameter free steepest descent, we show an improvement of the new evaluation function over the classical one.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Avanthay, C., Hertz, A., Zufferey, N.: A variable neighborhood search for graph coloring. European Journal of Operational Research 151(2), 379–388 (2003)
Dorne, R., Hao, J.K.: Tabu search for graph coloring, T-colorings and set T-colorings. Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, 77–92 (1998)
Eiben, A.E., van der Hauw, J.K.: Adaptive penalties for evolutionary graph coloring. In: Rao, A., Singh, M.P., Wooldridge, M.J. (eds.) ATAL 1997. LNCS, vol. 1365, pp. 95–106. Springer, Heidelberg (1998)
Falkenauer, E.: A hybrid grouping genetic algorithm for bin packing. Journal of Heuristics 2, 5–30 (1996)
Fleurent, C., Ferland, J.A.: Genetic and hybrid algorithms for graph coloring. Annals of Operations Research 63, 437–461 (1996)
Galinier, P., Hao, J.K.: Hybrid Evolutionary Algorithms for Graph Coloring. Journal of Combinatorial Optimization 3(4), 379–397 (1999)
Hertz, A., de Werra, D.: Using tabu search techniques for graph coloring. Computing 39(4), 345–351 (1987)
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. (eds.): Cliques, Coloring, and Satisfiability: 2nd DIMACS Implementation Challenge. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26, AMS, USA (1996)
Karp, R.M.: Reducibility among combinatorial problems. Complexity of Computer Computations 43, 85–103 (1972)
Leighton, F.T.: A graph coloring algorithm for large scheduling problems. Journal of Research of the National Bureau of Standards 84(6), 489–503 (1979)
Morgenstern, C.: Distributed Coloration Neighborhood Search. In: [9], pp. 335–357 (1996)
Rodriguez-Tello, E., Hao, J.K., Torres-Jimenez, J.: An improved evaluation function for the bandwidth minimization problem. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 650–659. Springer, Heidelberg (2004)
Rodriguez-Tello, E., Hao, J.K.: On the role of evaluation functions for heuristic search (working paper, 2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Porumbel, D.C., Hao, JK., Kuntz, P. (2008). A Study of Evaluation Functions for the Graph K-Coloring Problem. In: Monmarché, N., Talbi, EG., Collet, P., Schoenauer, M., Lutton, E. (eds) Artificial Evolution. EA 2007. Lecture Notes in Computer Science, vol 4926. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79305-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-79305-2_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79304-5
Online ISBN: 978-3-540-79305-2
eBook Packages: Computer ScienceComputer Science (R0)