Abstract
In this chapter a new formulation of the robust graph coloring problem (RGCP) is proposed. In opposition to classical GCP defined for the given graph \({ G(V, E)}\) not only elements of E but also Ē can be subject of color conflicts in edge vertices. Conflicts in Ē are assigned penalties \(0<\mathrm{P(e)}<1\). In addition to satisfying constraints related to the number of colors and/or a threshold of the acceptable sum of penalties for color conflicts in graph complementary edges (rigidity level), a new bound called the relative robustness threshold (RRT) is proposed. Then three metaheuristics—SA, TS, EA and their parallel analogues PSA, PTS, PEA—for that version of RGCP are presented and experimentally tested. For comparison we use DIMACS graph coloring instances in which a selected percentage of graph edges E is randomly moved to Ē. Since graph densities and chromatic numbers of DIMACS GCP instances are known in advance, the RGCP instances generated on their basis are more suitable for testing algorithms than totally random instances used so far. The results of the conducted experiments are presented and discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alba, E. (ed.): Parallel Metaheuristic - A New Class of Algorithms. Wiley, Hoboken (2005)
Archetti, C., Bianchessi N, Hertz, A.: A branch-and-price algorithm for the robust graph coloring problem. Les Cahiers du Gerad, G-2011–75, Montreal (2011)
Bouziri, H., Jouini, M.: A tabu search approach for the sum coloring problem. Electron. Notes Discrete Math. 36, 915–922 (2010)
Bracho, R.L., Rodriguez, J.R., Martinez, F.J.: Algorithms for robust graph coloring on paths. In: Proceedings of 2nd International Conference on Electrical and Electronics Engineering, Mexico, pp. 9–12. IEEE (2005)
Chrząszcz, G.: Parallel evolutionary algorithm for robust scheduling in power systems. M.Sc. thesis, Cracow University of Technology (in Polish) (2009)
COLOR web site. http://mat.gsia.cmu.edu/COLOR/instances.html
Dąbrowski, J.: Parallelization techniques for tabu search. In: Proceediongs of 8th International Conference on Applied Parallel Computing: State of the Art in Scientific Computing (2007)
DIMACS ftp site. ftp://dimacs.rutgers.edu/pub/challenge/graph/benchmarks/
Deleplanque, S., Derutin, J.-P., Quilliot, A.: Anticipation in the dial-a-ride problem: an introduction to the robustness. In: Proceedings of the 2013 Federated Conference on Computer Science and Information Systems, FedCSIS’2013, pp. 299–305. Kraków, Poland (2013)
Dey, A., Pradhan, R., Pal, A., Pal, T.: The fuzzy robust graph coloring problem. In: Satapathy, S.C., et al. (eds.) Proceedings of the 3rd International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA) 2014 - 1. Advances in Intelligent Systems and Computing Proceedings, vol. 327, pp. 805–813. Springer, New York (2015)
Galinier, P., Hao, J.-P.: Hybrid evolutionary algorithm for graph coloring. J. Comb. Optim. 3(4), 374–397 (1999)
Garey, R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
Gendreau, M., Potvin, J.Y. (eds.): Handbook of Metaheuristics. International Series in Operations Research & Management Science. Springer, New York (2010)
Glover, F., Kochenberger, G.A. (eds.): Handbook of Metaheuristics. Kluwer, Boston (2003)
Gładysz, B.: Fuzzy robust courses scheduling problem. Fuzzy Optim. Decis. Mak. 6, 155–161 (2007)
Hutchinson, G.: Partitioning algorithms for finite sets. Commun. ACM 6, 613–614 (1963)
Jensen, T.R., Toft, B.: Graph Coloring Problems. Wiley Interscience, New York (1995)
Johnson, D.S., Trick, M.A.: Cliques, Coloring and Satisfiability: Second DIMACS Implementation Challenge. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26 (1996)
Kokosiński, Z., Kołodziej, M., Kwarciany, K.: Parallel genetic algorithm for graph coloring problem. In: Proceedings of the International Conference on Computational Science, ICCS’2004, LNCS, vol. 3036, pp. 215–222 (2004)
Kokosiński, Z., Kwarciany, K., Kołodziej, M.: Efficient graph coloring with parallel genetic algorithms. Comput. Inf. 24, 123–147 (2005)
Kokosiński, Z.: Parallel metaheuristics in graph coloring. Bulletin of the National University “Lviv Politechnic”. Series: Computer sciences and information technologies, vol. 744, pp. 209–214 (2012)
Kokosiński, Z., Ochał, Ł.: Evalution of metaheuristics for robust graph coloring problem. In: Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, FedCSIS’2015, Łódź, Poland. Annals of Computer Science and Information Systems, vol. 5, pp. 519–524 (2015)
Kong, Y., Wang, F., Lim, A., Guo, S.: A new hybrid genetic algorithm for the robust graph coloring problem. AI 2003, LNAI, vol. 2903, pp. 125-136 (2003)
Kubale, M. (ed.): Graph Colorings. American Mathematical Society, Providence (2004)
Lim, A., Wang, F.: Metaheuristic for robust graph coloring problem. In: Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence, ICTAI (2004)
Lim, A., Wang, F.: Robust graph coloring for uncertain supply chain management. In: Proceedings of 38th Annual Hawaii International Conference on System Science, HICSS 2005, IEEE, 81b (2005)
Łukasik, S., Kokosiński, Z., Świętoń, G.: Parallel simulated annealing algorithm for graph coloring problem. In: Proceedings of International Conference Parallel Processing and Applied Mathematics, PPAM’2007, LNCS, vol. 4967, pp. 229–238 (2008)
Myszkowski, P.B.: Solving scheduling problems by evolutionary algorithms for graph coloring problem. In: Xhafa, F., Abraham, A. (eds.): Metaheuristics for Scheduling in Industrial and Manufacturing Applications. Studies in Computational Intelligence, vol. 128, pp. 145–167 (2008)
Pahlavani, A., Eshghi, K.: A hybrid algorithm of simulated annealing and tabu search for graph colouring problem. Int. J. Oper. Res. 11(2), 136–159 (2011)
Ruta, D.: Robust method of sparse feature selection for multi-label classification with naive Bayes. In: Proceedings of the 2014 Federated Conference on Computer Science and Information Systems, FedCSIS’2014, Warsaw, Poland, pp. 375–380 (2014)
Wang, F., Xu, Z.: Metaheuristics for robust graph coloring. J. Heuristics 19(4), 529–548 (2013)
Xu, M., Wang, Y., Wei, A.: Robust graph coloring based on the matrix semi-tensor product with application to examination timetabling. Control Theory Technol. 12(2), 187–197 (2014)
Yáñez, J., Ramirez, J.: The robust coloring problem. Eur. J. Oper. Res. 148(3), 546–558 (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Kokosiński, Z., Ochał, Ł., Chrząszcz, G. (2016). Parallel Metaheuristics for Robust Graph Coloring Problem. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol 655. Springer, Cham. https://doi.org/10.1007/978-3-319-40132-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-40132-4_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40131-7
Online ISBN: 978-3-319-40132-4
eBook Packages: EngineeringEngineering (R0)