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A Memetic Algorithm with Two Distinct Solution Representations for the Partition Graph Coloring Problem

  • Petrica C. Pop
  • Bin Hu
  • Günther R. Raidl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8111)

Abstract

In this paper we propose a memetic algorithm (MA) for the partition graph coloring problem. Given a clustered graph G = (V,E), the goal is to find a subset V * ⊂ V that contains exactly one node for each cluster and a coloring for V * so that in the graph induced by V *, two adjacent nodes have different colors and the total number of used colors is minimal. In our MA we use two distinct solution representations, one for the genetic operators and one for the local search procedure, which are tailored for the corresponding situations, respectively. The algorithm is evaluated on a common benchmark instances set and the computational results show that compared to a state-of-the-art branch and cut algorithm, our MA achieves solid results in very short run-times.

Keywords

Crossover Operator Genetic Operator Memetic Algorithm Network Design Problem Coloring Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bontoux, B., Artigues, C., Feillet, D.: A memetic algorithm with a large neighborhood crossover operator for the generalized traveling salesman problem. Computers and Operations Research 37(11), 1844–1852 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Brélaz, D.: New methods to color the vertices of a graph. Communication of ACM 22(4), 251–256 (1979)CrossRefzbMATHGoogle Scholar
  3. 3.
    Demange, M., Monnot, J., Pop, P., Ries, B.: Selective graph coloring in some special classes of graphs. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds.) ISCO 2012. LNCS, vol. 7422, pp. 320–331. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Demange, M., Monnot, J., Pop, P., Ries, B.: On the complexity of the selective graph coloring problem in some special classes of graphs. Theoretical Computer Science (in press, 2013)Google Scholar
  5. 5.
    Frota, Y., Maculan, N., Noronha T.F., Ribeiro, C.C.: Instances for the partition coloring problem, www.ic.uff.br/~celso/grupo/pcp.htm
  6. 6.
    Frota, Y., Maculan, N., Noronha, T.F., Ribeiro, C.C.: A branch-and-cut algorithm for the partition coloring problem. Networks 55(3), 194–204 (2010)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Glover, F., Parker, M., Ryan, J.: Coloring by tabu branch and bound. DIMACS Series on Discrete Mathematics and Theoretical Computer Science 26, 285–308 (1996)MathSciNetGoogle Scholar
  8. 8.
    Gualandi, S., Malucelli, F.: Exact solution of graph coloring problems via constraint programming and column generation. INFORMS Journal on Computing 24(1), 81–100 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hoshino, E.A., Frota, Y.A., de Souza, C.C.: A branch-and-price approach for the partition coloring problem. Operations Research Letters 39(2), 132–137 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Li, G., Simha, R.: The partition coloring problem and its application to wavelength routing and assignment. In: 1st Workshop on Optical Networks (2000)Google Scholar
  11. 11.
    Lü, Hao, J.: A memetic algorithm for graph coloring. European Journal of Operational Research 203, 241–250 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Mehrotra, A., Trick, M.A.: A column generation approach for graph coloring. INFORMS Journal on Computing 8, 344–354 (1996)CrossRefzbMATHGoogle Scholar
  13. 13.
    Moscato, P.: Memetic algorithms: A short introduction. In: Corne, D., et al. (eds.) New Ideas in Optimization, pp. 219–234. McGraw Hill (1999)Google Scholar
  14. 14.
    Ngueveu, S.U., Prins, C., Calvo, R.W.: An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Computers and Operations Research 37(11), 1877–1885 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Noronha, T.F., Ribeiro, C.C.: Routing and wavelength assignment by partition colouring. European Journal of Operational Research 171(3), 797–810 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Pop, P.C.: Generalized network design problems. Modeling and Optimization. De Gruyter Series in Discrete Mathematics and Applications, Germany (2012)Google Scholar
  17. 17.
    Pop, P.C., Hu, B., Raidl, G.R.: A memetic algorithm for the partition graph coloring problem. In: Extended Abstracts of the 14th International Conference on Computer Aided Systems Theory, Gran Canaria, Spain, pp. 167–169 (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Petrica C. Pop
    • 1
  • Bin Hu
    • 2
  • Günther R. Raidl
    • 2
  1. 1.Tech. Univ. Cluj-Napoca, North Univ. Center Baia-MareBaia-MareRomania
  2. 2.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

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