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Solving Dynamic Graph Coloring Problem Using Dynamic Pool Based Evolutionary Algorithm

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Applications of Evolutionary Computation (EvoApplications 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10200))

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Abstract

Graph coloring problem is one of the main optimization problems from the literature. Many real world problems interacting with changing environments can be modeled with dynamic graphs. Genetic algorithms are a good choice to solve dynamic graph coloring problem because they can adopt to dynamic environments and are suitable for problems with NP-hard complexity. In this paper, we propose a dynamic pool based evolutionary algorithm (DPBEA) for solving the dynamic graph coloring problem, which contains a partition based representation to adopt to the dynamic changes of the graph and carry the valuable information obtained in history. The proposed algorithm uses a novel special purpose pool based crossover operator that targets to minimize the number of colors used in the solutions and a local search method that tries to increase the diversity of the solutions. We compared the performance of our algorithm with a well known heuristic for solving the graph coloring problem and a genetic algorithm with a dynamic population using a large number of dynamic graphs. The experimental evaluation indicates that our algorithm outperforms these algorithms with respect to number of colors used by the algorithms in most of the test cases provided.

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References

  1. Briggs, P., Cooper, K., Torczon, L.: Improvements to graph coloring register allocation. Trans. Program. Lang. Syst. 16(3), 428–455 (1994)

    Article  Google Scholar 

  2. Aardal, K., van Hoesel, S.P.M., Koster, A.M.C.A., Mannino, C., Sassano, A.: Models and solution techniques for frequency assignment problems. Ann. Oper. Res. 153(1), 79129 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Galinier, P., Hamiez, J.-P., Hao, J.-K., Porumbel, D.: Recent advances in graph vertex coloring. In: Zelinka, I., et al. (eds.) Handbook of Optimization. ISRL, vol. 38, pp. 505–528. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H Freeman and Company, New York (1979)

    MATH  Google Scholar 

  5. Fleurent, C., Ferland, J.: Genetic and hybrid algorithms for graph coloring. Ann. Oper. Res. 63, 437–461 (1996)

    Article  MATH  Google Scholar 

  6. Dorne, R.Ë., Hao, J.-K.: A new genetic local search algorithm for graph coloring. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 745–754. Springer, Heidelberg (1998). doi:10.1007/BFb0056916

    Chapter  Google Scholar 

  7. Erdos, P., Renyi, A.: On the evolution of random graphs. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)

    MathSciNet  MATH  Google Scholar 

  8. Fotakis, D.A., Likothanassis, S.D., Stefanakos, S.K.: An evolutionary annealing approach to graph coloring. In: Boers, E.J.W. (ed.) EvoWorkshops 2001. LNCS, vol. 2037, pp. 120–129. Springer, Heidelberg (2001). doi:10.1007/3-540-45365-2_13

    Chapter  Google Scholar 

  9. Galinier, P., Hao, J.-K.: Hybrid evolutionary algorithms for graph coloring. J. Comb. Optim. 3(4), 379–397 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Nguyen, T.T., Yang, S., Branke, J.: Evolutionary dynamic optimization: a survey of the state of the art. Swarm Evol. Comput. 6, 1–24 (2012)

    Article  Google Scholar 

  11. Harary, F., Gupta, G.: Dynamic graph models. Math. Comput. Model. 25, 79–88 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Monical, C., Stonedahl, F.: Static vs. dynamic populations in genetic algorithms for coloring a dynamic graph. In: Proceedings of the 2014 Conference on Genetic and Evolutionary Computation, pp. 469–476. ACM, Vancouver (2014)

    Google Scholar 

  13. Brelaz, D.: New methods to color the vertices of a graph. Commun. ACM 22(4), 251–256 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  14. Starkweather, T., Mcdaniel, S., Whitley, D., Mathias, K., Whitley, D.: A comparison of genetic sequencing operators. In: Proceedings of the fourth International Conference on Genetic Algorithms, pp. 69–76. Morgan Kaufmann (1991)

    Google Scholar 

  15. Van Der Hauw, K.: Evaluating and Improving Steady State Evolutionary Algorithms on Constraint Satisfaction Problems. Master’s thesis, Leiden University (1996)

    Google Scholar 

  16. Sungu, G., Boz, B.: An evolutionary algorithm for weighted graph coloring problem. In: Proceedings of the Companion Publication of the 2015 Annual Conference on Genetic and Evolutionary Computation, pp. 1233–1236. ACM, Madrid (2015)

    Google Scholar 

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Authors and Affiliations

  1. Computer Engineering Department, Marmara University, 34722, Istanbul, Turkey

    Gizem Sungu & Betul Boz

Authors
  1. Gizem Sungu
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  2. Betul Boz
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Correspondence to Betul Boz .

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Editors and Affiliations

  1. Politecnico di Torino, Turin, Italy

    Giovanni Squillero

  2. Edinburgh Napier University, Edinburgh, United Kingdom

    Kevin Sim

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Sungu, G., Boz, B. (2017). Solving Dynamic Graph Coloring Problem Using Dynamic Pool Based Evolutionary Algorithm. In: Squillero, G., Sim, K. (eds) Applications of Evolutionary Computation. EvoApplications 2017. Lecture Notes in Computer Science(), vol 10200. Springer, Cham. https://doi.org/10.1007/978-3-319-55792-2_13

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  • DOI: https://doi.org/10.1007/978-3-319-55792-2_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55791-5

  • Online ISBN: 978-3-319-55792-2

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