Solving Three-Objective Optimization Problems Using a New Hybrid Cellular Genetic Algorithm

  • Juan José Durillo
  • Antonio Jesús Nebro
  • Francisco Luna
  • Enrique Alba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)

Abstract

In this work we present a new hybrid cellular genetic algorithm. We take MOCell as starting point, a multi-objective cellular genetic algorithm, and, instead of using the typical genetic crossover and mutation operators, they are replaced by the reproductive operators used in differential evolution. An external archive is used to store the nondominated solutions found during the search process and the SPEA2 density estimator is applied when the archive becomes full. We evaluate the resulting hybrid algorithm using a benchmark composed of three-objective test problems, and we compare the results with several state of the art multi-objective metaheuristics. The obtained results show that our proposal outperforms the other algorithms according to the two considered quality indicators.

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References

  1. 1.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  2. 2.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), ETH Zurich (2001)Google Scholar
  3. 3.
    Knowles, J., Corne, D.: The pareto archived evolution strategy: A new baseline algorithm for multiobjective optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation, pp. 9–105. IEEE Press, Piscataway (1999)Google Scholar
  4. 4.
    Coello, C., Van Veldhuizen, D., Lamont, G.: Evolutionary Algorithms for Solving Multi-Objective Problems. In: Genetic Algorithms and Evolutionary Computation, 2nd edn. Kluwer Academic Publishers, Dordrecht (2007)Google Scholar
  5. 5.
    Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)MATHGoogle Scholar
  6. 6.
    Nebro, A.J., Durillo, J.J., Luna, F., Dorronsoro, B., Alba, E.: Design issues in a multiobjective cellular genetic algorithm. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 126–140. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multi-Objective Optimization. Technical Report 112, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (2001)Google Scholar
  8. 8.
    Storn, R., Price, K.: Differential evolution - a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012, Berkeley, CA (1995)Google Scholar
  9. 9.
    Price, K., Storn, R., Lampinen, J.: Differential Evolution A Practical Approach to Global Optimization. Natural Computing Series. Springer, Berlin (2005)MATHGoogle Scholar
  10. 10.
    Lampinen, J.: De’s selection rule for multiobjective optimization. Technical report, Lappeenranta University of Technology, Department of Information Technology (2001)Google Scholar
  11. 11.
    Kukkonen, S., Lampinen, J.: GDE3: The third Evolution Step of Generalized Differential Evolution. In: IEEE Congress on Evolutionary Computation (CEC 2005), pp. 443–450 (2005)Google Scholar
  12. 12.
    Hernández-Díaz, A.G., Santana-Quintero, L.V., Coello, C.A.C., Caballero, R., Molina, J.: A new proposal for multi-objective optimization using differential evolution and rough sets theory. In: Conference on Genetic and Evolutionary Computation (GECCO 2006), pp. 675–682 (2006)Google Scholar
  13. 13.
    Huband, S., Hingston, P., Barone, L., While, L.: A Review of Multiobjective Test Problems and a Scalable Test Problem Toolkit. IEEE Transactions on Evolutionary Computation 10(5), 477–506 (2006)CrossRefGoogle Scholar
  14. 14.
    Alba, E., Tomassini, M.: Parallelism and evolutionary algorithms. IEEE Transactions on Evolutionary Computation 6(5), 443–462 (2002)CrossRefGoogle Scholar
  15. 15.
    Kukkonen, S., Deb, K.: Improved pruning of non-dominated solutions based on crowding distance for bi-objective optimization problems. In: 2006 IEEE Congress on Evolutionary Computation (CEC 2006), pp. 1179–1186 (2006)Google Scholar
  16. 16.
    Durillo, J.J., Nebro, A.J., Luna, F., Dorronsoro, B., Alba, E.: jMetal: a java framework for developing multi-objective optimization metaheuristics. Technical Report ITI-2006-10, Dpto. de Lenguajes y Ciencias de la Computación, University of Málaga (2006)Google Scholar
  17. 17.
    Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)CrossRefGoogle Scholar
  18. 18.
    Knowles, J., Thiele, L., Zitzler, E.: A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers. Technical Report 214, Computer Engineering and Networks Laboratory (TIK), ETH Zurich (2006)Google Scholar
  19. 19.
    Demšar, J.: Statistical comparisons of classifiers over multiple data sets. J. Mach. Learn. Res. 7, 1–30 (2006)MATHMathSciNetGoogle Scholar
  20. 20.
    Hochberg, Y., Tamhane, A.C.: Multiple Comparison Procedures. Wiley, Chichester (1987)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Juan José Durillo
    • 1
  • Antonio Jesús Nebro
    • 1
  • Francisco Luna
    • 1
  • Enrique Alba
    • 1
  1. 1.Department of Computer ScienceUniversity of MálagaSpain

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