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A Study on the Performance of Substitute Distance Based Approaches for Evolutionary Many Objective Optimization

  • Hemant K. Singh
  • Amitay Isaacs
  • Tapabrata Ray
  • Warren Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5361)

Abstract

Non-dominated Sorting Genetic Algorithm (NSGA-II) [1] and the Strength Pareto Evolutionary Algorithm (SPEA2) [2] are the two most widely used evolutionary multi-objective optimization algorithms. Although, they have been quite successful so far in solving a wide variety of real life optimization problems mostly 2 or 3 objective in nature, their performance is known to deteriorate significantly with an increasing number of objectives. The term many objective optimization refers to problems with number of objectives significantly larger than two or three. In this paper, we provide an overview of the challenges involved in solving many objective optimization problems and provide an in depth study on the performance of recently proposed substitute distance based approaches, viz. Subvector dominance, -eps-dominance, Fuzzy Pareto Dominance and Sub-objective dominance count for NSGA-II to deal with many objective optimization problems. The present study has been conducted on scalable benchmark functions (DTLZ2-DTLZ3) and the recently proposed P* problem [3] since their convergence and diversity measures can be compared conveniently. An alternative substitute distance approach is introduced in this paper and compared with existing ones on the set of benchmark problems.

Keywords

Pareto Front Multiobjective Optimisation Objective Optimization Problem Strength Pareto Evolutionary Algorithm Genetic Local Search 
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.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on Evolutionary Computation 6, 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, Switzerland (2002)Google Scholar
  3. 3.
    Koppen, M., Yoshida, K.: Substitute distance assignments in NSGA-II for handling many-objective optimization problems. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 727–741. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization. In: 3rd International Workshop on Genetic and Evolving Systems (GEFS 2008), pp. 47–52 (March 2008)Google Scholar
  5. 5.
    Khare, V., Yao, X., Deb, K.: Performance Scaling of Multi-objective Evolutionary Algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 376–390. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Corne, D.W., Knowles, J.D.: Techniques for highly multiobjective optimisation: some nondominated points are better than others. In: Proceedings of the 9th annual conference on Genetic and evolutionary computation (GECCO 2007), pp. 773–780. ACM, New York (2007)CrossRefGoogle Scholar
  7. 7.
    Sato, H., Aguirre, H., Tanaka, K.: Controlling dominance area of solutions and its impact on the performance of moeas. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 5–20. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Ishibuchi, H., Murata, T.: A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 28(3), 392–403 (1998)CrossRefGoogle Scholar
  9. 9.
    Ishibuchi, H., Yoshida, T., Murata, T.: Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Transactions on Evolutionary Computation 7(2), 204–223 (2003)CrossRefGoogle Scholar
  10. 10.
    Jaszkiewicz, A.: Genetic local search for multi-objective combinatorial optimization. European Journal of Operational Research 127(1), 50–71 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Zitzler, E., Kunzli, S.: Indicator-Based Selection in Multiobjective Search. 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. 832–842. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Deb, K., Sundar, J.: Reference point based multi-objective optimization using evolutionary algorithms. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation (GECCO 2006), pp. 635–642. ACM, New York (2006)CrossRefGoogle Scholar
  13. 13.
    Fleming, P., Purshouse, R., Lygoe, R.: Many-Objective Optimization: An Engineering Design Perspective. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 14–32. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Thiele, L., Miettinen, K., Korhonen, P., Molina, J.: A preference-based interactive evolutionary algorithm for multiobjective optimization. Technical Report W-412, Helsinki School of Economics (2007)Google Scholar
  15. 15.
    Obayashi, S., Sasaki, D.: Visualization and data mining of pareto solutions using self-organizing map. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 796–809. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Pryke, A., Sanaz Mostaghim, A.N.: Heatmap visualization of population based multi objective algorithms. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 361–375. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Koppen, M., Yoshida, K.: Many-objective particle swarm optimization by gradual leader selection. In: Beliczynski, B., Dzielinski, A., Iwanowski, M., Ribeiro, B. (eds.) ICANNGA 2007. LNCS, vol. 4431, pp. 323–331. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    Saxena, D.K., Deb, K.: Trading on infeasibility by exploiting constraints criticality through multi-objectivization: A system design perspective. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2007), September 25-28, 2007, pp. 919–926 (2007)Google Scholar
  19. 19.
    Koppen, M., Vincente-Garcia, R., Nickolay, B.: Fuzzy-pareto-dominance and its application in evolutionary multi-objective optimization. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 399–412. Springer, Heidelberg (2003)Google Scholar
  20. 20.
    Wagner, T., Beume, N., Naujoks, B.: Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 742–756. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  21. 21.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the 2002 Congress on Evolutionary Computation (CEC 2002), vol. 1, pp. 825–830 (May 2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hemant K. Singh
    • 1
  • Amitay Isaacs
    • 1
  • Tapabrata Ray
    • 1
  • Warren Smith
    • 1
  1. 1.School of Aerospace, Civil and Mechanical EngineeringUniversity of New South Wales, Australian Defence Force AcademyCanberra, ACTAustralia

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