skip to main content
10.1145/1389095.1389225acmconferencesArticle/Chapter ViewAbstractPublication PagesgeccoConference Proceedingsconference-collections
research-article

Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems

Published:12 July 2008Publication History

ABSTRACT

Recently a number of approaches have been proposed to improve the scalability of evolutionary multiobjective optimization (EMO) algorithms to many-objective problems. In this paper, we examine the effectiveness of those approaches through computational experiments on multiobjective knapsack problems with two, four, six, and eight objectives. First we briefly review related studies on evolutionary many-objective optimization. Next we explain why Pareto dominance-based EMO algorithms do not work well on many-objective optimization problems. Then we explain various scalability improvement approaches. We examine their effects on the performance of NSGA-II through computational experiments. Experimental results clearly show that the diversity of solutions is decreased by most scalability improvement approaches while the convergence of solutions to the Pareto front is improved. Finally we conclude this paper by pointing out future research directions.

References

  1. Abraham, A., Jain, L. C., and Goldberg, R. (eds.) Evolutionary Multiobjective Optimization: Theoretical Advances and Applications. Springer, Berlin (2005).]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Branke, J., Kaußler, T., and Schmeck, H. Guidance in evolutionary multi-objective optimization. Advances in Engineering Software 32, 6 (2001) 499--507.]]Google ScholarGoogle ScholarCross RefCross Ref
  3. Brockhoff, D., and Zitzler, E. Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization. Lecture Notes in Computer Science 4193: Parallel Problem Solving from Nature - PPSN IX, Springer, Berlin (2006) 533--542.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Brockhoff, D., and Zitzler, E. Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods. Proc. of 2007 IEEE Congress on Evolutionary Computation (2007) 2086--2093.]]Google ScholarGoogle Scholar
  5. Coello, C. A. C., and Lamont, G. B. Applications of Multi-Objective Evolutionary Algorithms. World Scientific, Singapore (2004).]]Google ScholarGoogle Scholar
  6. Coello, C. A. C., van Veldhuizen, D. A., and Lamont, G. B. Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer, Boston (2002).]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Corne, D., and Knowles, J. Techniques for highly multiobjective optimization: Some non-dominated points are better than others. Proc. of 2007 Genetic and Evolutionary Computation Conference (2007) 773--780.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Deb, K. Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001).]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6, 2 (2002) 182--197.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Deb, K., and Saxena, D. K. On finding Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. KanGAL Report, No. 2005011, Kanpur Genetic Algorithms Laboratory (KanGAL), Indian Institute of Technology Kanpur (2005).]]Google ScholarGoogle Scholar
  11. Deb, K., and Saxena, K. Searching for Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. Proc. of 2006 IEEE Congress on Evolutionary Computation (2006) 3353--3360.]]Google ScholarGoogle Scholar
  12. Deb, K., and Sundar, J. Preference point based multi-objective optimization using evolutionary algorithms. Proc. of 2006 Genetic and Evolutionary Computation Conference (2006) 635--642.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Drechsler, N., Drechsler, R., and Becker, B. Multi-objective optimization based on relation favour. Lecture Notes in Computer Science 1993: Evolutionary Multi-Criterion Optimization - EMO 2001, Springer, Berlin (2001) 154--166.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Fleming, P. J., Purshouse, R. C., and Lygoe, R. J. Many-objective optimization: An engineering design perspective. Lecture Notes in Computer Science 3410: Evolutionary Multi-Criterion Optimization - EMO 2005, Springer, Berlin (2005) 14--32.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Hughes, E. J. Evolutionary many-objective optimization: Many once or one many?. Proc. of 2005 IEEE Congress on Evolutionary Computation (2005) 222--227.]]Google ScholarGoogle Scholar
  16. Hughes, E. J. MSOPS-II: A general-purpose many-objective optimizer. Proc. of 2007 IEEE Congress on Evolutionary Computation (2007) 3944--3951.]]Google ScholarGoogle Scholar
  17. Ikeda, K., Kita, H., and Kobayashi, S. Failure of Pareto-based MOEAs: Does non-dominated really mean near to optimal?. Proc. of 2001 IEEE Congress on Evolutionary Computation (2001) 957--962.]]Google ScholarGoogle Scholar
  18. Ishibuchi, H., Doi, T., and Nojima, Y. Incorporation of scalarizing fitness functions into evolutionary multiobjective optimization algorithms. Lecture Notes in Computer Science 4193: Parallel Problem Solving from Nature - PPSN IX, Springer, Berlin (2006) 493--502.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Ishibuchi, H., and Nojima, Y. Optimization of scalarizing functions through evolutionary multiobjective optimization. Lecture Notes in Computer Science 4403: Evolutionary Multi-Criterion Optimization - EMO 2007, Springer, Berlin (2007) 51--65.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Ishibuchi, H., Tsukamoto, N., and Nojima, Y. Iterative approach to indicator-based multiobjective optimization. Proc. of 2007 IEEE Congress on Evolutionary Computation (2007) 3697--3704.]]Google ScholarGoogle Scholar
  21. Ishibuchi, H., Tsukamoto, N., and Nojima, Y. Evolutionary many-objective optimization: A short review. Proc. of 2008 IEEE Congress on Evolutionary Computation (in press).]]Google ScholarGoogle Scholar
  22. Jaszkiewicz, A. On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - A comparative experiment. IEEE Trans. on Evolutionary Computation 6, 4 (2002) 402--412.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Jaszkiewicz, A. On the computational efficiency of multiple objective metaheuristics: The knapsack problem case study. European Journal of Operational Research 158, 2 (2004) 418--433.]]Google ScholarGoogle ScholarCross RefCross Ref
  24. Khara, V., Yao, X., and Deb, K. Performance scaling of multi-objective evolutionary algorithms. Lecture Notes in Computer Science 2632: Evolutionary Multi-Criterion Optimization - EMO 2003, Springer, Berlin (2004) 367--390.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Köppen, M. and Yoshida, K. Substitute distance assignments in NSGA-II for handling many-objective optimization problems. Lecture Notes in Computer Science 4403: Evolutionary Multi-Criterion Optimization - EMO 2007, Springer, Berlin (2007) 727--741.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Kukkonen, S., and Lampinen, J. Ranking-dominance and many-objective optimization. Proc. of 2007 IEEE Congress on Evolutionary Computation (2007) 3983--3990.]]Google ScholarGoogle Scholar
  27. Purshouse, R. C., and Fleming, P. J. Evolutionary many-objective optimization: An exploratory analysis. Proc. of 2003 IEEE Congress on Evolutionary Computation (2003) 2066--2073.]]Google ScholarGoogle Scholar
  28. Sato, H., Aguirre, H. E., and Tanaka, K. Controlling dominance area of solutions and its impact on the performance of MOEAs. Lecture Notes in Computer Science 4403: Evolutionary Multi-Criterion Optimization - EMO 2007, Springer, Berlin (2007) 5--20.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Sülflow, A., Drechsler, N., and Drechsler, R. Robust multi-objective optimization in high dimensional spaces. Lecture Notes in Computer Science 4403: Evolutionary Multi-Criterion Optimization - EMO 2007, Springer, Berlin (2007) 715--726.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Thiele, L., Miettinen, K., Korhonen, P. J., and Molina, J. A preference-based interactive evolutionary algorithm for multiobjective optimization. Helsinki School of Economics, Working Paper (2007) W-412.]]Google ScholarGoogle Scholar
  31. Wagner, T., Beume, N., and Naujoks, B. Pareto-, aggregation-, and indicator-based methods in many-objective optimization. Lecture Notes in Computer Science 4403: Evolutionary Multi-Criterion Optimization - EMO 2007, Springer, Berlin (2007) 742--756.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Zhang, Q., and Li, H. MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. on Evolutionary Computation 11, 6 (2007) 712--731.]] Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Zitzler, E., and Thiele, L. Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Trans. on Evolutionary Computation 3 , 4 (1999) 257--271.]] Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in
    • Published in

      cover image ACM Conferences
      GECCO '08: Proceedings of the 10th annual conference on Genetic and evolutionary computation
      July 2008
      1814 pages
      ISBN:9781605581309
      DOI:10.1145/1389095
      • Conference Chair:
      • Conor Ryan,
      • Editor:
      • Maarten Keijzer

      Copyright © 2008 ACM

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 12 July 2008

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article

      Acceptance Rates

      Overall Acceptance Rate1,669of4,410submissions,38%

      Upcoming Conference

      GECCO '24
      Genetic and Evolutionary Computation Conference
      July 14 - 18, 2024
      Melbourne , VIC , Australia

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader