skip to main content
10.1145/2463372.2463456acmconferencesArticle/Chapter ViewAbstractPublication PagesgeccoConference Proceedingsconference-collections
research-article

Revisiting the NSGA-II crowding-distance computation

Published:06 July 2013Publication History

ABSTRACT

This paper improves upon the reference NSGA-II procedure by removing an instability in its crowding distance operator. This instability stems from the cases where two or more individuals on a Pareto front share identical fitnesses. In those cases, the instability causes their crowding distance to either become null, or to depend on the individual's position within the Pareto front sequence. Experiments conducted on nine different benchmark problems show that, by computing the crowding distance on unique fitnesses instead of individuals, both the convergence and diversity of NSGA-II can be significantly improved.

References

  1. C. Coello Coello. Recent trends in evolutionary multiobjective optimization. In A. Abraham, L. Jain, and R. Goldberg, editors, Evolutionary Multiobjective Optimization, Advanced Information and Knowledge Processing, pages 7--32. Springer London, 2005.Google ScholarGoogle Scholar
  2. D. Corne, J. Knowles, and M. Oates. The pareto envelope-based selection algorithm for multiobjective optimization. In Parallel Problem Solving from Nature PPSN VI, pages 839--848. Springer, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. K. Deb and R. Agrawal. Simulated binary crossover for continuous search space. Complex Systems, 9:1--34, 1994.Google ScholarGoogle Scholar
  4. K. Deb and H. Jain. Handling many-objective problems using an improved NSGA-II procedure. In Evolutionary Computation (CEC), 2012 IEEE Congress on, pages 1--8, June 2012.Google ScholarGoogle ScholarCross RefCross Ref
  5. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2):182--197, Apr. 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. K. Deb, L. Thiele, M. Laumanns, and E. Zitzler. Scalable multi-objective optimization test problems. In Congress on Evolutionary Computation (CEC 2002), pages 825--830. IEEE Press, 2002.Google ScholarGoogle ScholarCross RefCross Ref
  7. F.-A. Fortin, F.-M. De Rainville, M.-A. Gardner, M. Parizeau, and C. Gagné. DEAP: Evolutionary algorithms made easy. Journal of Machine Learning Research, 2171--2175(13), Jul. 2012.Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. F.-A. Fortin, S. Grenier, and M. Parizeau. Generalizing the improved run-time complexity algorithm for non-dominated sorting. In Proc. of Genetic and Evolutionary Computation Conference (GECCO 2013), July 2013. to appear. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. N. Hansen, A. Auger, R. Ros, S. Finck, and P. Posik. Comparing results of 31 algorithms from the black-box optimization benchmarking bbob-2009. In ACM, editor, Workshop Proceedings of the GECCO Genetic and Evolutionary Computation Conference, pages 1689--1696, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. J. Knowles and D. Corne. Approximating the nondominated front using the pareto archived evolution strategy. Evolutionary computation, 8(2):149--172, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. K. Price. Differential evolution vs. the functions of the 2nd iceo. In Evolutionary Computation, 1997., IEEE International Conference on, pages 153--157, Apr. 1997.Google ScholarGoogle Scholar
  12. K. Sindhya, K. Miettinen, and K. Deb. A hybrid framework for evolutionary multi-objective optimization. IEEE Transactions on Evolutionary Computation, 2012. in press.Google ScholarGoogle Scholar
  13. N. Srinivas and K. Deb. Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation, 2(3):221--248, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. A. Zhou, B.-Y. Qu, H. Li, S.-Z. Zhao, P. N. Suganthan, and Q. Zhang. Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm and Evolutionary Computation, 1(1):32--49, 2011.Google ScholarGoogle ScholarCross RefCross Ref
  15. E. Zitzler, K. Deb, and L. Thiele. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2):173--195, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. E. Zitzler, M. Laumanns, and L. Thiele. SPEA2: Improving the strength Pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Gloriastrasse 35, CH-8092 Zurich, Switzerland, May 2001.Google ScholarGoogle Scholar

Index Terms

  1. Revisiting the NSGA-II crowding-distance computation

    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 '13: Proceedings of the 15th annual conference on Genetic and evolutionary computation
      July 2013
      1672 pages
      ISBN:9781450319638
      DOI:10.1145/2463372
      • Editor:
      • Christian Blum,
      • General Chair:
      • Enrique Alba

      Copyright © 2013 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: 6 July 2013

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article

      Acceptance Rates

      GECCO '13 Paper Acceptance Rate204of570submissions,36%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