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Do Hypervolume Regressions Hinder EMOA Performance? Surprise and Relief

  • Leonard Judt
  • Olaf Mersmann
  • Boris Naujoks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7811)

Abstract

Decreases in dominated hypervolume w.r.t a fixed reference point for the (μ + 1)-SMS-EMOA are able to appear. We examine the impact of these decreases and different reference point handling techniques by providing four different algorithmic variants for selection. In addition, we show that yet further decreases can occur due to numerical instabilities that were previously not being expected. Fortunately, our findings do indicate that all detected decreases do not have a negative effect on the overall performance.

Keywords

EMO hypervolume decreases reference point handling numerical instabilities 

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References

  1. 1.
    Bader, J., Zitzler, E.: HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization. Evolutionary Computation 19(1), 45–76 (2011)CrossRefGoogle Scholar
  2. 2.
    Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181(3), 1653–1669 (2007)MATHCrossRefGoogle Scholar
  3. 3.
    Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, New York (2007)MATHGoogle Scholar
  4. 4.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester (2001)MATHGoogle Scholar
  5. 5.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Congress on Evolutionary Computation (CEC 2002), pp. 825–830. IEEE Press (2002)Google Scholar
  6. 6.
    Igel, C., Hansen, N., Roth, S.: Covariance Matrix Adaptation for Multi-objective Optimization. Evolutionary Computation 15(1), 1–28 (2007)CrossRefGoogle Scholar
  7. 7.
    Judt, L., Mersmann, O., Naujoks, B.: Non-monotonicity of Obtained Hypervolume in 1-greedy S-Metric Selection. Journal of Multi-Criteria Decision Analysis (2011), maanvs03.gm.fh-koeln.de/webpub/CIOPReports.d/Judt11a.d/ (accepted for publication, preprint)
  8. 8.
    Judt, L., Mersmann, O., Naujoks, B.: Effect of SMS-EMOA Parameterizations on Hypervolume Decreases. In: Hamadi, Y., Schoenauer, M. (eds.) LION 6. LNCS, vol. 7219, pp. 419–424. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Mersmann, O.: emoa: Evolutionary Multiobjective Optimization Algorithms (2011), http://CRAN.R-project.org/package=emoa (R package version 0.4-8)
  10. 10.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8(2), 173–195 (2000)CrossRefGoogle Scholar
  11. 11.
    Zitzler, E., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms — A Comparative Case Study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN V. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. 12.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Leonard Judt
    • 1
  • Olaf Mersmann
    • 1
  • Boris Naujoks
    • 2
  1. 1.Faculty of StatisticsTU Dortmund UniversityDortmundGermany
  2. 2.Cologne University of Applied SciencesGummersbachGermany

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