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Do Hypervolume Regressions Hinder EMOA Performance? Surprise and Relief

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Evolutionary Multi-Criterion Optimization (EMO 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7811))

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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.

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References

  1. Bader, J., Zitzler, E.: HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization. Evolutionary Computation 19(1), 45–76 (2011)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  4. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester (2001)

    MATH  Google Scholar 

  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. Igel, C., Hansen, N., Roth, S.: Covariance Matrix Adaptation for Multi-objective Optimization. Evolutionary Computation 15(1), 1–28 (2007)

    Article  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  9. Mersmann, O.: emoa: Evolutionary Multiobjective Optimization Algorithms (2011), http://CRAN.R-project.org/package=emoa (R package version 0.4-8)

  10. Zitzler, E., Deb, K., Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8(2), 173–195 (2000)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

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Judt, L., Mersmann, O., Naujoks, B. (2013). Do Hypervolume Regressions Hinder EMOA Performance? Surprise and Relief. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds) Evolutionary Multi-Criterion Optimization. EMO 2013. Lecture Notes in Computer Science, vol 7811. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37140-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-37140-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37139-4

  • Online ISBN: 978-3-642-37140-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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