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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bader, J., Zitzler, E.: HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization. Evolutionary Computation 19(1), 45–76 (2011)
Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181(3), 1653–1669 (2007)
Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, New York (2007)
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester (2001)
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)
Igel, C., Hansen, N., Roth, S.: Covariance Matrix Adaptation for Multi-objective Optimization. Evolutionary Computation 15(1), 1–28 (2007)
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)
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)
Mersmann, O.: emoa: Evolutionary Multiobjective Optimization Algorithms (2011), http://CRAN.R-project.org/package=emoa (R package version 0.4-8)
Zitzler, E., Deb, K., Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8(2), 173–195 (2000)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)