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International Conference on Parallel Problem Solving from Nature

PPSN 2014: Parallel Problem Solving from Nature – PPSN XIII pp 518–527Cite as

Generic Postprocessing via Subset Selection for Hypervolume and Epsilon-Indicator

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8672))

Abstract

Most biobjective evolutionary algorithms maintain a population of fixed size μ and return the final population at termination. During the optimization process many solutions are considered, but most are discarded. We present two generic postprocessing algorithms which utilize the archive of all non-dominated solutions evaluated during the search. We choose the best μ solutions from the archive such that the hypervolume or ε-indicator is maximized. This postprocessing costs no additional fitness function evaluations and has negligible runtime compared to most EMOAs.

We experimentally examine our postprocessing for four standard algorithms (NSGA-II, SPEA2, SMS-EMOA, IBEA) on ten standard test functions (DTLZ 1–2,7, ZDT 1–3, WFG 3–6) and measure the average quality improvement. The median decrease of the distance to the optimal ε-indicator is 95%, the median decrease of the distance to the optimal hypervolume value is 86%. We observe similar performance on a real-world problem (wind turbine placement).

The research leading to these results has received funding from the Australian Research Council (ARC) under grant agreement DP140103400 and from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no 618091 (SAGE). K.B. is a recipient of the Google Europe Fellowship in Randomized Algorithms, and this research is supported in part by this Google Fellowship.

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Author information

Authors and Affiliations

  1. Max Planck Institute for Informatics, Saarbrücken, Germany

    Karl Bringmann

  2. Friedrich-Schiller-Universität Jena, Jena, Germany

    Tobias Friedrich

  3. Universität des Saarlandes, Saarbrücken, Germany

    Patrick Klitzke

Authors
  1. Karl Bringmann
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  2. Tobias Friedrich
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  3. Patrick Klitzke
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Editor information

Editors and Affiliations

  1. Faculty of Computer and Engineering Sciences, Cologne University of Applied Sciences, Steinmüllerallee 1, 51643, Gummersbach, Germany

    Thomas Bartz-Beielstein

  2. Warwick Business School, University of Warwick, CV8 2SY, Coventry, UK

    Jürgen Branke

  3. Department of Intelligent Systems, JožefStefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia

    Bogdan Filipič

  4. Department of Computer Science and Creative Technologies, University of the West of England, BS16 1QY, Bristol, UK

    Jim Smith

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Bringmann, K., Friedrich, T., Klitzke, P. (2014). Generic Postprocessing via Subset Selection for Hypervolume and Epsilon-Indicator. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_51

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  • DOI: https://doi.org/10.1007/978-3-319-10762-2_51

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10761-5

  • Online ISBN: 978-3-319-10762-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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