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Approximate Hypervolume Calculation with Guaranteed or Confidence Bounds

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Parallel Problem Solving from Nature – PPSN XVI (PPSN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12269))

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Abstract

We present a new version of the Quick Hypervolume algorithm allowing calculation of guaranteed lower and upper bounds for the value of hypervolume, which is one of the most often used and recommended quality indicators in multiobjective optimization. To ensure fast convergence of these bounds, we use a priority queue of subproblems instead of the depth-first search applied in the original recursive Quick Hypervolume algorithm. We also combine this new algorithm with the Monte Carlo sampling approach, which allows obtaining better confidence intervals than the standard Monte Carlo sampling. The performance of the two proposed methods is compared with that of a straightforward adaptation of recursive Quick Hypervolume algorithm and the standard Monte Carlo sampling in a comprehensive computational experiment.

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Notes

  1. 1.

    All data instances used in this experiment, source code and the detailed results are available at https://chmura.put.poznan.pl/s/c6dClctKDDo3vSc.

  2. 2.

    In all cases we use our own C++ implementations of the methods.

  3. 3.

    To save space, Fig. 1 omits charts for the uniformly spherical data sets (which are basically indistinguishable from those for the convex data sets).

  4. 4.

    As already mentioned, because of the 10 prematurely terminated runs of QHV-BQ for the instances of type concave and d = 10 only 153 data instances were used in the test performed after 100% of the computing time.

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Acknowledgement

We are grateful to our Reviewers for their insightful suggestions. Our paper has been supported by local Statutory Funds (SBAD-2020) of the affiliated institute.

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Authors and Affiliations

  1. Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965, Poznań, Poland

    A. Jaszkiewicz, R. Susmaga & P. Zielniewicz

Authors
  1. A. Jaszkiewicz
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  2. R. Susmaga
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  3. P. Zielniewicz
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Corresponding author

Correspondence to A. Jaszkiewicz .

Editor information

Editors and Affiliations

  1. Leiden University, Leiden, The Netherlands

    Thomas Bäck

  2. Leiden University, Leiden, The Netherlands

    Mike Preuss

  3. Leiden University, Leiden, The Netherlands

    André Deutz

  4. Sorbonne University, Paris, France

    Hao Wang

  5. Sorbonne University, Paris, France

    Carola Doerr

  6. Leiden University, Leiden, The Netherlands

    Michael Emmerich

  7. University of Münster, Münster, Germany

    Heike Trautmann

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Jaszkiewicz, A., Susmaga, R., Zielniewicz, P. (2020). Approximate Hypervolume Calculation with Guaranteed or Confidence Bounds. In: Bäck, T., et al. Parallel Problem Solving from Nature – PPSN XVI. PPSN 2020. Lecture Notes in Computer Science(), vol 12269. Springer, Cham. https://doi.org/10.1007/978-3-030-58112-1_15

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  • DOI: https://doi.org/10.1007/978-3-030-58112-1_15

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  • Print ISBN: 978-3-030-58111-4

  • Online ISBN: 978-3-030-58112-1

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