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A Fast Incremental BSP Tree Archive for Non-dominated Points

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Evolutionary Multi-Criterion Optimization (EMO 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10173))

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Abstract

Maintaining an archive of all non-dominated points is a standard task in multi-objective optimization. Sometimes it is sufficient to store all evaluated points and to obtain the non-dominated subset in a post-processing step. Alternatively the non-dominated set can be updated on the fly. While keeping track of many non-dominated points efficiently is easy for two objectives, we propose an efficient algorithm based on a binary space partitioning (BSP) tree for the general case of three or more objectives. Our analysis and our empirical results demonstrate the superiority of the method over the brute-force baseline method, as well as graceful scaling to large numbers of objectives.

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Notes

  1. 1.

    http://www.ini.rub.de/PEOPLE/glasmtbl/code/ParetoArchive/.

  2. 2.

    http://bbcomp.ini.rub.de.

  3. 3.

    This is usually sufficient for the needs of evolutionary optimization. In data base query problems larger sets must be processed. Hence in some applications memory consumption is still a concern.

  4. 4.

    For \(a>0\) the values \(a=0.1\), \(a=0.2\), \(a=0.5\), and \(a=1\) were used with \(m=2\), \(m=3\), \(m=5\), and \(m=10\) objectives, respectively.

  5. 5.

    http://shark-ml.org.

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Author information

Authors and Affiliations

  1. Institute for Neural Computation, Ruhr-University Bochum, Bochum, Germany

    Tobias Glasmachers

Authors
  1. Tobias Glasmachers
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Correspondence to Tobias Glasmachers .

Editor information

Editors and Affiliations

  1. University of Münster, Münster, Germany

    Heike Trautmann

  2. TU Dortmund University, Dortmund, Germany

    Günter Rudolph

  3. University of Wuppertal, Wuppertal, Germany

    Kathrin Klamroth

  4. CINVESTAV-IPN, Mexico City, Mexico

    Oliver Schütze

  5. Clemson University, Clemson, South Carolina, USA

    Margaret Wiecek

  6. University of Surrey, Guildford, United Kingdom

    Yaochu Jin

  7. University of Münster, Münster, Germany

    Christian Grimme

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Glasmachers, T. (2017). A Fast Incremental BSP Tree Archive for Non-dominated Points. In: Trautmann, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2017. Lecture Notes in Computer Science(), vol 10173. Springer, Cham. https://doi.org/10.1007/978-3-319-54157-0_18

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  • DOI: https://doi.org/10.1007/978-3-319-54157-0_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54156-3

  • Online ISBN: 978-3-319-54157-0

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