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Towards Fixed-Target Black-Box Complexity Analysis

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Parallel Problem Solving from Nature – PPSN XVII (PPSN 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13399))

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Abstract

Recently, fine-grained measures of performance of randomized search heuristics received attention in the theoretical community. In particular, some results were proven specifically for fixed-target runtime analysis. However, this research domain still lacks an important counterpart, namely, the (black-box) complexity analysis, which shall augment runtime analyses of particular algorithms with the bounds on what can be achieved with the best possible algorithms.

This paper makes few first steps in this direction. We prove upper and lower bounds on the fixed-target black-box complexity of the standard benchmark function OneMax given the problem size n and the target fitness k that we want to achieve. On the way to these bounds, we prove a general lower bound theorem suitable to derive bounds not only in fixed-target settings, but also in settings where a problem instance may have multiple optima.

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Authors and Affiliations

  1. ITMO University, Saint Petersburg, Russia

    Dmitry Vinokurov & Maxim Buzdalov

Authors
  1. Dmitry Vinokurov
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  2. Maxim Buzdalov
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Corresponding author

Correspondence to Maxim Buzdalov .

Editor information

Editors and Affiliations

  1. TU Dortmund, Dortmund, Germany

    Günter Rudolph

  2. Leiden University, Leiden, The Netherlands

    Anna V. Kononova

  3. Shinshu University, Nagano, Japan

    Hernán Aguirre

  4. Technische Universität Dresden, Dresden, Germany

    Pascal Kerschke

  5. University of Stirling, Stirling, UK

    Gabriela Ochoa

  6. Jožef Stefan Institute, Ljubljana, Slovenia

    Tea Tušar

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Vinokurov, D., Buzdalov, M. (2022). Towards Fixed-Target Black-Box Complexity Analysis. In: Rudolph, G., Kononova, A.V., Aguirre, H., Kerschke, P., Ochoa, G., Tušar, T. (eds) Parallel Problem Solving from Nature – PPSN XVII. PPSN 2022. Lecture Notes in Computer Science, vol 13399. Springer, Cham. https://doi.org/10.1007/978-3-031-14721-0_42

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  • DOI: https://doi.org/10.1007/978-3-031-14721-0_42

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-14720-3

  • Online ISBN: 978-3-031-14721-0

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