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First Steps Towards a Runtime Analysis When Starting with a Good Solution

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

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12270))

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Abstract

The mathematical runtime analysis of evolutionary algorithms traditionally regards the time an algorithm needs to find a solution of a certain quality when initialized with a random population. In practical applications it may be possible to guess solutions that are better than random ones. We start a mathematical runtime analysis for such situations. We observe that different algorithms profit to a very different degree from a better initialization. We also show that the optimal parameterization of the algorithm can depend strongly on the quality of the initial solutions. To overcome this difficulty, self-adjusting and randomized heavy-tailed parameter choices can be profitable. Finally, we observe a larger gap between the performance of the best evolutionary algorithm we found and the corresponding black-box complexity. This could suggest that evolutionary algorithms better exploiting good initial solutions are still to be found. These first findings stem from analyzing the performance of the \((1+1)\) evolutionary algorithm and the static, self-adjusting, and heavy-tailed \((1 + (\lambda ,\lambda ))\) GA on the OneMax benchmark, but we are optimistic that the question how to profit from good initial solutions is interesting beyond these first examples.

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Notes

  1. 1.

    This argument can be seen as a formalization of the intuitive argument that there are \(\left( {\begin{array}{c}n\\ D\end{array}}\right) \) different solution candidates, each fitness evaluation has up to \(n+1\) different answers, hence if the runtime is less than \(\log _{n+1} \left( {\begin{array}{c}n\\ D\end{array}}\right) \) then there are two solution candidates that receive the same sequence of answers and hence are indistinguishable.

  2. 2.

    All the omitted proofs can be found in preprint  [2].

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Acknowledgements

This work was supported by the Government of Russian Federation, grant number 08-08, and by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH, in a joint call with Gaspard Monge Program for optimization, operations research and their interactions with data sciences.

Author information

Authors and Affiliations

  1. ITMO University, St. Petersburg, Russia

    Denis Antipov & Maxim Buzdalov

  2. Laboratoire d’Informatique (LIX), CNRS, École Polytechnique, Institut Polytechnique de Paris, Palaiseau, France

    Denis Antipov & Benjamin Doerr

Authors
  1. Denis Antipov
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  2. Maxim Buzdalov
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  3. Benjamin Doerr
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Corresponding author

Correspondence to Denis Antipov .

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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Antipov, D., Buzdalov, M., Doerr, B. (2020). First Steps Towards a Runtime Analysis When Starting with a Good Solution. In: Bäck, T., et al. Parallel Problem Solving from Nature – PPSN XVI. PPSN 2020. Lecture Notes in Computer Science(), vol 12270. Springer, Cham. https://doi.org/10.1007/978-3-030-58115-2_39

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  • DOI: https://doi.org/10.1007/978-3-030-58115-2_39

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  • Online ISBN: 978-3-030-58115-2

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