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On binary unbiased operators returning multiple offspring

Published: 15 July 2017 Publication History

Abstract

The notion of unbiased black-box complexity plays an important role in theory of randomized search heuristics. A black-box algorithm is usually defined as an algorithm which uses unbiased variation operations. In all known papers, the analysed variation operators take k arguments and produce one offspring. On the other hand, many practitioners use crossovers which produce two offspring, and in many living organisms a diploid cell produces two distinct haploid genotypes.
We investigate how the binary-to-binary, or (2 → 2), unbiased variation operators look like, and how they can be used to improve randomized search heuristics. We show that the (2 → 2) unbiased black-box complexity of Needle coincides with its unrestricted black-box complexity. We also show that it can be used to put strong worst-case guarantees for solving OneMax.

References

[1]
Anne Auger and Benjamin Doerr. 2011. Theory of Randomized Search Heuristics: Foundations and Recent Developments. World Scientific Publishing Co., Inc., River Edge, NJ, USA.
[2]
Benjamin Doerr and Carola Doerr. 2015. Optimal Parameter Choices Through Self-Adjustment: Applying the 1/5-th Rule in Discrete Settings. In Proceedings of Genetic and Evolutionary Computation Conference. 1335--1342.
[3]
Benjamin Doerr, Carola Doerr, and Franziska Ebel. 2015. From black-box complexity to designing new genetic algorithms. Theoretical Computer Science 567 (2015), 87--104.
[4]
Benjamin Doerr, Daniel Johannsen, Timo Kötzing, Per Kristian Lehre, Markus Wagner, and Carola Winzen. 2011. Faster black-box algorithms through higher arity operators. In Proceedings of Foundations of Genetic Algorithms. 163--172.
[5]
Stefan Droste, Thomas Jansen, and Ingo Wegener. 2006. Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization. Theory of Computing Systems 39, 4 (2006), 525--544.
[6]
Thomas Jansen and Ingo Wegener. 2002. The Analysis of Evolutionary Algorithms-A Proof that Crossover Really Can Help. Algorithmica 34 (2002), 47--66.
[7]
Per Kristian Lehre and Carsten Witt. 2012. Black-box Search by Unbiased Variation. Algorithmica 64 (2012), 623--642.
[8]
Dirk Sudholt. 2012. Crossover speeds up building-block assembly. In Proceedings of Genetic and Evolutionary Computation Conference. 689--696.

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  • (2023)Improving Time and Memory Efficiency of Genetic Algorithms by Storing Populations as Minimum Spanning Trees of PatchesProceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3596388(1873-1881)Online publication date: 15-Jul-2023

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    cover image ACM Conferences
    GECCO '17: Proceedings of the Genetic and Evolutionary Computation Conference Companion
    July 2017
    1934 pages
    ISBN:9781450349390
    DOI:10.1145/3067695
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    Published: 15 July 2017

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    Author Tags

    1. OneMax
    2. black-box complexity
    3. crossovers
    4. needle

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    • (2023)Improving Time and Memory Efficiency of Genetic Algorithms by Storing Populations as Minimum Spanning Trees of PatchesProceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3596388(1873-1881)Online publication date: 15-Jul-2023

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