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A note on the CMA-ES for functions with periodic variables

Authors:

Takahiro Yamaguchi,

Youhei AkimotoAuthors Info & Claims

GECCO '18: Proceedings of the Genetic and Evolutionary Computation Conference Companion

Pages 227 - 228

https://doi.org/10.1145/3205651.3205669

Published: 06 July 2018 Publication History

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Abstract

In this short paper, we reveal the issue of the covariance matrix adaptation evolution strategy when solving a function with periodic variables. We investigate the effect of a simple modification that the coordinate-wise standard deviation of the sampling distribution is restricts to the one-fourth of the period length. This is achieved by pre- and post-multiplying a diagonal matrix to the covariance matrix.

References

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Dirk V Arnold. 2014. On the Use of Evolution Strategies for Optimization on Spherical Manifolds. In International Conference on Parallel Problem Solving from Nature. Springer, 882--891.

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N. Hansen. 2016. The CMA Evolution Strategy: A Tutorial. ArXiv e-prints (April 2016). arXiv:cs.LG/1604.00772

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Nikolaus Hansen, Sibylle D. Muller, and Petros Koumoutsakos. 2003. Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolutionary Computation 11, 1 (2003), 1--18.

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Nikolaus Hansen and Andreas Ostermeier. 2001. Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation 9, 2 (2001), 159--195.

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Miyagi AMiyauchi YMaki AFukuchi KSakuma JAkimoto Y(2023)Covariance Matrix Adaptation Evolutionary Strategy with Worst-Case Ranking Approximation for Min–Max Optimization and Its Application to Berthing Control TasksACM Transactions on Evolutionary Learning and Optimization10.1145/36037163:2(1-32)Online publication date: 28-Jun-2023
https://dl.acm.org/doi/10.1145/3603716
Miyagi AFukuchi KSakuma JAkimoto YWagner M(2022)Black-box min-max continuous optimization using CMA-ES with worst-case ranking approximationProceedings of the Genetic and Evolutionary Computation Conference10.1145/3512290.3528702(823-831)Online publication date: 8-Jul-2022
https://dl.acm.org/doi/10.1145/3512290.3528702

Index Terms

A note on the CMA-ES for functions with periodic variables
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
      2. Mixed discrete-continuous optimization
        Bio-inspired optimization

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Published In

GECCO '18: Proceedings of the Genetic and Evolutionary Computation Conference Companion

July 2018

1968 pages

ISBN:9781450357647

DOI:10.1145/3205651

Editor:
Hernan Aguirre
Shinshu University
,
General Chair:
Keiki Takadama
The University of Electro-Communications

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

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Published: 06 July 2018

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GECCO '18: Genetic and Evolutionary Computation Conference

July 15 - 19, 2018

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Miyagi AMiyauchi YMaki AFukuchi KSakuma JAkimoto Y(2023)Covariance Matrix Adaptation Evolutionary Strategy with Worst-Case Ranking Approximation for Min–Max Optimization and Its Application to Berthing Control TasksACM Transactions on Evolutionary Learning and Optimization10.1145/36037163:2(1-32)Online publication date: 28-Jun-2023
https://dl.acm.org/doi/10.1145/3603716
Miyagi AFukuchi KSakuma JAkimoto YWagner M(2022)Black-box min-max continuous optimization using CMA-ES with worst-case ranking approximationProceedings of the Genetic and Evolutionary Computation Conference10.1145/3512290.3528702(823-831)Online publication date: 8-Jul-2022
https://dl.acm.org/doi/10.1145/3512290.3528702

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Recommendations

Bi-population CMA-ES agorithms with surrogate models and line searches

Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed

Black-box optimization benchmarking of IPOP-saACM-ES and BIPOP-saACM-ES on the BBOB-2012 noiseless testbed

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