skip to main content
10.1145/3040718.3040725acmconferencesArticle/Chapter ViewAbstractPublication PagesfogaConference Proceedingsconference-collections
research-article

Qualitative and Quantitative Assessment of Step Size Adaptation Rules

Published: 12 January 2017 Publication History

Abstract

We present a comparison of step size adaptation methods for evolution strategies, covering recent developments in the field. Following recent work by Hansen et al. we formulate a concise list of performance criteria: a) fast convergence of the mean, b) near-optimal fixed point of the normalized step size dynamics, and c) invariance to adding constant dimensions of the objective function. Our results show that algorithms violating these principles tend to underestimate the step size or are unreliable when the function does not fit to the algorithm's tuned hyperparameters. In contrast, we find that cumulative step size adaptation (CSA) and two-point adaptation (TPA) provide reliable estimates of the optimal step size. We further find that removing the evolution path of CSA still leads to a reliable algorithm without the computational requirements of CSA.

References

[1]
O. Ait Elhara, A. Auger, and N. Hansen. A median success rule for non-elitist evolution strategies: Study of feasibility. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), pages 415--422. ACM, 2013.
[2]
A. Auger. Convergence results for the (1,λ)-SA-ES using the theory of ρ-irreducible Markov chains. Theoretical Computer Science, 334(1-3):35--69, 2005.
[3]
H.-G. Beyer and B. Sendhoff. Covariance matrix adaptation revisited--the CMSA evolution strategy. In Parallel Problem Solving from Nature (PPSN), pages 123--132. Springer, 2008.
[4]
A. Chotard, A. Auger, and N. Hansen. Markov chain analysis of evolution strategies on a linear constraint optimization problem. In Evolutionary Computation (CEC), 2014 IEEE Congress on, pages 159--166. IEEE, 2014.
[5]
T. Glasmachers, T. Schaul, Y. Sun, D. Wierstra, and J. Schmidhuber. Exponential natural evolution strategies. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), 2010.
[6]
N. Hansen. CMA-ES with two-point step-size adaptation. arXiv N. arXiv:0805.0231, 2008.
[7]
N. Hansen, A. Atamna, and A. Auger. How to assess step-size adaptation mechanisms in randomised search. In Parallel Problem Solving from Nature (PPSN), pages 60--69. Springer, 2014.
[8]
N. Hansen and A. Ostermeier. Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9(2):159--195, 2001.
[9]
C. Igel, T. Suttorp, and N. Hansen. A computational efficient covariance matrix update and a (1 + 1)-CMA for evolution strategies. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), pages 453--460. ACM, 2006.
[10]
O. Krause, D. R. Arbonès, and C. Igel. CMA-ES with optimal covariance update and storage complexity. In Advances in Neural Information Processing Systems (NIPS), 2016.
[11]
O. Krause and C. Igel. A more efficient rank-one covariance matrix update for evolution strategies. In J. He, T. Jansen, G. Ochoa, and C. Zarges, editors, Foundations of Genetic Algorithms (FOGA 2015), pages 129--136. ACM Press, 2015.
[12]
I. Loshchilov. A computationally efficient limited memory CMA-ES for large scale optimization. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), pages 397--404. ACM, 2014.
[13]
I. Loshchilov, M. Schoenauer, M. Sebag, and N. Hansen. Maximum likelihood-based online adaptation of hyper-parameters in cma-es. In Parallel Problem Solving from Nature (PPSN), pages 70--79. Springer, 2014.
[14]
Y. Ollivier, L. Arnold, A. Auger, and N. Hansen. Information-geometric optimization algorithms: a unifying picture via invariance principles. arXiv preprint arXiv:1106.3708v3, 2014.
[15]
A. Ostermeier, A. Gawelczyk, and N. Hansen. Step-size adaptation based on non-local use of selection information. In Parallel Problem Solving from Nature (PPSN), pages 189--198. Springer, 1994.
[16]
I. Rechenberg. Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog, 1973.
[17]
R. Salomon. Evolutionary algorithms and gradient search: similarities and differences. IEEE Transactions on Evolutionary Computation, 2(2):45--55, 1998.

Cited By

View all
  • (2021)Tuning as a means of assessing the benefits of new ideas in interplay with existing algorithmic modulesProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3449726.3463167(1375-1384)Online publication date: 7-Jul-2021
  • (2021)MMES: Mixture Model-Based Evolution Strategy for Large-Scale OptimizationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2020.303476925:2(320-333)Online publication date: Apr-2021
  • (2019)Uncrowded hypervolume improvementProceedings of the Genetic and Evolutionary Computation Conference10.1145/3321707.3321852(638-646)Online publication date: 13-Jul-2019
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
FOGA '17: Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms
January 2017
170 pages
ISBN:9781450346511
DOI:10.1145/3040718
Permission to make digital or hard copies of all or part 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 components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 January 2017

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. comparison
  2. evolution strategies
  3. step size adaptation

Qualifiers

  • Research-article

Funding Sources

Conference

FOGA '17
Sponsor:
FOGA '17: Foundations of Genetic Algorithms XIV
January 12 - 15, 2017
Copenhagen, Denmark

Acceptance Rates

FOGA '17 Paper Acceptance Rate 13 of 23 submissions, 57%;
Overall Acceptance Rate 72 of 131 submissions, 55%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)7
  • Downloads (Last 6 weeks)1
Reflects downloads up to 22 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2021)Tuning as a means of assessing the benefits of new ideas in interplay with existing algorithmic modulesProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3449726.3463167(1375-1384)Online publication date: 7-Jul-2021
  • (2021)MMES: Mixture Model-Based Evolution Strategy for Large-Scale OptimizationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2020.303476925:2(320-333)Online publication date: Apr-2021
  • (2019)Uncrowded hypervolume improvementProceedings of the Genetic and Evolutionary Computation Conference10.1145/3321707.3321852(638-646)Online publication date: 13-Jul-2019
  • (2019)Large-scale noise-resilient evolution-strategiesProceedings of the Genetic and Evolutionary Computation Conference10.1145/3321707.3321724(682-690)Online publication date: 13-Jul-2019
  • (2018)PSA-CMA-ESProceedings of the Genetic and Evolutionary Computation Conference10.1145/3205455.3205467(865-872)Online publication date: 2-Jul-2018

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media