Cited by 4,397Metaheuristic Optimization Algorithms ResearchEvolutionary Algorithms and ApplicationsEvolution and Genetic Dynamics

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Completely Derandomized Self-Adaptation in Evolution Strategies

Hansen, Nikolaus, Ostermeier, Andreas·2001·Evolutionary Computation

DOI 10.1162/106365601750190398

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Abstract

This paper puts forward two useful methods for self-adaptation of the mutation distribution - the concepts of derandomization and cumulation. Principle shortcomings of the concept of mutative strategy parameter control and two levels of derandomization are reviewed. Basic demands on the self-adaptation of arbitrary (normal) mutation distributions are developed. Applying arbitrary, normal mutation distributions is equivalent to applying a general, linear problem encoding. The underlying objective of mutative strategy parameter control is roughly to favor previously selected mutation steps in the future. If this objective is pursued rigorously, a completely derandomized self-adaptation scheme results, which adapts arbitrary normal mutation distributions. This scheme, called covariance matrix adaptation (CMA), meets the previously stated demands. It can still be considerably improved by cumulation - utilizing an evolution path rather than single search steps. Simulations on various test functions reveal local and global search properties of the evolution strategy with and without covariance matrix adaptation. Their performances are comparable only on perfectly scaled functions. On badly scaled, non-separable functions usually a speed up factor of several orders of magnitude is observed. On moderately mis-scaled functions a speed up factor of three to ten can be expected.

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“It is generally recognized that the typical values for μ = 15 and λ = 100 are not sufficient for this adaptation mechanism (Bäck et al., 1997).”
Background
Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation
Hansen, N., & Ostermeier, A. (2002) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/icec.1996.542381 · Cited by 1,110
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Research works printed but not linked: 2

Cerveri P., 2001, IEEE Transactions on Evolutionary Computation, in press.
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Authors: Hansen, N., & Ostermeier, A.
Affiliations: Technische Universität Berlin (DE)
ORCID: Hansen, Nikolaus
Venue: Evolutionary Computation
Publisher: MIT Press
Published: 2001-06
Volume: 9
Issue: 2
Pages: 159-195
ISSN: 1063-6560 (ISSN-L)
1530-9304
DOI: 10.1162/106365601750190398
OpenAlex: W2112036188
Cited by: 4,397
References: 41
Citations by year: 2026: 342 · 2025: 296 · 2024: 247 · 2023: 260 · 2022: 261 · 2021: 295 · 2020: 279 · 2019: 253 · 2018: 243 · 2017: 202 · 2016: 204 · 2015: 174 · 2014: 210 · 2013: 152 · 2012: 179
FWCI: 31.27
Type: journal article
Language: en
Open access: closed
Locations: Evolutionary Computation (publishedVersion)
PubMed (publishedVersion)
Topics: Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
Physical Sciences › Computer Science › Artificial Intelligence › Evolutionary Algorithms and Applications
Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
Keywords: evolution strategies, self-adaptation, derandomization, covariance matrix adaptation, mutation distribution, cumulation, evolution path, global and local search
MeSH terms: Algorithms, Computer Simulation, Biological Evolution, Models, Genetic, Mutation, Stochastic Processes, Models, Statistical

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Completely Derandomized Self-Adaptation in Evolution Strategies

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