research-article

Global convergence for evolution strategies in spherical problems

Authors:

Alexis Bienvenüe,

Olivier FrançoisAuthors Info & Claims

Theoretical Computer Science, Volume 306, Issue 1

Pages 269 - 289

Published: 05 September 2003 Publication History

Abstract

This paper presents simple proofs for the global convergence of evolution strategies in spherical problems. We investigate convergence properties for both adaptive and self-adaptive strategies. Regarding adaptive strategies, the convergence rates are computed explicitly and compared with the results obtained in the so-called “rate-of-progress” theory. Regarding self-adaptive strategies, the computation is conditional to the knowledge of a specific induced Markov chain. An explicit example of chaotic behavior illustrates the complexity in dealing with such chains. In addition to these proofs, this work outlines a number of difficulties in dealing with evolution strategies.

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Cited By

Agapie ASolomon OBădin L(2023)Theory of (1+1) ES on SPHERE RevisitedIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.321752427:4(938-948)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1109/TEVC.2022.3217524
Rolet PTeytaud O(2010)Bandit-based estimation of distribution algorithms for noisy optimizationProceedings of the 4th international conference on Learning and intelligent optimization10.5555/1893659.1893668(97-110)Online publication date: 18-Jan-2010
https://dl.acm.org/doi/10.5555/1893659.1893668
Jebalia MAuger A(2010)Log-linear convergence of the scale-invariant (µ/µw, λ)-ES and optimal µ for intermediate recombination for large population sizesProceedings of the 11th international conference on Parallel problem solving from nature: Part I10.5555/1885031.1885038(52-62)Online publication date: 11-Sep-2010
https://dl.acm.org/doi/10.5555/1885031.1885038
Show More Cited By

Index Terms

Global convergence for evolution strategies in spherical problems
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic representations
      1. Markov networks
    2. Stochastic processes
      1. Markov processes
2. Theory of computation
  1. Design and analysis of algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Markov decision processes

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cover image Theoretical Computer Science

Theoretical Computer Science Volume 306, Issue 1

September 2003

544 pages

ISSN:0304-3975

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Copyright © Elsevier B.V.

Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 05 September 2003

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Cited By

Agapie ASolomon OBădin L(2023)Theory of (1+1) ES on SPHERE RevisitedIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.321752427:4(938-948)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1109/TEVC.2022.3217524
Rolet PTeytaud O(2010)Bandit-based estimation of distribution algorithms for noisy optimizationProceedings of the 4th international conference on Learning and intelligent optimization10.5555/1893659.1893668(97-110)Online publication date: 18-Jan-2010
https://dl.acm.org/doi/10.5555/1893659.1893668
Jebalia MAuger A(2010)Log-linear convergence of the scale-invariant (µ/µw, λ)-ES and optimal µ for intermediate recombination for large population sizesProceedings of the 11th international conference on Parallel problem solving from nature: Part I10.5555/1885031.1885038(52-62)Online publication date: 11-Sep-2010
https://dl.acm.org/doi/10.5555/1885031.1885038
Akimoto YNagata YOno IKobayashi SPelikan MBranke J(2010)Theoretical analysis of evolutionary computation on continuously differentiable functionsProceedings of the 12th annual conference on Genetic and evolutionary computation10.1145/1830483.1830742(1401-1408)Online publication date: 7-Jul-2010
https://dl.acm.org/doi/10.1145/1830483.1830742
François O(2008)Convergence Analysis of Evolution Strategies with Random Numbers of OffspringProceedings of the 10th International Conference on Parallel Problem Solving from Nature --- PPSN X - Volume 519910.5555/2951659.2951663(21-30)Online publication date: 13-Sep-2008
https://dl.acm.org/doi/10.5555/2951659.2951663
Jebalia MAuger ALiardet P(2007)Log-linear convergence and optimal bounds for the (1 + 1)-ESProceedings of the Evolution artificielle, 8th international conference on Artificial evolution10.5555/1793671.1793693(207-218)Online publication date: 29-Oct-2007
https://dl.acm.org/doi/10.5555/1793671.1793693
Teytaud O(2007)Conditioning, halting criteria and choosing λProceedings of the Evolution artificielle, 8th international conference on Artificial evolution10.5555/1793671.1793692(196-206)Online publication date: 29-Oct-2007
https://dl.acm.org/doi/10.5555/1793671.1793692
Meyer-Nieberg SBeyer H(2007)Mutative self-adaptation on the sharp and parabolic ridgeProceedings of the 9th international conference on Foundations of genetic algorithms10.5555/1757524.1757529(70-96)Online publication date: 8-Jan-2007
https://dl.acm.org/doi/10.5555/1757524.1757529
Auger AHansen NCattolico M(2006)Reconsidering the progress rate theory for evolution strategies in finite dimensionsProceedings of the 8th annual conference on Genetic and evolutionary computation10.1145/1143997.1144081(445-452)Online publication date: 8-Jul-2006
https://dl.acm.org/doi/10.1145/1143997.1144081
Auger A(2005)Convergence results for the (1, λ)-SA-ES using the theory of ϕ-irreducible Markov chainsTheoretical Computer Science10.1016/j.tcs.2004.11.017334:1-3(35-69)Online publication date: 11-Apr-2005
https://dl.acm.org/doi/10.1016/j.tcs.2004.11.017
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