skip to main content
10.1145/1276958.1277094acmconferencesArticle/Chapter ViewAbstractPublication PagesgeccoConference Proceedingsconference-collections
Article

On the use of evolution strategies for optimising certain positive definite quadratic forms

Published: 07 July 2007 Publication History

Abstract

This paper studies the performance of multi-recombinative evolution strategies using isotropically distributed mutations on a class of convex quadratic objective functions that is characterised by the presence of only two different eigenvalues of their Hessian. A simplified model of the strategy's behaviour is developed. Using it, expressions that approximately describe the stationary state that is attained when the mutation strength is adapted are derived. The performance achieved when using cumulative step length adaptation is compared with that obtained when using optimally adapted step lengths.

References

[1]
D. V. Arnold. Noisy Optimization with Evolution Strategies. Kluwer Academic Publishers, 2002.
[2]
D. V. Arnold and H.-G. Beyer. Local performance of the (μ/μI,λ)-ES in a noisy environment. In W. N. Martin et al., editors, Foundations of Genetic Algorithms 6, pages 127--141. Morgan Kaufmann, 2001.
[3]
D. V. Arnold and H.-G. Beyer. Performance analysis of evolutionary optimization with cumulative step length adaptation. IEEE Transactions on Automatic Control, 49(4):617--622, 2004.
[4]
H.-G. Beyer. The Theory of Evolution Strategies. Springer Verlag, 2001.
[5]
H.-G. Beyer and D. V. Arnold. The steady state behavior of (μ/μI,λ)-ES on ellipsoidal fitness models disturbed by noise. In E. Cantú-Paz et al., editors, Genetic and Evolutionary Computation - GECCO 2003, pages 525--536. Springer Verlag, 2003.
[6]
H.-G. Beyer and H.-P. Schwefel. Evolution strategies - A comprehensive introduction. Natural Computing, 1(1):3--52, 2002.
[7]
N. Hansen and A. Ostermeier. Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9(2):159--195, 2001.
[8]
J. Jägersküpper. Analysis of a simple evolutionary algorithm for minimization in Euclidean spaces. In Automata, Languages, and Programming - ICALP 2003, pages 1068--1079. Springer Verlag, 2003.
[9]
J. Jägersküpper. Rigorous runtime analysis of the (1 + 1) ES: 1/5-rule and ellipsoidal fitness landscapes. In A. H. Wright et al., editors, Foundations of Genetic Algorithms 8, pages 260--281. Springer Verlag, 2005.
[10]
J. Jägersküpper. How the (1 + 1) ES using isotropic mutations minimizes positive definite quadratic forms. Theoretical Computer Science, 361(1):38--56, 2006.
[11]
A. Ostermeier, A. Gawelczyk, and N. Hansen. Step-size adaptation based on non-local use of selection information. In Y. Davidor et al., editors, Parallel Problem Solving from Nature - PPSN III, pages 189--198. Springer Verlag, 1994.
[12]
I. Rechenberg. Evolutionsstrategie '94. Friedrich Frommann Verlag, 1994.
[13]
H.-P. Schwefel. Evolution and Optimum Seeking. Wiley, 1995.

Cited By

View all
  • (2017)Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic FunctionsProceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms10.1145/3040718.3040720(111-126)Online publication date: 12-Jan-2017
  • (2016)The dynamics of cumulative step size adaptation on the ellipsoid modelEvolutionary Computation10.1162/EVCO_a_0014224:1(25-57)Online publication date: 1-Mar-2016
  • (2012)The Dynamical Systems Approach — Progress Measures and Convergence PropertiesHandbook of Natural Computing10.1007/978-3-540-92910-9_25(741-814)Online publication date: 2012
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
GECCO '07: Proceedings of the 9th annual conference on Genetic and evolutionary computation
July 2007
2313 pages
ISBN:9781595936974
DOI:10.1145/1276958
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 ACM 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: 07 July 2007

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. cumulative step length adaptation
  2. evolution strategy
  3. positive definite quadratic form

Qualifiers

  • Article

Conference

GECCO07
Sponsor:

Acceptance Rates

GECCO '07 Paper Acceptance Rate 266 of 577 submissions, 46%;
Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 16 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2017)Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic FunctionsProceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms10.1145/3040718.3040720(111-126)Online publication date: 12-Jan-2017
  • (2016)The dynamics of cumulative step size adaptation on the ellipsoid modelEvolutionary Computation10.1162/EVCO_a_0014224:1(25-57)Online publication date: 1-Mar-2016
  • (2012)The Dynamical Systems Approach — Progress Measures and Convergence PropertiesHandbook of Natural Computing10.1007/978-3-540-92910-9_25(741-814)Online publication date: 2012
  • (2011)Analysis of a repair mechanism for the (1,λ)-ES applied to a simple constrained problemProceedings of the 13th annual conference on Genetic and evolutionary computation10.1145/2001576.2001693(853-860)Online publication date: 12-Jul-2011
  • (2011)On the behaviour of the (1,λ)-es for a simple constrained problemProceedings of the 11th workshop proceedings on Foundations of genetic algorithms10.1145/1967654.1967657(15-24)Online publication date: 5-Jan-2011
  • (2010)On the behaviour of evolution strategies optimising cigar functionsEvolutionary Computation10.1162/EVCO_a_0002318:4(661-682)Online publication date: 1-Dec-2010
  • (2010)Active covariance matrix adaptation for the (1+1)-CMA-ESProceedings of the 12th annual conference on Genetic and evolutionary computation10.1145/1830483.1830556(385-392)Online publication date: 7-Jul-2010
  • (2010)Performance of the (µ/µ, λ)-σSA-ES on a class of PDQFsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2009.203358114:3(400-418)Online publication date: 1-Jun-2010
  • (2009)On the behaviour of weighted multi-recombination evolution strategies optimising noisy cigar functionsProceedings of the 11th Annual conference on Genetic and evolutionary computation10.1145/1569901.1569969(483-490)Online publication date: 8-Jul-2009
  • (2009)Weighted recombination evolution strategy on a class of PDQF'sProceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms10.1145/1527125.1527127(1-12)Online publication date: 9-Jan-2009
  • Show More Cited By

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