Article

A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies

Authors:

Christian Igel,

Thorsten Suttorp,

Nikolaus HansenAuthors Info & Claims

GECCO '06: Proceedings of the 8th annual conference on Genetic and evolutionary computation

Pages 453 - 460

https://doi.org/10.1145/1143997.1144082

Published: 08 July 2006 Publication History

Abstract

First, the covariance matrix adaptation (CMA) with rank-one update is introduced into the (1+1)-evolution strategy. An improved implementation of the 1/5-th success rule is proposed for step size adaptation, which replaces cumulative path length control. Second, an incremental Cholesky update for the covariance matrix is developed replacing the computational demanding and numerically involved decomposition of the covariance matrix. The Cholesky update can replace the decomposition only for the update without evolution path and reduces the computational effort from O(n³) to O(n²). The resulting (1+1)-Cholesky-CMA-ES is an elegant algorithm and the perhaps simplest evolution strategy with covariance matrix and step size adaptation. Simulations compare the introduced algorithms to previously published CMA versions.

References

[1]

D. H. Ackley. A connectionist machine for genetic hillclimbing. Kluwer, Boston, 1987.

[2]

T. Bäck. Evolutionary algorithms in theory and practice. Oxford University Press, 1996.

Digital Library

[3]

H.-G. Beyer and H.-P. Schwefel. Evolution strategies: A comprehensive introduction. Natural Computing, 1(1):3--52, 2002.

Digital Library

[4]

M. S. Grewal and A. P. Andrews. Kalman Filtering: Theory and Practice. Prentice-Hall, 1993.

Digital Library

[5]

N. Hansen. An analysis of mutative σ-self-adaptation on linear fitness functions. Evolutionary Computation, 14(3), 2006.

Digital Library

[6]

N. Hansen and S. Kern. Evaluating the CMA evolution strategy on multimodal test functions. In X. Yao, E. Burke, J. A. Lozano, J. Smith, J. J. Merelo-Guervós, J. A. Bullinaria, J. Rowe, P. Tivño, A. Kabán, and H.-P. Schwefel, editors, Parallel Problem Solving from Nature (PPSN VIII), volume 3242 of LNCS, pages 282--291. Springer-Verlag, 2004.

[7]

N. Hansen, S. D. Müller, and P. Koumoutsakos. Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolutionary Computation, 11(1):1--18, 2003.

Digital Library

[8]

N. Hansen and A. Ostermeier. Adapting arbitrary normal mutation distributions in evolution strategies: The covariance matrix adaptation. In Proceedings of the 1996 IEEE Conference on Evolutionary Computation (ICEC '96), pages 312--317, 1996.

Digital Library

[9]

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

Digital Library

[10]

S. Kern, S. Müller, N. Hansen, D. Büche, J. Ocenasek, and P. Koumoutsakos. Learning probability distributions in continuous evolutionary algorithms - A comparative review. Natural Computing, 3:77--112, 2004.

Digital Library

[11]

H. Mühlenbein, D. Schomisch, and J. Born. The Parallel Genetic Algorithm as Function Optimizer. Parallel Computing, 17(6-7):619--632, 1991.

Digital Library

[12]

I. Rechenberg. Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution. Frommann-Holzboog, 1973.

[13]

G. Rudolph. On correlated mutations in evolution strategies. In R. Männer and B. Manderick, editors, Parallel Problem Solving from Nature 2 (PPSN II), pages 105--114. Elsevier, 1992.

[14]

H.-P. Schwefel. Evolution and Optimum Seeking. Sixth-Generation Computer Technology Series. John Wiley & Sons, 1995.

Digital Library

[15]

A. Törn and A. Zilinskas. Global Optimization, volume 350 of LNCS. Springer-Verlag, 1989.

Digital Library

Cited By

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A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies

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cover image ACM Conferences

GECCO '06: Proceedings of the 8th annual conference on Genetic and evolutionary computation

July 2006

2004 pages

ISBN:1595931864

DOI:10.1145/1143997

General Chair:
Mike Cattolico
Tiger Mountain Scientific, Inc., USA

Copyright © 2006 ACM.

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Published: 08 July 2006

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July 8 - 12, 2006

Washington, Seattle, USA

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GECCO '06 Paper Acceptance Rate 205 of 446 submissions, 46%;

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Filho JDiniz P(2024)A Sparse Fixed-Point Online KPCA Extraction AlgorithmIEEE Transactions on Signal Processing10.1109/TSP.2024.344651272(4604-4617)Online publication date: 2024
https://doi.org/10.1109/TSP.2024.3446512
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https://doi.org/10.1109/TPDS.2024.3437688
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