Abstract
Most studies concerned with the effects of noise on evolutionary computation have assumed a Gaussian noise model. However, practical optimization strategies frequently face situations where the noise is not Gaussian, and sometimes it does not even have a finite variance. In particular, outliers may be present. In this paper, Cauchy distributed noise is used for modeling such situations. A performance law that describes how the progress of an evolution strategy using intermediate recombination scales in the presence of such noise is derived. Implications of that law are studied numerically, and comparisons with the case of Gaussian noise are drawn.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1965)
Arnold, D.V.: Noisy Optimization with Evolution Strategies. Genetic Algorithms and Evolutionary Computation Series. Kluwer Academic Publishers, Norwell (2002)
Arnold, D.V., Beyer, H.-G.: Efficiency and self-adaptation of the(μ / μ I, λ)-ES in a noisy environment. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X., et al. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 39–48. Springer, Heidelberg (2000)
Arnold, D.V., Beyer, H.-G.: Local performance of the(μ / μ I, λ)-ES in a noisy environment. In: Martin, W.N., Spears, W.M. (eds.) Foundations of Genetic Algorithms 6, pp. 127–141. Morgan Kaufmann, San Francisco (2001)
Arnold, D.V., Beyer, H.-G.: Local performance of the (1 + 1)-ES in a noisy environment. IEEE Transactions on Evolutionary Computation 6(1), 30–41 (2002)
Arnold, D.V., Beyer, H.-G.: Performance analysis of evolution strategies with multi-recombination in high- dimensional IRN-search spaces disturbed by noise. Theoretical Computer Science 289(1), 629–647 (2002)
Arnold, D.V., Beyer, H.-G.: A comparison of evolution strategies with other direct search methods in the presence of noise. Computational Optimization and Applications 24(1), 135–159 (2003)
Beyer, H.-G.: Evolutionary algorithms in noisy environments: Theoretical issues and guidelines for practice. Computer Methods in Mechanics and Applied Engineering 186, 239–267 (2000)
Beyer, H.-G., Olhofer, M., Sendhoff, B.: On the behavior of(μ / μ I, λ)-ES optimiz- ing functions disturbed by generalized noise. In: Rowe, J., et al. (eds.) Foundations of Genetic Algorithms 7, Morgan Kaufmann, San Francisco (2003) (in press)
David, H.A., Nagaraja, H.N.: Concomitants of order statistics. In: Balakr-ishnan, N., Rao, C.R. (eds.) Handbook of Statistics, vol. 16, pp. 487–513. Elsevier, Amsterdam (1998)
Fitzpatrick, J.M., Grefenstette, J.J.: Genetic algorithms in noisy environments. Machine Learning 3, 101–120 (1988)
Miller, B.L., Goldberg, D.E.: Genetic algorithms, selection schemes, and the varying effects of noise. Evolutionary Computation 4(2), 113–131 (1997)
Rattray, M., Shapiro, J.: Noisy fitness evaluation in genetic algorithms and the dynamics of learning. In: Belew, R.K., Vose, M.D. (eds.) Foundations of Genetic Algorithms 4, pp. 117–139. Morgan Kaufmann, San Francisco (1997)
Rechenberg, I.: Evolutionsstrategie: Optimierung technischer Systeme nach den Prinzipien der biologischen Evolution. Frommann-Holzboog, Stuttgart (1973)
Rudolph, G.: Local convergence rates of simple evolutionary algorithms with Cauchy mutations. IEEE Transactions on Evolutionary Computation 1(4), 249–258 (1997)
Stuart, A., Ord, J.K.: Kendall’s Advanced Theory of Statistics. In: Distribution Theory, 6th edn., Edward Arnold, London (1994)
Szu, H., Hartley, R.: Fast simulated annealing. Physics Letters A 122, 157–162 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arnold, D.V., Beyer, HG. (2003). On the Effects of Outliers on Evolutionary Optimization. In: Liu, J., Cheung, Ym., Yin, H. (eds) Intelligent Data Engineering and Automated Learning. IDEAL 2003. Lecture Notes in Computer Science, vol 2690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45080-1_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-45080-1_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40550-4
Online ISBN: 978-3-540-45080-1
eBook Packages: Springer Book Archive