Abstract
The progress rate of a self-adaptive evolution strategy is sub-optimal on ridge functions because the global step-size, denoted σ, becomes too small. On the parabolic ridge we conjecture that σ will stabilize when selection is unbiased towards larger or smaller step-sizes. On the sharp ridge, where the bias in selection is constant, σ will continue to decrease. We show that this is of practical interest because ridges can cause even the best solutions found by self-adaptation to be of little value on ridge problems where spatially close parameters tend to have similar values.
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
Arnold, D.V., Beyer, H.-G.: Evolution strategies with cumulative step-length adaptation on the noisy parabolic ridge. Technical report, Dalhousie University (2006)
Bäck, T.: Evolutonary Algorithms in Theory and Practice. Oxford University Press, New York (1996)
Beyer, H.-G.: On the Performance of (1,λ)-Evolution Strategies for the Ridge Function Class. IEEE Transactions on Evolutionary Computation 5(3), 218–235 (2001)
Beyer, H.-G., Schwefel, H.-P.: Evolution strategies - a comprehensive introduction. Natural Computing: an international journal 1(1), 3–52 (2002)
Englen, R., Denning, A., Gurney, K., Stephens, G.: Global observations of the carbon budget: I. expected satellite capabilities for emission spectroscopy in the eos and npoess eras. Journal of Geophysical Research 106(20), 055–20,068 (2001)
Hansen, N.: Invariance, self-adaptation and correlated mutations in evolution strategies. In: Proceedings of Parallel Problem Solving from Nature, pp. 355–364 (2000)
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)
Herdy, M.: Reproductive isolation as strategy parameter in hierarchically organized evolution strategies. In: Proceedings of Parallel Problem Solving from Nature, pp. 207–217 (1992)
Ostermeier, A., Gawelczyk, A., Hansen, N.: A derandomized approach to self-adaptation of evolution strategies. Evolutionary Computation 2(4), 369–380 (1994)
Oyman, A.I., Beyer, H., Schwefel, H.: Where elitists start limping evolution strategies at ridge functions. In: Parallel Problem Solving from Nature – PPSN V
Oyman, A.I., Beyer, H.-G.: Analysis of the (μ/μ, λ)-ES on the Parabolic Ridge. Evolutionary Computation 8(3), 267–289 (2000)
Oyman, A.I., Beyer, H.-G., Schwefel, H.-P.: Analysis of the (1, λ)-ES on the Parabolic Ridge. Evolutionary Computation 8(3), 249–265 (2000)
Salomon, R.: Applying evolutionary algorithms to real-world-inspired problems with physical smoothness constraints. In: Proceedings of the Congress on Evolutionary Computation
Salomon, R.: The curse of high dimensional search spaces: Observing premature convergence in unimodal functions. In: Proceedings of the Congress on Evolutionary Computation, pp. 918–923. IEEE Press, Los Alamitos (2004)
Whitley, D., Lunacek, M., Knight, J.: Ruffled by ridges: How evolutionary algorithms can fail. In: Proceedings of GECCO (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lunacek, M., Whitley, D. (2006). Searching for Balance: Understanding Self-adaptation on Ridge Functions. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_9
Download citation
DOI: https://doi.org/10.1007/11844297_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38990-3
Online ISBN: 978-3-540-38991-0
eBook Packages: Computer ScienceComputer Science (R0)