Abstract
We revisit Gaussian Adaptation (GaA), a black-box optimizer for discrete and continuous problems that has been developed in the late 1960’s. This largely neglected search heuristic shares several interesting features with the well-known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and with Simulated Annealing (SA). GaA samples single candidate solutions from a multivariate normal distribution and continuously adapts its first and second moments (mean and covariance) such as to maximize the entropy of the search distribution. Sample-point selection is controlled by a monotonically decreasing acceptance threshold, reminiscent of the cooling schedule in SA. We describe the theoretical foundations of GaA and analyze some key features of this algorithm. We empirically show that GaA converges log-linearly on the sphere function and analyze its behavior on selected non-convex test functions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Kirkpatrick, S., Gelatt, C., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Hansen, N., Ostermeier, A.: Completely Derandomized Self-Adaption in Evolution Strategies. Evolutionary Computation 9(2), 159–195 (2001)
Kjellström, G.: Network Optimization by Random Variation of Component Values. Ericsson Technics 25(3), 133–151 (1969)
Kjellström, G., Taxen, L.: Stochastic Optimization in System Design. IEEE Trans. Circ. and Syst. 28(7) (July 1981)
Hansen, N., Kern, S.: Evaluating the CMA Evolution Strategy on Multimodal Test Functions. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 282–291. Springer, Heidelberg (2004)
Hansen, N.: The CMA Evolution Strategy: A Tutorial (2007)
Auger, A., Hansen, N.: A restart CMA evolution strategy with increasing population size. In: Proc. of IEEE Congress on Evolutionary Computation (CEC 2005), vol. 2, pp. 1769–1776 (2005)
Igel, C., Suttorp, T., Hansen, N.: A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies. In: GECCO 2006: Proceedings of the 8th annual conference on Genetic and evolutionary computation, pp. 453–460. ACM, New York (2006)
Jaynes, E.T.: Information Theory and Statistical Mechanics. Phys. Rev. 106(4), 620–630 (1957)
Kjellström, G.: On the Efficiency of Gaussian Adaptation. J. Optim. Theory Appl. 71(3) (December 1991)
Kjellström, G.: Personal communication
Kjellström, G., Taxen, L.: Gaussian Adaptation, an evolution-based efficient global optimizer. In: Comp. Appl. Math., pp. 267–276. Elsevier Science, Amsterdam (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Müller, C.L., Sbalzarini, I.F. (2010). Gaussian Adaptation Revisited – An Entropic View on Covariance Matrix Adaptation. In: Di Chio, C., et al. Applications of Evolutionary Computation. EvoApplications 2010. Lecture Notes in Computer Science, vol 6024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12239-2_45
Download citation
DOI: https://doi.org/10.1007/978-3-642-12239-2_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12238-5
Online ISBN: 978-3-642-12239-2
eBook Packages: Computer ScienceComputer Science (R0)