Abstract
One goal of this book is to empirically answer the question of how efficient ES are in a setting of few function evaluations with a focus on modern ES from Sect. 2.2.2. This chapter addresses the experiments conducted and is organized as follows. Section 4.1 introduces two measures to evaluate the efficiency of ES, the fixed cost error (FCE) and the expected run time (ERT).
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
Notes
- 1.
Actually, these runs were five independent runs of the (μ,λ)-MSC-ES on the 10-dimensional sphere function (f 1 in BBOB).
- 2.
For a plus-strategy these two values are the same.
- 3.
- 4.
N. Hansen and A. Auger’s CMA-ES is available at https://www.lri.fr/~hansen/cmaes_inmatlab.html; Y. Sun’s xNES is available at http://www.idsia.ch/~tom/code/xnes.m.
- 5.
The Octave source code is available for non-commercial use at the web site of divis intelligent solutions GmbH (http://www.divis-gmbh.com/es-software.html), see Sect. 1.4.
- 6.
This allows for comparing comma and plus strategies.
- 7.
We used the free statistics software R [50] for this purpose.
- 8.
The Euclidian distance of two points uniformly drawn from a hyper box in \({\mathbb{R}}^{n}\) is distributed according to the normal distribution \(N(\sqrt{n}, 1/\sqrt{2})\) (see e.g. [53]). Hence, with increasing n the variance decreases w.r.t. the mean.
- 9.
In detail these are the (1 + 1)-ES, the (1 + 1)-Cholesky-CMA-ES and the (1 + 1)-Active-CMA-ES.
- 10.
Monotonicity for comma-strategies can be guaranteed by using the so-far best \(\Delta {f}^{{\ast}}\) instead of the \(\Delta {f}^{{\ast}}\) of the current iteration.
Bibliography
A. Auger, N. Hansen, Performance evaluation of an advanced local search evolutionary algorithm, in Proceedings of the IEEE Congress on Evolutionary Computation (CEC’05), Edinburgh, vol. 2, ed. by B. McKay et al. (IEEE, Piscataway, 2005), pp. 1777–1784
J.W. Eaton, GNU Octave Manual (Network Theory Limited, Godalming, 2002)
A.E. Eiben, M. Jelasity, A critical note on experimental research methodology in EC, in Proceedings of the 2002 Congress on Evolutionary Computation (CEC’02), Honolulu, ed. by R. Eberhart et al. (IEEE, Piscataway, 2002), pp. 582–587
N. Hansen, A. Auger, S. Finck, R. Ros, Real-parameter black-box optimization benchmarking 2010: experimental setup. Research report RR-7215, INRIA, 2010
J. Hartung, B. Elpelt, K.H. Klösener, Statistik, 14th edn. (Oldenbourg, München, 2005)
R. Li, Mixed-integer evolution strategies for parameter optimization and their applications to medical image analysis. PhD thesis, Leiden Institute of Advanced Computer Science (LIACS), Faculty of Science, Leiden University, 2009
K.V. Price, Differential evolution vs. the functions of the second ICEO, in Proceedings of the IEEE International Congress on Evolutionary Computation, Indianapolis, ed. by B. Porto et al. (IEEE, Piscataway, 1997), pp. 153–157
R Development Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, 2011. ISBN:3-900051-07-0
I. Rechenberg, Evolutionsstrategie’94 (Frommann-Holzboog, Stuttgart, 1994)
B.L. Welch, The generalization of “Student’s” problem when several different population variances are involved. Biometrika 34, 28–35 (1947)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bäck, T., Foussette, C., Krause, P. (2013). Empirical Analysis. In: Contemporary Evolution Strategies. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40137-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-40137-4_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40136-7
Online ISBN: 978-3-642-40137-4
eBook Packages: Computer ScienceComputer Science (R0)