Graceful Scaling on Uniform Versus Steep-Tailed Noise
Recently, different evolutionary algorithms (EAs) have been analyzed in noisy environments. The most frequently used noise model for this was additive posterior noise (noise added after the fitness evaluation) taken from a Gaussian distribution. In particular, for this setting it was shown that the \((\mu +1)\)-EA on OneMax does not scale gracefully (higher noise cannot efficiently be compensated by higher \(\mu \)).
In this paper we want to understand whether there is anything special about the Gaussian distribution which makes the \((\mu +1)\)-EA not scale gracefully. We keep the setting of posterior noise, but we look at other distributions. We see that for exponential tails the \((\mu +1)\)-EA on OneMax does also not scale gracefully, for similar reasons as in the case of Gaussian noise. On the other hand, for uniform distributions (as well as other, similar distributions) we see that the \((\mu +1)\)-EA on OneMax does scale gracefully, indicating the importance of the noise model.
KeywordsEvolutionary algorithm Noisy fitness Theory
The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 618091 (SAGE) and the German Research Foundation (DFG) under grant agreement no. FR 2988 (TOSU).
- 2.Dang, D.-C., Lehre, P.K.: Evolution under partial information. In: Proceedings of GECCO 2014, pp. 1359–1366 (2014)Google Scholar
- 3.Doerr, B., Hota, A., Kötzing, T.: Ants easily solve stochastic shortest path problems. In: Proceedings of GECCO 2012, pp. 17–24 (2012)Google Scholar
- 5.Feldmann, M., Kötzing, T.: Optimizing expected path lengths with ant colony optimization using fitness proportional update. In: Proceedings of FOGA 2013, pp. 65–74 (2013)Google Scholar
- 7.Gießen, C., Kötzing, T.: Robustness of populations in stochastic environments. In: Proceedings of GECCO 2014, pp. 1383–1390 (2014)Google Scholar
- 11.Lehre, P.K.: Negative drift in populations. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 244–253. Springer, Heidelberg (2010)Google Scholar
- 12.Prügel-Bennett, A., Rowe, J.E., Shapiro, J.: Run-time analysis of population-based evolutionary algorithm in noisy environments. In: Proceedings of FOGA 2015, pp. 69–75 (2015)Google Scholar
- 14.Witt, C.: Runtime analysis of the \((\mu + 1)\) EA on simple pseudo-boolean functions. Evol. Comput. 14, 65–86 (2006)Google Scholar