Mirrored Variants of the (1,2)-CMA-ES Compared on the Noisy BBOB-2010 Testbed

Anne Auger 1 Dimo Brockhoff 1, * Nikolaus Hansen 1
* Corresponding author
1 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : Derandomization by means of mirrored samples has been recently introduced to enhance the performances of $(1,\lambda)$ and $(1+2)$ Evolution-Strategies (ESs) with the aim of designing fast local search stochastic algorithms. In this paper, we investigate the impact of mirrored samples for noisy optimization. Since elitist selection is detrimental for noisy optimization, we investigate non-elitist ESs only here. We compare on the BBOB-2010 noisy benchmark testbed two variants of the (1,2)-CMA-ES where mirrored samples are implemented with the baseline (1,2)-CMA-ES. Each algorithm implements a restart mechanism. A total budget of $10^{4} D$ function evaluations per trial has been used, where $D$ is the dimension of the search space. The experiments clearly show a ranking among the three algorithms: both mirroring variants have lower expected running times than the (1,2)-CMA-ES by at least 50% on 5 functions and they solve three additional functions in 20D that the (1,2)-CMA-ES cannot solve (or only with small probability). The comparison between the two mirroring variants is in favor of the algorithm employing a sequential selection in addition---outperforming the algorithm with only mirrored samples on five functions by at least 17% whereas no statistically significant worsening can be observed. Both algorithms using mirrored samples also outperform the function-wise best algorithm of the BBOB-2009 benchmarking on three (respectively four) functions comprising Cauchy noise by up to 65%.
Document type :
Conference papers
Complete list of metadatas

https://hal.inria.fr/inria-00502436
Contributor : Dimo Brockhoff <>
Submitted on : Wednesday, July 14, 2010 - 10:33:43 PM
Last modification on : Thursday, April 5, 2018 - 12:30:12 PM
Long-term archiving on : Friday, October 15, 2010 - 3:31:17 PM

Files

ws1p20-augerAuthorVersion.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Anne Auger, Dimo Brockhoff, Nikolaus Hansen. Mirrored Variants of the (1,2)-CMA-ES Compared on the Noisy BBOB-2010 Testbed. GECCO workshop on Black-Box Optimization Benchmarking (BBOB'2010), Jul 2010, Portland, OR, United States. pp.1575-1582, ⟨10.1145/1830761.1830775⟩. ⟨inria-00502436⟩

Share

Metrics

Record views

360

Files downloads

124