Comparing Mirrored Mutations and Active Covariance Matrix Adaptation in the IPOP-CMA-ES on the Noiseless BBOB Testbed

Dimo Brockhoff 1, * Anne Auger 2 Nikolaus Hansen 2
* Corresponding author
1 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
2 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : This paper investigates two variants of the well-known Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Active covariance matrix adaptation allows for negative weights in the covariance matrix update rule such that "bad" steps are (actively) taken into account when updating the covariance matrix of the sample distribution. On the other hand, mirrored mutations via selective mirroring also take the "bad" steps into account. In this case, they are first evaluated when taken in the opposite direction (mirrored) and then considered for regular selection. In this study, we investigate the difference between the performance of the two variants empirically on the noiseless BBOB testbed. The CMA-ES with selectively mirrored mutations only outperforms the active CMA-ES on the sphere function while the active variant statistically significantly outperforms mirrored mutations on 10 of 24 functions in several dimensions.
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Dimo Brockhoff, Anne Auger, Nikolaus Hansen. Comparing Mirrored Mutations and Active Covariance Matrix Adaptation in the IPOP-CMA-ES on the Noiseless BBOB Testbed. GECCO Companion '12, Jul 2012, Philadelphia, PA, United States. pp.297-303, ⟨10.1145/2330784.2330827⟩. ⟨hal-00746120⟩

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