Mirrored Variants of the (1,4)-CMA-ES Compared on the Noiseless BBOB-2010 Testbed

Anne Auger 1 Dimo Brockhoff 1, * Nikolaus Hansen 1
* Corresponding author
1 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 : Derandomization by means of mirrored samples has been recently introduced to enhance the performances of $(1,\lambda)$-Evolution-Strategies (ESs) with the aim of designing fast and robust stochastic local search algorithms. This paper compares on the BBOB-2010 noiseless benchmark testbed two variants of the (1,4)-CMA-ES where the mirrored samples are used. Independent restarts are conducted up to a total budget of $10^{4} D$ function evaluations, where $D$ is the dimension of the search space. The results show that the improved variants are significantly faster than the baseline (1,4)-CMA-ES on 4 functions in 20D (respectively 7 when using sequential selection in addition) by a factor of up to 3 (on the attractive sector function). In no case, the (1,4)-CMA-ES is significantly faster on any tested target function value in 5D and 20D. Moreover, the algorithm employing both mirroring and sequential selection is significantly better than the algorithm without sequentialism on five functions in 20D with expected running times that are about 20% smaller.
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Anne Auger, Dimo Brockhoff, Nikolaus Hansen. Mirrored Variants of the (1,4)-CMA-ES Compared on the Noiseless BBOB-2010 Testbed. GECCO workshop on Black-Box Optimization Benchmarking (BBOB'2010), Jul 2010, Portland, OR, United States. pp.1559-1566, ⟨10.1145/1830761.1830773⟩. ⟨inria-00502437⟩

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