# Comparing the (1+1)-CMA-ES with a Mirrored (1+2)-CMA-ES with Sequential Selection on the Noiseless BBOB-2010 Testbed

* 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 : In this paper, we compare the (1+1)-CMA-ES to the (1+2$_m^s$)-CMA-ES, a recently introduced quasi-random (1+2)-CMA-ES that uses mirroring as derandomization technique as well as a sequential selection. Both algorithms were tested using independent restarts till a total number of function evaluations of $10^{4} D$ was reached, where $D$ is the dimension of the search space. On the non-separable ellipsoid function in dimension 10, 20 and 40, the performances of the (1+2$_m^s$)-CMA-ES are better by 17% than the best performance among algorithms tested during BBOB-2009 (for target values of $10^{-5}$ and $10^{-7}$). Moreover, the comparison shows that the (1+2$_m^s$)-CMA-ES variant improves the performance of the (1+1)-CMA-ES by about 20% on the ellipsoid, the discus, and the sum of different powers functions and by 12% on the sphere function. Besides, we never observe statistically significant results where the (1+2$_m^s$)-CMA-ES is worse than the (1+1)-CMA-ES.
Document type :
Conference papers
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https://hal.inria.fr/inria-00502430
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Submitted on : Wednesday, July 14, 2010 - 9:03:36 PM
Last modification on : Friday, January 7, 2022 - 5:48:03 PM
Long-term archiving on: : Friday, October 15, 2010 - 3:27:59 PM

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### Citation

Anne Auger, Dimo Brockhoff, Nikolaus Hansen. Comparing the (1+1)-CMA-ES with a Mirrored (1+2)-CMA-ES with Sequential Selection on the Noiseless BBOB-2010 Testbed. GECCO workshop on Black-Box Optimization Benchmarking (BBOB'2010), Jul 2010, Portland, OR, United States. pp.1543-1550, ⟨10.1145/1830761.1830772⟩. ⟨inria-00502430⟩

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