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

Anne Auger 1 Dimo Brockhoff 1, * Nikolaus Hansen 1
* Auteur correspondant
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.
Type de document :
Communication dans un congrès
GECCO workshop on Black-Box Optimization Benchmarking (BBOB'2010), Jul 2010, Portland, OR, United States. pp.1543-1550, 2010, GECCO (Companion) 2010. 〈10.1145/1830761.1830772〉
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https://hal.inria.fr/inria-00502430
Contributeur : Dimo Brockhoff <>
Soumis le : mercredi 14 juillet 2010 - 21:03:36
Dernière modification le : jeudi 5 avril 2018 - 12:30:12
Document(s) archivé(s) le : vendredi 15 octobre 2010 - 15:27:59

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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, 2010, GECCO (Companion) 2010. 〈10.1145/1830761.1830772〉. 〈inria-00502430〉

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