Benchmarking the (1,4)-CMA-ES With Mirrored Sampling and Sequential Selection on the Noiseless BBOB-2010 Testbed

Anne Auger (1) , Dimo Brockhoff (1) , Nikolaus Hansen (1)

1 TAO - Machine Learning and Optimisation

The well-known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a robust stochastic search algorithm for optimizing functions defined on a continuous search space $\R^{D}$. Recently, mirrored samples and sequential selection have been introduced within CMA-ES to improve its local search performances. In this paper, we benchmark the (1,4$_m^s$)-CMA-ES which implements mirrored samples and sequential selection on the BBOB-2010 noiseless testbed. Independent restarts are conducted until a maximal number of $10^{4} D$ function evaluations is reached. The experiments show that 11 of the 24 functions are solved in 20D (and 13 in 5D respectively). Compared to the function-wise target-wise best algorithm of the BBOB-2009 benchmarking, on 25% of the functions the (1,4$_m^s$)-CMA-ES is at most by a factor of 3.1 (and 3.8) slower in dimension 20 (and 5) for targets associated to budgets larger than $10D$. Moreover, the (1,4$_m^s$)-CMA-ES slightly outperforms the best algorithm on the rotated ellipsoid function in 20D and would be ranked two on the Gallagher function with 101 peaks in 10D and 20D---being 25 times faster than the BIPOP-CMA-ES and about 3 times faster than the (1+1)-CMA-ES on this function.

Domains: Neural and Evolutionary Computing [cs.NE]

Anne Auger, Dimo Brockhoff, Nikolaus Hansen. Benchmarking the (1,4)-CMA-ES With Mirrored Sampling and Sequential Selection on the Noiseless BBOB-2010 Testbed. GECCO workshop on Black-Box Optimization Benchmarking (BBOB'2010), Jul 2010, Portland, OR, United States. pp.1617-1624, ⟨10.1145/1830761.1830781⟩. ⟨inria-00502439⟩