Benchmarking the (1,4)-CMA-ES with mirrored sampling and sequential selection on the noisy BBOB-2010 testbed

The 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 noisy testbed. Independent restarts are conducted until a maximal number of 10⁴D function evaluations is reached. Although the tested (1,4_m^s)-CMA-ES is only a local search strategy, it solves 8 of the noisy BBOB-2010 functions in 20D and 9 of them in 5D for a target of 10^-8. There is also one additional function in 20D and 5 additional functions in 5D where a successful run for at least one of the 15 instances can be reported. Moreover, on 7 of the 8 functions that are solved by the (1,4_m^s)-CMA-ES in 20D, we see a large improvement over the best algorithm of the BBOB-2009 benchmarking for the corresponding functions - ranging from an 37% improvement on the sphere with moderate Cauchy noise to a speed-up by a factor of about 3 on the Gallagher function with Cauchy noise.