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

The Covariance-Matrix-Adaptation Evolution-Strategy (CMA-ES) is a robust stochastic search algorithm for op-timizing functions defined on a continuous search space RD. Recently, mirrored samples and sequential selection have been introduced within CMA-ES to improve its local search performances. In this paper, we benchmark the (1,4sm)-CMA-ES which implements mirrored samples and sequen-tial selection on the BBOB-2010 noisy testbed. Independent restarts are conducted until a maximal number of 104D func-tion evaluations is reached. Although the tested (1,4sm)-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 (1,4sm)-CMA-ES in 20D, we see a large improve-ment over the best algorithm of the BBOB-2009 benchmark-ing 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