Investigating the impact of sequential selection in the (1,4)-CMA-ES on the noisy BBOB-2010 testbed

Sequential selection, introduced for Evolution Strategies (ESs) with the aim of accelerating their convergence, consists in performing the evaluations of the different offspring sequentially, stopping the sequence of evaluations as soon as an offspring is better than its parent and updating the new parent to this offspring solution. This paper investigates the impact of the application of sequential selection to the (1,4)-CMA-ES on the BBOB-2010 noisy benchmark testbed. The performance of the (1,4^s)-CMA-ES, where sequential selection is implemented, is compared to the baseline algorithm (1,4)-CMA-ES. Independent restarts for the two algorithms are conducted till a maximum of 10⁴D function evaluations per trial was reached, where D is the dimension of the search space. The results show that the sequential selection within the (1,4^s)-CMA-ES clearly outperforms the baseline algorithm (1,4)-CMA-ES by at least 12% on 7 functions in 20D whereas no statistically significant worsening can be observed. Moreover, the (1,4^s)-CMA-ES shows shorter expected running times on 6 functions of up to 32% compared to the function-wise best algorithm of the BBOB-2009 benchmarking (in 20D and for a target value of 10^-7).