  The covariance matrix adaptation evolution strategy (CMA-ES) is one of the
most successful methods for solving black-box continuous optimization problems.
One practically useful aspect of the CMA-ES is that it can be used without
hyperparameter tuning. However, the hyperparameter settings still have a
considerable impact, especially for difficult tasks such as solving multimodal
or noisy problems. In this study, we investigate whether the CMA-ES with
default population size can solve multimodal and noisy problems. To perform
this investigation, we develop a novel learning rate adaptation mechanism for
the CMA-ES, such that the learning rate is adapted so as to maintain a constant
signal-to-noise ratio. We investigate the behavior of the CMA-ES with the
proposed learning rate adaptation mechanism through numerical experiments, and
compare the results with those obtained for the CMA-ES with a fixed learning
rate. The results demonstrate that, when the proposed learning rate adaptation
is used, the CMA-ES with default population size works well on multimodal
and/or noisy problems, without the need for extremely expensive learning rate
tuning.
