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.

翻译：协方差矩阵自适应进化策略（CMA-ES）是求解黑箱连续优化问题最成功的方法之一。CMA-ES在实际应用中的优势在于无需超参数调优即可使用。然而，超参数设置仍具有显著影响，尤其是在处理多模态或噪声问题等复杂任务时。本研究探讨了采用默认种群规模的CMA-ES能否解决多模态与噪声问题。为此，我们提出了一种新颖的CMA-ES学习率自适应机制，通过调整学习率以维持恒定的信噪比。通过数值实验研究了采用所提学习率自适应机制的CMA-ES的行为，并将其结果与固定学习率的CMA-ES进行了对比。结果表明，当采用所提学习率自适应机制时，默认种群规模的CMA-ES能够有效处理多模态和/或噪声问题，且无需进行极其繁重的学习率调优。