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）是解决黑箱连续优化问题最成功的算法之一。CMA-ES的一个实用特性是可免于超参数调参直接使用。然而，超参数设置仍具有显著影响，尤其在求解多模态或噪声问题等困难任务时。本研究探讨了采用默认种群规模的CMA-ES能否有效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，通过动态调整学习率以维持恒定的信噪比。通过数值实验考察所提学习率自适应机制下CMA-ES的行为特征，并与固定学习率CMA-ES的优化结果进行对比。实验结果表明，采用所提学习率自适应机制时，默认种群规模的CMA-ES能够在无需繁琐学习率调参的前提下，有效处理多模态及/或噪声问题。