This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. In contract to the Gaussian sampling in CMA-ES, the proposed method generates mutation vectors from a mixture model, which facilitates exploiting the rich variable correlations of the problem landscape within a limited time budget. We analyze the probability distribution of this mixture model and show that it approximates the Gaussian distribution of CMA-ES with a controllable accuracy. We use this sampling method, coupled with a novel method for mutation strength adaptation, to formulate the mixture model-based evolution strategy (MMES)—a CMA-ES variant for large-scale optimization. The numerical simulations show that, while significantly reducing the time complexity of CMA-ES, MMES preserves the rotational invariance, is scalable to high dimensional problems, and is competitive against the state-of-the-arts in performing global optimization.

中文翻译：

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MMES：基于混合模型的大规模优化进化策略

这项工作为大规模设置中的协方差矩阵适应进化策略（CMA-ES）提供了一种有效的采样方法。与CMA-ES中的高斯抽样相一致，所提出的方法从混合模型生成突变向量，这有助于在有限的时间预算内利用问题态势的丰富变量相关性。我们分析了这种混合模型的概率分布，并表明它以可控的精度近似了CMA-ES的高斯分布。我们使用这种采样方法，结合突变强度适应的新方法，来制定基于混合模型的进化策略（MMES），这是一种用于大规模优化的CMA-ES变体。数值模拟表明，在显着降低CMA-ES的时间复杂度的同时，