Covariance matrix adaptation evolution strategy (CMA-ES) is a successful gradient-free optimization algorithm. Yet, it can hardly scale to handle high-dimensional problems. In this paper, we propose a fast variant of CMA-ES (Fast CMA-ES) to handle large-scale black-box optimization problems. We approximate the covariance matrix by a low-rank matrix with a few vectors and use two of them to generate each new solution. The algorithm achieves linear internal complexity on the dimension of search space. We illustrate that the covariance matrix of the underlying distribution can be considered as an ensemble of simple models constructed by two vectors. We experimentally investigate the algorithm's behaviors and performances. It is more efficient than the CMA-ES in terms of running time. It outperforms or performs comparatively to the variant limited memory CMA-ES on large-scale problems. Finally, we evaluate the algorithm's performance with a restart strategy on the CEC'2010 large-scale global optimization benchmarks, and it shows remarkable performance and outperforms the large-scale variants of the CMA-ES.

中文翻译：

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快速协方差矩阵自适应，可进行大规模黑箱优化。

协方差矩阵适应进化策略（CMA-ES）是一种成功的无梯度优化算法。但是，它很难扩展以解决高维问题。在本文中，我们提出了一种CMA-ES的快速变体（快速CMA-ES）来处理大规模黑箱优化问题。我们通过带有几个向量的低秩矩阵来近似协方差矩阵，并使用其中的两个来生成每个新的解。该算法在搜索空间维度上实现了线性内部复杂度。我们说明了基础分布的协方差矩阵可以看作是由两个向量构成的简单模型的集合。我们通过实验研究了该算法的行为和性能。就运行时间而言，它比CMA-ES更高效。在大规模问题上，它的性能优于或优于变型有限内存CMA-ES。最后，我们在CEC'2010大规模全球优化基准测试中使用重新启动策略评估了算法的性能，该算法显示了出众的性能，并且胜过了CMA-ES的大型变体。