In this paper, we discuss a method for generating new individuals such that their mean vector and the covariance matrix are defined by formulas analogous to the covariance matrix adaptation evolution strategy (CMA-ES). In contrast to CMA-ES, which generates new individuals using multivariate Gaussian distribution with an explicitly defined covariance matrix, the introduced method uses combinations of difference vectors between archived individuals and univariate Gaussian random vectors along directions of past shifts of the population midpoints. We use this method to formulate the differential evolution strategy (DES)—an algorithm that is a crossover between differential evolution (DE) and CMA-ES. The numerical results presented in this paper indicate that DES is competitive against CMA-ES in performing both local and global optimization.

中文翻译：

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迈向无矩阵协方差矩阵适应进化策略

在本文中，我们讨论了一种生成新个体的方法，使得它们的平均向量和协方差矩阵由类似于协方差矩阵适应进化策略 (CMA-ES) 的公式定义。与使用具有明确定义的协方差矩阵的多元高斯分布生成新个体的 CMA-ES 不同，引入的方法使用存档个体之间的差异向量和沿人口中点过去移动方向的单变量高斯随机向量的组合。我们使用这种方法来制定差分进化策略 (DES)——一种在差分进化 (DE) 和 CMA-ES 之间交叉的算法。本文中的数值结果表明 DES 在执行局部和全局优化方面与 CMA-ES 相比具有竞争力。