Simplify Your Covariance Matrix Adaptation Evolution Strategy
提出一种矩阵自适应进化策略（MA-ES），通过消除一条进化路径和协方差矩阵本身来简化标准CMA-ES，在标准测试函数上性能几乎不变，并可用于双种群搜索。
The standard covariance matrix adaptation evolution strategy (CMA-ES) comprises two evolution paths, one for the learning of the mutation strength and one for the rank-1 update of the covariance matrix. In this paper, it is shown that one can approximately transform this algorithm in such a manner that one of the evolution paths and the covariance matrix itself disappear. That is, the covariance update and the covariance matrix square root operations are no longer needed in this novel so-called matrix adaptation (MA) ES. The MA-ES performs nearly as well as the original CMA-ES. This is shown by empirical investigations considering the evolution dynamics and the empirical expected runtime on a set of standard test functions. Furthermore, it is shown that the MA-ES can be used as a search engine in a bi-population (BiPop) ES. The resulting BiPop-MA-ES is benchmarked using the BBOB comparing continuous optimizers (COCO) framework and compared with the performance of the CMA-ES-v3.61 production code. It is shown that this new BiPop-MA-ES-while algorithmically simpler-performs nearly equally well as the CMA-ES-v3.61 code.