协方差矩阵自适应演化策略学习机制综述

摘要

基于协方差矩阵自适应(CMA)的演化策略算法(ES)是一种优秀的、不依赖于梯度信息的随机局部优化算法.基于CMA的学习机制使其对搜索空间的任意可逆线性变换具有不变性,对于病态的、高度不可分的问题有优秀的求解能力.CMA学习机制具有较强的数学理论基础,这对设计其他演化算法有很好的借鉴意义.本文旨在详细分析CMA-ES的各种学习机制,并给出其所依赖的主要理论基础.最后通过实验比较CMA-ES各种变体的优势与不足,并着重比较本文改进的CMA-ES变体与其它变体在性能上的差异.%The evolution strategy (ES) based on covariance matrix adaptation (CMA) is an excellent,gradient-free stochastic local optimization method.The learning mechanism based on CMA enables evolution strategy algorithm to have invariance to any invertible linear transformation of the search space,and to have outstanding capability for solving the illconditioned and/or highly non-separable problems.The learning mechanism of CMA has a solid theoretical foundation in mathematics,which may have a certain reference significance to guide the design of other evolutionary algorithms.This paper aims at analyzing the learning mechanisms of CMA-ES in detail,and providing its main mathematical foundations.Finally,the advantages and disadvantages of various CMA-ES variants are compared by a series of experiments,and the difference in performance is compared seriously between our improved variant and other CMA-ES variants.