The Overview of Learning Mechanism of Covariance Matrix Adaptation Evolution Strategy

LI Huan-zhe; WU Zhi-jian; WANG Shen-wen; GUO Zhao-lu

doi:10.3969/j.issn.0372-2112.2017.01.033

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The Overview of Learning Mechanism of Covariance Matrix Adaptation Evolution Strategy

更新时间：2025-07-16

- The Overview of Learning Mechanism of Covariance Matrix Adaptation Evolution Strategy
- Acta Electronica Sinica Vol. 45, Issue 1, Pages: 238-245(2017)
- 作者机构：
  
  1. 武汉大学计算机学院软件工程国家重点实验室,湖北,武汉,430072
  2. 河北地质大学信息工程学院,河北,石家庄,050031
  3. 江西理工大学理学院,江西,赣州,341000
  4. 武汉大学计算机学院软件工程国家重点实验室,湖北,武汉,430072
  5. 河北地质大学信息工程学院,河北,石家庄,050031
  6. 江西理工大学理学院,江西,赣州,341000
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2017.01.033
  CLC： TP18
- Published Online：25 January 2017，
  
  Published：2017
- 稿件说明：
移动端阅览
LI Huan-zhe, WU Zhi-jian, WANG Shen-wen, et al. The Overview of Learning Mechanism of Covariance Matrix Adaptation Evolution Strategy[J]. Acta Electronica Sinica, 2017, 45(1): 238-245.
DOI：

LI Huan-zhe, WU Zhi-jian, WANG Shen-wen, et al. The Overview of Learning Mechanism of Covariance Matrix Adaptation Evolution Strategy[J]. Acta Electronica Sinica, 2017, 45(1): 238-245. DOI： 10.3969/j.issn.0372-2112.2017.01.033.

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.

Abstract

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 ill-conditioned 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.

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