Research on Convergence of Grey Wolf Optimization Algorithm Based on Markov Chain

ZHANG Meng-jian; LONG Dao-yin; WANG Xiao; YANG Jing

doi:10.3969/j.issn.0372-2112.2020.08.018

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Research on Convergence of Grey Wolf Optimization Algorithm Based on Markov Chain

更新时间：2025-07-16

- Research on Convergence of Grey Wolf Optimization Algorithm Based on Markov Chain
- Acta Electronica Sinica Vol. 48, Issue 8, Pages: 1587-1595(2020)
- 作者机构：
  
  1. 贵州大学电气工程学院,贵州,贵阳,550025
  2. 中国电建集团贵州工程有限公司,贵州,贵阳,550001
  3. 贵州大学电气工程学院,贵州,贵阳,550025
  4. 中国电建集团贵州工程有限公司,贵州,贵阳,550001
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61861007, No.61640014);Science and Technology Support Project of Guizhou Province (No.[2019]2152, No.[2017]2520-1);Postgraduate Innovation Fund of Guizhou Province (No.YJSCXJH[2019]005);Case Base of Internet of Things Theory and Application in Guizhou Province (No.KCALK201708);Discipline Construction in Guizhou Province (No.ZDXK[2015]8)
- DOI：10.3969/j.issn.0372-2112.2020.08.018
  CLC： TP301.6
- Published Online：25 August 2020，
  
  Published：2020
- 稿件说明：
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ZHANG Meng-jian, LONG Dao-yin, WANG Xiao, et al. Research on Convergence of Grey Wolf Optimization Algorithm Based on Markov Chain[J]. Acta Electronica Sinica, 2020, 48(8): 1587-1595.
DOI：

ZHANG Meng-jian, LONG Dao-yin, WANG Xiao, et al. Research on Convergence of Grey Wolf Optimization Algorithm Based on Markov Chain[J]. Acta Electronica Sinica, 2020, 48(8): 1587-1595. DOI： 10.3969/j.issn.0372-2112.2020.08.018.

摘要

针对灰狼优化算法（Grey Wolf Optimization，GWO）在收敛性研究上的不足，首先，通过定义灰狼群状态转移序列，建立了GWO算法的马尔科夫（Markov）链模型，通过分析Markov链的性质，证明它是有限齐次 Markov链；其次，通过分析灰狼群状态序列最终转移状态，结合随机搜索算法的收敛准则，验证了GWO算法的全局收敛性；最后，对典型测试函数、偏移函数及旋转函数进行仿真实验，并与多种群体智能算法进行对比分析.实验结果表明，GWO算法具有全局收敛性强、计算耗时短和寻优精度高等优势.

Abstract

The global convergence is one of the important features of an intelligent algorithm. In this paper

we take the initiative to handle the convergence of Grey Wolf Optimization (GWO) with Markov chain. Firstly

a Markov chain model of the GWO algorithm is established through defining the state transition sequence of a gray wolf population. Analyzing the properties of the Markov chain proves that it is homogeneous finite. Secondly

based on the convergence criteria of random search algorithms

the global convergence of the GWO algorithm is verified via analyzing the final state transition sequence of the grey wolf population. Finally

simulation studies on typical testing functions

shifting functions and rotating functions are carried out comparing with a few typical swarm intelligent algorithms. The experimental results show that the GWO algorithm has excellent performance on the global convergence

the computational time and precision of optimization.

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