电子学报 ›› 2020, Vol. 48 ›› Issue (8): 1587-1595.DOI: 10.3969/j.issn.0372-2112.2020.08.018

• 学术论文 • 上一篇    下一篇

基于马尔科夫链的灰狼优化算法收敛性研究

张孟健1, 龙道银2, 王霄1, 杨靖1   

  1. 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
  • 收稿日期:2019-11-13 修回日期:2020-02-18 出版日期:2020-08-25 发布日期:2020-08-25
  • 通讯作者: 杨靖
  • 作者简介:张孟健 男,1996年出生于安徽芜湖,贵州大学电气工程学院硕士研究生,研究方向为群体智能优化算法、无线传感器网络. E-mail:2311082906@qq.com
  • 基金资助:
    国家自然科学基金(No.61861007,No.61640014);贵州省科技支撑计划(No.[2019]2152,No.[2017]2520-1);贵州省研究生创新基金(No.YJSCXJH[2019]005);贵州省物联网理论与应用案例库(No.KCALK201708);贵州省学科建设(No.ZDXK[2015]8)

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

ZHANG Meng-jian1, LONG Dao-yin2, WANG Xiao1, YANG Jing1   

  1. 1. Electrical Engineering College, Guizhou University, Guiyang, Guizhou 550025, China;
    2. Power China Guizhou Engineering Company Limited, Guiyang, Guizhou 550001, China
  • Received:2019-11-13 Revised:2020-02-18 Online:2020-08-25 Published:2020-08-25

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.

关键词: 灰狼优化, 灰狼群状态空间, 马尔科夫链, 状态转移概率, 收敛准则

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.

Key words: Grey Wolf Optimization, grey wolf population state space, Markov chain, state transition probability, convergence criteria

中图分类号: