基于鞅论的灰狼优化算法全局收敛性分析
作者:
作者单位:

河南工业大学

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中图分类号:

TP273

基金项目:

国家自然科学基金(61803146,61973104)、河南省优秀青年科学基金(212300410036)、河南省高校科技创新人才支持计划(21HASTIT029)、河南省高等学校青年骨干教师培养计划(2019GGJS089)、河南省青年人才托举工程项目(2019HYTP005)、河南省科技攻关项目(212102210169,212102210086)、河南省高等教育教学改革研究与实践项目(2019SJGLX270)、河南工业大学自科创新基金支持计划(2020ZKCJ06)、河南工业大学青年骨干教师培育计划(21420080)、粮食信息处理与控制教育部重点实验室开放基金(KFJJ2020107,KFJJ2020111,KFJJ2020114)、河南工业大学本科教育教学改革研究与实践项目(JXYJ2019009)


Global Convergence Analysis of Grey Wolf Optimization Algorithm Based on Martingale Theory
Author:
Affiliation:

Henan University of Technology

Fund Project:

The National Natural Science Foundation of China(61803146,61973104),The Henan Excellent Young Scientists Fund (212300410036),The Program for Science and Technology Innovation Talents in Universities of Henan Province(21HASTIT029),The Training Program for Young Backbone Teachers in Universities of Henan Province(2019GGJS089),the Henan Province Young Talent Support Project(2019HYTP005),The Key Science and Technology Projects in Henan Province(212102210169,212102210086),The Research and Practice Project of Higher Education Teaching Reform in Henan Province(2019SJGLX270),The Innovative Funds Plans of Henan University of Technology(2020ZKCJ06),the Cultivation Program of Young Backbone Teachers in Henan University of Technology(21420080),The Open Fund from Research Platform of Grain Information Processing Center in Henan University of Technology(KFJJ2020107,KFJJ2020111,KFJJ2020114),The Research and Practice Project of Undergraduate Education Reform in Henan University of Technology(JXYJ2019)

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    摘要:

    灰狼优化(Grey Wolf Optimization, GWO)算法是一种基于群体智能的随机优化算法,已成功地应用于许多 复杂的优化问题的求解.当前GWO算法有很多改进形式,但缺少严谨的收敛性分析,导致改进后的算法不具备理 论支撑.为了弥补这一不足,本文首次运用鞅论分析其收敛性.首先,根据GWO算法原理建立其基本的数学模型.通 过定义灰狼状态空间及灰狼群状态空间,建立了GWO算法的Markov链模型,并分析了该算法的Markov性质.其 次,介绍了鞅理论,推导出一个上鞅作为最优适应度值的群进化序列.然后,运用上鞅收敛定理,并结合其Markov性 对GWO算法进行收敛性分析.证明GWO算法能以1的可能性达到全局收敛.最后,通过数值实验验证其收敛性 能.实验结果表明,GWO算法具有全局收敛性强、计算耗时较低、寻优精度高等特点.

    Abstract:

    Grey Wolf Optimization (GWO) algorithm is a stochastic optimization algorithm based on swarm intelligence that has been successfully applied to solve many complex optimization problems. At present, there are many improved forms of the GWO algorithm, but the lack of rigorous convergence analysis leads to the improved algorithm does not have theoretical support. In order to make up for this deficiency, In this paper, martingale theory is used to analyze its convergence for the first time. Firstly, the basic mathematical model is established according to the principle of the GWO algorithm. By defining the gray wolf state space and the gray wolf group state space, the Markov chain model of the GWO algorithm is established, and the Markov properties of the algorithm are analyzed. Secondly, the martingale theory is introduced, a swarm evolution sequence with the supermartingale as the optimal fitness value is derived. Then, the convergence of the GWO algorithm is analyzed by using the supermartingale convergence theorem and its Markov properties. It is proved that the GWO algorithm can achieve global convergence with the possibility of 1. Finally, the convergence performance is verified by numerical experiments. The experimental results show that the GWO algorithm has strong global convergence, low computation time and high optimization accuracy.

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历史
  • 收稿日期:2021-04-15
  • 最后修改日期:2021-07-28
  • 录用日期:2021-07-30
  • 在线发布日期: 2021-09-01
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