鲸鱼优化算法的全局收敛性分析及参数选择研究

Global convergence analysis and research on parameter selection of whale optimization algorithm

中文关键词  鲸鱼优化算法  马尔科夫链  依概率收敛  差分方程  参数选择

英文关键词  whale optimization algorithm  Markov chain  convergence in probability  difference equation  parameter selection

中文摘要

      鲸鱼优化算法是一种设计新颖的智能优化算法, 近年来已广泛应用于各种工程优化问题. 但是关于鲸鱼优 化算法的收敛性尚未明确, 而且缺乏对算法中合理参数选择范围的理论分析. 本文利用随机过程理论中的马尔科夫 链分析了鲸鱼优化算法的全局收敛性, 证明了算法中的收缩包围机制是决定鲸鱼优化算法是否收敛的关键因素. 进 一步建立了鲸鱼优化算法收缩包围机制的双层有限差分模型, 并基于冯诺依曼稳定准则给出了算法收缩包围机制 稳定或发散时的控制参数取值范围, 在标准测试函数上的仿真实验结果也验证了理论分析的正确性.

英文摘要

      The whale optimization algorithm (WOA) is a novel swarm intelligence algorithm which has been widely used in different applications. However, the convergence property and the reasonable parameter selection approach ofWOA is ambiguity. This paper analyzes the global Convergence property of WOA by using the Markov chain of the stochastic process theory. It’s proved that the convergence property of WOA is determined by its shrinking encircling mechanism. Moreover, the two level finite difference scheme of WOA is established. The stable range and unstable range of control parameters in shrinking encircling mechanism are given based on von Neumann stability criterion. The simulation results on benchmark functions verify the validity of the theoretical analysis of WOA.