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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报

• • 上一篇    下一篇

多根非线性方程组求解的探路者灰狼算法

逯  苗,   曲良东,   何登旭   

  1. 广西民族大学数学与物理学院，南宁 530006
  • 出版日期:2022-12-15 发布日期:2022-12-15
  • 通讯作者: 何登旭 E-mail: dengxuhe@126.com
  • 基金资助:
    国家自然科学基金 (11961006).

Pathfinder Grey Wolf Algorithm for Solving Multiple-roots Nonlinear Equations

LU Miao,   QU Liangdong,   HE Dengxu   

  1. School of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006
  • Online:2022-12-15 Published:2022-12-15
  • Contact: D. He. E-mail address: dengxuhe@126.com
  • Supported by:
    The National Natural Science Foundation of China (11961006).

PDF (PC)

170

摘要：

针对传统算法在多根非线性方程组求解时依赖初始值的选定，求解个数不完全，求解精度不高的问题，提出了一种结合探路者算法的灰狼优化算法 (PGWO)。由于灰狼优化算法存在后期收敛速度慢等问题，结合了探路者算法，根据探路者中跟随者的更新机制对灰狼个体的位置进行改变，进而平衡算法的全局搜索和局部搜索能力。通过 9 组多根非线性方程组的仿真实验结果和其他群智能算法进行比较，实验结果表明 PGWO 算法提高了多根非线性方程组求解的精度，在求解个数上得到明显提升，进而说明了算法的有效性。

关键词: 多根非线性方程组, 探路者算法, 灰狼优化算法, 仿真实验

Abstract:

In order to overcome the shortcomings of traditional algorithms such as depending on the selection of initial value, the non-complete number of solutions and the poor solution accuracy, a gray wolf optimization algorithm combined with pathfinder algorithm (PGWO) is proposed. Due to the slow convergence speed of the gray wolf optimization algorithm, this paper combines the pathfinder algorithm to modify the position of an individual gray wolf according to the update mechanism of the follower in the pathfinder algorithm, so as to balance the global search and local search abilities of the algorithm. Finally, the simulation results of nine groups of multi-roots nonlinear equations are compared with other swarm intelligent algorithms. The experimental results show that the PGWO method improves the solution accuracy of multi-roots nonlinear equations, and the number of solutions is significantly improved, which further proves the effectiveness of the proposed algorithm.

Key words: multiple-roots nonlinear equations, pathfinder algorithm, gray wolf optimization algorithm, simulation experiment

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