基于改进环拓扑混合群体智能算法的非线性方程组多根联解

A hybrid swarm intelligence with improved ring topology for nonlinear equations

求解非线性方程组要求在一次运行中同时求解(联解)其多个根,在数值计算中这是一项重要但困难的工作.为了实现非线性方程组多根求解,本文提出了一种改进的环拓扑混合群体智能算法,其主要特点是:(i)设计一种改进的环形拓扑结构,以弥补基于下标的相邻个体在搜索空间上不相邻的缺点,进而能更有效利用邻域信息;(ii)采用混合的群体智能方法以提升算法的搜索能力;(iii)引入个体重新初始化机制,以增强群体多样性.为了验证算法的性能,选择8个含有多个根的非线性方程组作为测试集.实验结果表明,所提出的方法不仅能在一次运行中找到多个根,而且与代表性算法对比,在找根率和成功率上有着显著优势.

Solving nonlinear equations(NEs) is one of the most important yet challenging tasks in numerical computation, especially for the simultaneous location of multiple roots in a single run. In this paper, a hybrid swarm intelligence approach with improved ring topology is proposed to tackle this problem. It has three main features:(i) the improved ring topology is developed to effectively use the neighborhood knowledge;(ii) the hybrid swarm intelligence enhances the search efficiency;and(iii) an individual reinitialization mechanism is proposed to enrich the population diversity. The performance of this approach is tested on eight NE problems with multiple roots, experimentally confirming that it can simultaneously locate multiple roots in a single run. In addition, it can provide better results than conventional methods in terms of both root and success rates.