求解非线性方程组的智能优化算法综述

非线性方程组的求解是优化领域的一个重要研究课题.近年来,利用智能优化算法求解非线性方程组已成为一个重要方向.首先介绍非线性方程组的定义;其次,根据智能优化算法求解非线性方程组问题的基本框架,从转化方法和智能优化算法两方面入手,对求解非线性方程组的算法的研究进展进行归纳总结;再次,对非线性方程组的测试函数及评价指标进行描述,对比了5个具有代表性算法的性能,分析了目前利用智能优化算法求解非线性方程组亟待解决的问题;最后,指出值得进一步研究的方向.

Overview of intelligent optimization algorithms for solving nonlinear equation systems

Solving nonlinear equation systems is an important research topic in optimization field. In recent years, using intelligent optimization algorithms to solve nonlinear equation systems has become an important research area. In this paper, the definition of nonlinear equation systems is firstly introduced. And then, based on the basic principles of intelligent optimization algorithms for solving nonlinear equations, state-of-the-art algorithms of solving nonlinear equation systems are surveyed from the aspects of transformation methods and intelligent optimization algorithms. In addition, the benchmark test functions and performance criteria of nonlinear equation systems are described, and the performances of five representative algorithms are compared, meanwhile, the problems that need to be solved are analyzed. Finally, the open research issues in this field are pointed out.