基于牛顿法和遗传算法求解非线性方程组的混合计算智能方法

A HYBRID COMPUTATIONAL INTELLIGENT ALGORITHM FOR NONLINEAR EQUATIONS BASED ON NEWTONIAN ALGORITHM AND GENETIC ALGORITHM

本文针对牛顿法的局部收敛性而容易导致求解失败，先讨论在全局空间搜索解的非线性方程组遗传算法（ＧＡ）。然后针对ＧＡ收敛慢，通过定义牛顿算子，适应度函数和选择算子，从而得到结合ＧＡ和牛顿法两者长处，既有较快收敛性，又能以较大概率求解非线性方程组的混合计算智能算法。数值计算表明本文方法显著优于牛顿法和ＧＡ。

Considered that the Newtonian method is with local convergence and then is often fail, a genetic algorithm(GA) which can search the solution in the full variable space for nonlinear equations is got. And then, considered that GA is with slow convergence, based on defining of a Newtonian operator, a fitness function, and a selecting operator, a hybrid computational intelligent algorithm for nonlinear equations, combined the advantages both of GA and Newtonian algorithm, is got with fast convergence and great probability for solving nonlinear solutions. The numerical computings show that the method is distinctly superior to GA and Newtonian algorithm.