求代数方程组数值解的智能新方法

A New Intelligent Method of Numerical Solution of Algebraic Equation Groups

本文针对解代数方程组计算复杂和非线性方程组的解难以得到问题,提出了一种适合于不同类型方程组的通用算法.模拟生物进化过程,利用仅以变异作为唯一基因操作的EP方法来求方程组的最优解或次最优解.首先建立智能化的通用方程组,再利用改进的EP方法(在自适应方法中引入小生境思想)来求解方程组.算法既简单又具有通用性,最后举例说明本方法的有效性.

A method is presented in the paper to solve the problems of complex calculation in solving the algebraic equations and the difficulty in solving no nlinear equations. With imitating evolution of biology, EP is used to resolve sy stem of equations. Because mutation is the only operation to change genes of chr omosome, so algorithm is quite simply. In this method, a intelligent model is es tablished for all kinds of algebraic equation groups, at first,and then an impro ved EP method (using niche technology in adaptive evolutionary programming) is u sed to resolve system of equations.At last,two examples are used to prove the ef fectiveness of the given method.