求解相容非线性方程组的拟牛顿法和混合计算智能算法

A QUASI-NEWTONIAN ALGORITHM AND A HYBRID COMPUTATIONAL-INTELLIGENT ALGORITHM FOR CONSISTENT NONLINEAR EQUATIONS

本文针对变量数与方程数不一致的相容非线性方程组(CNLE),先给出拟牛顿(QN)法。针对该算法的局部收敛性容易导致求解失败,通过在遗传算法(GA)中嵌入QN算子,并定义适当的适应度,从而得到结合GA和QN法两者长处,既有较快收敛性,又能以较大概率求解CNLE的混合计算智能算法。计算结果表明本文方法显著优于GA和QN法。

In this paper,a quasi-Newtonian(QN) method for consistent nonlinear equations(CNLE) , which number of equations may be unidentified with the number of variables, is given firstly. Considered that the QN method is with local convergence and then is often fail, through a QN operator is embedded into the genetic algorithm(GA) and a proper fitness function is defined,a hybrid computational-intelligent algorithm, combined the advances of both of GA and QN method, is got with fast convergence and greater probability for solving CNLE. The computing results show that the method is superior to GA or QN method. '