基于LM算法和遗传算法求解非线性方程组

Based on the LM Algorithm and Genetic Algorithm for Solving Non-linear Equations

文章利用混合遗传算法求解非线性方程组。该混合遗传算法是在遗传算法的基础上,引入Levenberg-Marquardt算法对其进行了改进,通过算例验证了混合遗传算法的求解精度。该非线性方程组的解分别采用3种方法计算,混合遗传算法解的计算结果要比耦合神经网络算法的结果更接近于解析解,且不用考虑初始点的问题。结果表明,混合遗传算法是有效的。

For solving nonlinear equations is one of the common problems in numerical calculation,this paper to solve the nonlinear equations by using hybrid genetic algorithm. The hybrid genetic algorithm which combines Levenberg-Marquardt optimization algorithm with genetic algorithm. The example calculation precision of the hybrid genetic algorithm is verified. The solution of the nonlinear equations is calculated by 3 methods. The result of the hybrid genetic algorithm is more close to the analytical solution than the result of the coupled neural network algorithm,and the problem of the initial point is not considered. The results show that： The hybrid genetic algorithm is an effective way for nonlinear equations.