基于混合遗传算法求解非线性方程组

Solving Systems of Nonlinear Equations with Hybrid Genetic Algorithm

将非线性方程组的求解问题转化为函数优化问题,且综合考虑了拟牛顿法和遗传算法各自的优点,提出了一种用于求解非线性方程组的混合遗传算法。该混合算法充分发挥了拟牛顿法的局部搜索、收敛速度快和遗传算法的群体搜索、全局收敛的优点。为了证明该混合遗传算法的有效性,选择了几个典型的非线性方程组,从实验计算结果、收敛可靠性指标对比不同算法进行分析。数值模拟实验表明,该混合遗传算法具有很高的精确性和收敛性,是求解非线性方程组的一种有效算法。

The problems on solving nonlinear equations is transformed into that of function optimization. A hybrid genetic algorithm （HGA） was put forward, which combined the advantages of quasi - Newton method and genetic algorithm （GA）. The HGA sufficiently exerted the advantages of quasi- Newton method such as local search,high convergence rate and GA such as group search,global convergence. For sake of proving the reliability of the HGA, the results of experiments computation and the convergence reliability of different algorithms were compared by testing several classical equations of nonlinear equations. Numerical simulation experiments show that HGA has high precision and convergence characteristics, and is a reliable approach in solving systems of nonlinear equations.