MEMETIC算法在非线性方程组求解中的应用

Application of memetic algorithm for solving nonlinear equations

将非线性方程组求解问题转化为函数优化问题,在Memetic(文化基因)算法的框架下,采用了拟牛顿局部搜索与自适应多点交叉、随机变异相结合的策略进行求解,充分发挥Memetic算法的群体搜索和全局收敛性,有效克服了拟牛顿法的初始点敏感问题.选择了几个典型的非线性方程组进行求解,实验表明Memetic算法在求解非线性方程组应用上具有较高的收敛可靠性和精度.

The weekness of quasi-newton method was sensitive to the initied point of overcome. By association of quasi-newton method as the local search, adapting multi-point cross and random mutation to solve the function optimization problem, which is transformed from the problem of solving nonlinear equations under the frame of memetic algorithm, the algorithm fully exert the population search and global convergence of Memetic algorithm. Numerical experiments for some typical nonlinear equations problems indicated that the memetic algorithm have a high convergence reliability and precision for solution of the nonlinear equations.