基于混合遗传算法求非线性二阶两点边值问题的数值解

针对非线性二阶两点边值问题,构造了一种基于实数编码的混合遗传算法,将遗传算法和Levenberg-Marquardt算法进行了组合;由于前者全局优化能力强,后者有较强的局部优化能力,故改进后的算法不仅具有全局优化能力,计算的精度不会受到初始取值的影响,并且计算时间少,可以有效提高算法的收敛速度;最后,通过改进后的算法计算非线性二阶两点边值问题解析解和精确解的对比分析表明,该算法对非线性二阶两点边值问题计算有较大的优势,是一种有效的求数值解方法。

A New Kind of Curve Construction with Shape Parameters

According to nonlinear second order two point boundary problem, a hybrid genetic algorithm based on real coding is constructed by the combination of the genetic algorithm with Levenberg Marquardt algorithm. Because the former has the advantages of global optimization ability while the latter has strong local optimization ability, therefore, the improved algorithm not only has global optimization ability but also the calculation accuracy can not be affected by initial values, can use less computing time, and can effectively improve the convergence speed of the algorithm. Finally, the comparison between analytical solution and exact solution to nonlinear second order two point boundary value problems by using the improved algorithm indicates that the improved algorithm has big advantages of nonlinear second order two point boundary value problems computation and is an effective method for numerical solution.