基于遗传算法求任意函数的数值积分

Solving numerical integration based on genetic algorithms

针对复杂函数的数值积分问题,给出了若干个任意分割积分区间的数值积分的误差结果,并提出一种基于遗传算法的不等距节点分割的数值积分方法。该方法初始时在积分区间内任意选取一定的节点,通过遗传算法优化这些节点,在相邻节点间利用Simpson公式近似计算积分,最后得到较准确的积分结果。数值计算结果表明,该方法计算精度高,而且可以计算奇异函数及震荡函数的积分。

Several numerical integral error results based on subdividing the integral interval arbitrarily are presented, then an approach for solving numerical integration based on Genetic Algorithm （GA） is proposed. GA is used to optimize the points in the integral interval in order to get a more precise result with using Simpson＇ s rule in every small segment. Sim- ulation examples of integral validate that the algorithm can compute both singularity functions integral and oscillation function integral.