求解二重积分问题的差分进化算法  

Solving Double Integral Problem Based on Evolution Algorithm

作　　者：邓泽喜[1] 刘晓冀[2] 

机构地区：[1]毕节学院数学与计算机科学学院,贵州毕节551700 [2]广西民族大学数学与计算机科学学院,广西南宁530006

出　　处：《计算机仿真》2013年第1期319-322,共4页Computer Simulation

基　　金：国家自然科学基金(11061005);2010年度教育部科技重点项目(210164);贵州省教育厅自然科学基金资助项目(黔教科2010072)

摘　　要：传统计算二重积分方法大都是等距分割方法,但是在在被积函数区间变化快慢相差较大时,计算精度大为降低。为此,提出一种不等距点分割的差分进化算法用于求解复杂函数的二重积分问题。在积分区域x向与y向上选取一些节点,将积分区域分割成很多小的子矩形域,并通过差分进化算法对其进行优化,使函数变化较快的区域分得小一些,函数变化较慢的区域分得大一些,从而得到较准确的二重积分。仿真结果表明,提出的算法收敛速度快,计算精度高,能计算较复杂的二重积分。The traditional methods of calculating double integral mostly are equidistant segmentation, but these methods greatly reduce the accuracy of double integral when changes in the range of the integrand are large differ- ence. Thus an approach based on inequality point＇ s segmentation differential evolution（DE） algorithm was presented to solve the complex function double integral. The node points on the x and y direction range in the integral region were selected, and the integral region was divided into many small sub-rectangular domains. DE was used to optimize the small sub-rectangular domains and make the rapid-change interval of function smaller or make the slow-change interval of function bigger. Thus, a more precise result was obtained. The result show that the algorithm not only is an efficient method with fast convergence and high precision, but also can calculate complex double integral.

关 键 词：差分进化算法 二重积分 不等距点分割 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]