人工鱼群和蒙特卡罗混合算法的应用

为方便快捷地使用计算机求解二重积分的数值解,采用人工鱼群和蒙特卡罗的混合算法,将蒙特卡罗求解二重积分数值解的思想引入到人工鱼群算法中,改进了人工鱼群算法中的适应度函数和积分求和公式。最后,通过一个算例进行了验证,实验结果表明:当分割点数目仅为100时,误差已经降低为0.000 410 7;而进化策略的实验结果是:当分割点数目达到1 024时,误差才降为0.000 148.改进的后算法一方面很好的体现了人工鱼群算法易于和蒙特卡罗算法结合的优点,另一方面在保留改进的蒙特卡罗算法原有优点的基础上,也在一定程度上减少了分割点的数目,提高了算法的收敛速度和数值计算精度。经过分析研究与实例验证,其计算结果和其他方法进行比较表明该方法是可行有效的,对构建高效的二重积分数值求解算法进行了有益的探索。

Application of AFSA and monte carlo mixed method

In this paper, the AFSA and Monte Carlo mixed method is used for solving the numerical solu- tion of double numerical integration conveniently and quickly by computer. The idea of Monte Carlo Method for solving the numerical solution of double numerical integration is introduced for improving the step fitness function and the integral summation formula in the AFSA with increasing the numerical ac- curacy and accelerating the convergence of the algorithm. At the end of the article is verified by a nu- merical example ,the calculation results show that when the segmentation point number is 100, the error is 0. 000 410 7 ,while the evolution strategy of the experimental shows that when the segmentation point number is1024,the error is 0. 000 148. The method on the one hand, shows the good characteristics of easy for AFSA combined with Monte Carlo Method, on the other hand, reduce the number of the point of segmentation, improve the convergence speed of the algorithm and numerical calculation accuracy in the improved Monte Carlo Method with saving the basis of the original advantages in a certain extent. After researching and analyzing examples, the feasible and effective method is showed by its calculation results comparing with other methods, and it is a beneficial exploration on the construction of efficient numerical algorithm of double integral.