文档介绍：摘要
本文提出了利用基于浮点数编码的自适应遗传算法来训练多层径向基函数网络的中心
和宽度的算法，通过单元和多元实函数逼近的计算机实验，验证其具有比多层径向基函数网
络的聚类算法更高精度的逼近实函数的能力。
在此基础上，论文将基于浮点数编码的自适应遗传算法的多层径向基函数网络用于
Logistic 和 Mackey Glass 混沌时间序列的多步预测中，与基于聚类算法的多层 RBF 网络的
相比，其可预测的步数大大的提高了。
最后，论文将基于浮点数编码的自适应遗传算法的多层径向基函数网络应用于数理金融
中的偏微分方程的边值问题的数值解。通过计算机实验，结果表明，可以利用这种算法求解
偏微分方程的边值问题的数值解，其精度也很高。
关键字：多层径向基函数网络，实函数逼近，混沌时间序列，偏微分方程
I
Abstract
This article presents a kind of algorithm that is using adaptive genetic algorithm based on
floating point coding to train the center and width of t multi-layer radial basis function
computer simulation of the unit and multivariate function approximation,it
shows that the precision by this algorithm is much more higher than the precision by clustering
algorithm for multi-layer RBF networks.
On this basis,we apply the multi-layer radial basis function network based on adaptive
genetic algorithm of floating point coding to the prediction of Logistic and Mackey Glass chaotic
time with clustering algorithm for multi-layer RBF networks,the result shows the
predictive step is greatly improved.
Finally, the paper put the multi-layer radial basis function network based on adaptive genetic
algorithm of floating point coding into numerical solutions of boundary value problems on the
partial differential equation in mathematical finance. Through computer simulation,the result
shows that it can use the algorithm to solve the numerical solutions of boundary value problems
on the partial differential equation and the accuracy is very high.
Keywords: multi-layer radial basis function network, adaptive genetic algorithm, function
approximation, chaotic time series, partial differential equation
II
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