常微分方程组的演化建模  

THE EVOLUTIONARY MODELING ALGORITHM FOR SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS

作　　者：康立山[1] 曹宏庆[1] 陈毓屏[1] 

机构地区：[1]武汉大学软件工程国家重点实验室

出　　处：《计算机学报》1999年第8期871-876,共6页Chinese Journal of Computers

基　　金：国家自然科学基金;国家八六三高技术研究发展计划

摘　　要：利用演化算法的自适应、自组织、自学习的特性，设计了遗传程序设计与遗传算法相嵌套的常微分方程组混合演化建模算法，以遗传程序设计优化模型结构，以遗传算法优化模型参数，首次实现了常微分方程组建模过程自动化并可进行有效的预测．数值实验表明：采用这种算法能在较短的运行时间和较小的演化代数内搜索到多个较优的常微分方程组模型。Based on the properties of self adaptation, self organization and self learning of evolutionary algorithms, a hybrid evolutionary modeling algorithm is proposed in this paper to solve the modeling problem of ordinary differential equations (ODEs). Its main idea is to embed a genetic algorithm (GA) into genetic programming (GP) where GP is employed to optimize the structure of a model, while a GA is employed to optimize the parameters of the model. It has taken the first step to making the modeling process of ODEs done automatically as well as giving reliable predictions. The numerical experiments show that multiple highly precise ODEs models can be searched out in a reasonable time and within fewer generations, and their predicted values surprisingly coincide with the exact solutions of the known ODEs using this algorithm.

关 键 词：演化建模 常微分方程组 遗传算法 遗传程序设计 

分 类 号：O241.81[理学—计算数学] TP311[理学—数学]