动态系统的演化建模

A HYBRID EVOLUTIONARY MODELING ALGORITHM FOR DYNAMIC SYSTEMS

针对采用传统方法解决动态系统的微分方程建模问题所遇到的困难和存在的不足，文中设计了将遗传程序设计与遗传算法相嵌套的混合演化建模算法，以遗传程序设计优化模型结构，以遗传算法优化模型参数，成功地实现了动态系统的常微分方程组建模过程自动化．计算实例表明：采用此算法能在合理的运行时间内由计算机自动发现多个较优的常微分方程组模型，和现有的建模方法（如灰色系统方法）相比较，它具有建模过程智能化与自动化、模型结构更加灵活多样、方法适用性更广、数据拟合和预测的精度更高等优点．

To overcome the difficulties and drawbacks in modeling the dynamic systems by using traditional methods, a hybrid evolutionary modeling algorithm (HEMA) is proposed to model the dynamic system with a system of ordinary differential equations (ODEs) whose main idea is to embed genetic algorithm (GA) in genetic programming (GP) where GP is employed to optimize the structure of a model, and GA is employed to optimize the parameters of a model. It has succeeded in automating the modeling process of systems of ODEs for dynamic systems. The computational experiments indicate that, by running the HEMA, the computer can search out multiple superior ODEs models in a reasonable time. Compared with most available modeling methods, such as the grey systems method (GSM), this algorithm possesses the advantages of automation of the modeling process, more flexible and various model structures, wider range of applications, and higher precision of fitting and predicting data.