Research And Application Of Ordinary Differential Equation Model Based On Regularized GEP

The study of many complex systems in real world belongs to time series problems.And the variable process can be described by constructing a differential equation model which uses actual observation data and information analysis rules.The model can be used to predict their future behaviors as well.Gene expression programming(GEP)algorithm can automatically construct a differential equation model.Moreover,the unique coding method of GEP overcomes the expression defects of genetic programming.However,this algorithm still has several shortcomings such as over-fitting and insufficient ability to jump out of local optimal.In order to solve these problems,a multiple factors regularization gene expression programming is proposed to build an ordinary differential equation model.Considering the fluctuation in short term time series data,an improved algorithm based on differential regular terms is proposed.Then the proposed algorithm is compared and verified via stock price prediction experiments.The main work and innovations of this thesis are as follows:1.The traditional machine learning algorithms like logistic regression and ARIMA cannot construct a high-accuracy explicit expression prediction model to predict the time series data problem in complex systems.For this problem,considering the fluctuation characteristics of the time series data,numerical difference is used to preprocess the data.Then GEP is used to discover the mathematical models automatically.Finally,high-order ordinary differential equations are obtained to characterize data trends.2.When GEP deals with small-size data or severe noise data,it is prone to over-fitting.This can cause the model not fit practical problems.So a multiple factors regularization gene expression programming(MFR-GEP)is proposed.Based on the standard GEP,the algorithm adds constraints as a regular term to the fitness function.Moreover,the newly added indicator data is differentiated to enhance the data representation.3.In order to solve the poor fitting effect of GEP on the fluctuant data,a multi-factor differential regularization gene expression programming(MDR-GEP)is further proposed.On the basis of MFR-GEP,the differential data of variables are used to construct a compound indicator to change the regular term in the fitness function.Then a new fitness function can be obtained,which can guide the evolutionary direction of the population,and the fluctuation of the data can be better reflected.At last,both the fitting accuracy and prediction accuracy are improved.4.MFR-GEP,MDR-GEP were applied to the field of stock price forecasting.And they are compared with neural network,ARIMA and standard GEP algorithm.Finally,the simulation results of 10 stocks show that the average relative errors of the proposed methods are generally lower than other comparison methods.The results fully demonstrate the accuracy and effectiveness of the MFR-GEP and MDR-GEP.