A Self-Feedback GEP Algorithm And Its Applications On Statistical Modeling

With the rapid development of science and the technology of information explosion, all relevant information increased greatly(in a fast way). As one of the methods of information processing, the mathematical modeling has become more and more important in the reality, which also has been an important part of modern science and technology. And more and more applications of this method has been more deeper in life. There are quite a lot examples of the method solving the problem in real life. But there is no one of the methods can be universal. Different environment contains different factors interfere and conditions, in order to choose the best solution of the actual situation, we need to find and extract the critical, relational and regular factor from the problems that we need solve, then with environment factor and the association between them, we could construct a mathematical model that can reflect internal relations and change of things, these process is called mathematical modeling. After model creation, we could finally find the way to solve practical problem through the mathematical model’s solution. There are many method to solving the mathematical modeling, the GEP is the common one of it.At first, in this paper we will introduce several conventional methods of economic modeling-------Regression equation, based approach GA, GP, then General Description of GEP leads on the above-described method, and elaborate the concept of standardization GEP(containing GRCM method) in detail. After that, analysis the features and characteristics GEP included and the problems itself readily----- traditional GEP algorithm is easy to fall into local optimization solutions, which leads the algorithm to inaccurate. In the thesis, on the basis of the valid length of the GEP, and according to that GEP can search in a specific space unlimited access the non-coding regions, we will improve the evolution operator, design a kind of selffeedback gene expression programming algorithm, at last, real examples are used to test the improved GEP method, the standard conventional GEP and the commonly used regression equation. Then we compare the test results with the results obtained by traditional statistical regression methods such as line regression and traditional GEP to prove the effectiveness of the improved GEP algorithm.The research contents and innovations of this thesis are as follows:1. Propose the TIS insertion string operator. In the traditional GEP, Candida Ferreira presents some operators of expanding of diversity and evolutionary programming like, IS insertion string operator, RIS insertion string operator, cross, mutation, and according to different situation, set different selection operator. But in terms of the insertion string operator, there are some limitations in the operation of different insertion string operators, and the failure to take into account the effect of the length of the gene in the gene to reduce the concentration of the population and fall into the local optimal solution. Therefore, in order to ensure the stability of the valid length, we inserting valid string(TIS string operator) in the place from the beginning of last valid bits corresponding to the set of functions, through this way to improve the method, to guarantee the diversity of the population and improve the convergence rate of the algorithm.2. According to the method of inserting TIS insertion string operator, the self-feedback GEP algorithm(SGEP algorithm) is proposed, and the algorithm is applied to the enterprise’s statistical data modeling. Then provide the basis for analysis of the business situation and the enterprise’s macro policy.The improved SGEP algorithm has a more uniform population distribution than the one of the traditional GEP algorithm, So that it can better avoid the algorithm into local optimal solution, and the convergence speed of the algorithm is accelerated. By using this algorithm, the one dimension and multi-dimension modeling of the enterprise statistical data are proposed. The results show the effectiveness of the improved SGEP algorithm is better than the traditional statistical regression methods like line regression and parabolic regression, and the accuracy of the solutions are better.