| In our daily life and kinds of science field, you will find there are many systems or phenomena that will change over time, such as the change of the weather, the characteristics of population growth, the diffusion of epidemic in medical field, the fluctuation of stock price in economic field, and so on. In order to grasp the trend of these changes and solve related problems, we always use some known data to establish a mathematics model, we can predict the development situation in the future according to the model. These problems which will change over time are often expressed by differential equation. How to establish a effective and reasonable differential equation model with micro forward fitting error and backward prediction error is the most difficult problem we are facing.The traditional modeling method is to assume a model beforehand, then do some modification. This kind of modeling method needs the modelers have much experience, and it’s very hard for most people. With the rapid development of technology and the popularization of computer, everything is moving towards intelligence. We hope that the computer can establish the model automatically. Nowadays, the evolutionary modeling method is very popular, it adopts the evolutionary algorithm (EA) to search the model automatically. EA has the features of easy realization and high efficiency, and its application field is very wide. In2001, portuguese scientist Candida Ferreira put forward a new type of evolutionary algorithm called gene expression programming (GEP). GEP is based on genetic algorithm (GA) and genetic programming (GP), and GA and GP are two of the most popular EA. GEP shows much greater advantages, especially, when it is used for function modeling, the efficiency is very high. On the basis of analysis of traditional evolutionary modeling algorithm based on GP for system of ordinary differential equations (ODEs), a new evolutionary modeling algorithm based on GEP for ODEs is proposed in this paper.The following are the major work and innovations of this paper:(1) A new encoding method is proposed to apply for modeling algorithm for ODEs. In this new encoding method, each ordinary differential equation is expressed by a gene, then the ODEs which contains several equations can be expressed by a chromosome which is formed by several genes. This serial encoding method avoids the deficiencies of traditional tree encoding method, and it makes the evolutionary operation more convenient.(2) The elite-subspace evolutionary algorithm is employed to optimize the parameters of the ODEs model. The traditional evolutionary modeling method uses GA to optimize the parameters of the model, it has the disadvantages of time wasting and slow convergent speed, what’s more, it is easy to drop into local optimum. This kind of optimization algorithm based on elite-subspace evolutionary algorithm for parameters of the ODEs selects several elite parents for crossover operation, this method not only strengthen the global optimization ability, but also increase the convergent speed to much extent.(3) A evolutionary modeling algorithm based on GEP for ODEs is proposed. This new modeling algorithm adopts GEP to optimize the model, and it introduces the idea of the parallel evolutionary algorithm, at the same time, it uses the elite-subspace evolutionary algorithm to optimize the parameters of the model. The results show the ODEs models which the evolutionary modeling algorithm based on GEP for ODEs produced automatically have higher precision and cost less time, compared with the GEP evolutionary modeling algorithm. |
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