Research On Parameter Identification Problem Based On Gene Expression Programming

There are many problems can be described by the partial differential equation in the natural science and engineering technology field, studying the numeric solution of these partial differential equations is a strong tool for solving these problems. Generally speaking, if the operator, the right term, the boundary condition or the initial condition is not known and the solution of the equation isn't known either, the partial differential equation becomes an inverse problem. These inverse problems are ill-posed in the sense of Hadamard, and they represent primarily that the solution does not depend continuously on the data, i.e. the error between the solved approximation and the true value is very big when there is a small change in the right source term, which is unstable. The theory and the solving solution of the inverse problem are more difficult than those of the direct problems and related with many aspects because the inverse problem is nonlinear and ill-posed, and how to solve these problems become a new field that mathematics learners, natural science researchers and engineering technology learners try to study.Parameter identification problems belong to the partial differential equations inverse problems. They are also common in the field of natural science and engineering. Here, the parameters which we identify can be divided into the continuous and the discontinuous. There are many people that do the research on the continuous parameter identification. We always deal with these problems by genetic algorithm or genetic programming algorithm. Because of character of the discontinuous parameter, it is quite difficult for us to solve the problems by the above algorithms. The discontinuity of function divides function into several areas. In order to identify the whole function, we must find out the sub-function on each area at the same time. The complexity of discontinuous parameter identification is a challenging problem. Moreover, mathematical numeric methods have much chance to get stuck in local minima, unless a good starting point is available. And it will bring the complexcomputation. So, this paper is to propose a new algorithm—Gene ExpressionProgramming (GEP) to do the parameter identification. GEP is the succession anddevelopment of GA and GP. It integrates the advantages of the GA and GP. It is easy to solve the problems. Meanwhile, on the one hand GEP avoids the ill-posed of the inverse problem. On the other hand, it avoids the local minima of the numeric method. According to the characteristic of discontinuous function, we use the multi-expression mining method. This method has relatively low complexity. The results of the experiments show that the function mining method based on GEP is quite efficient while mining. For the different type of the objective function, the probability of successful mining is high.