Evolutionary Approximation of Multi dimensional Functions

Abstract

An evolutionary approximation method for multi dimensional functions is proposed in this paper. Firstly, combining sampling functions with spline functions, a class of base functions are constructed. Based on these base functions, an approximation model for monotone functions is given. Then, according to the limited variation property of sampling functions, the new model is extended to general function approximation. These approximation tasks are implemented by Genetic Algorithms. The newly proposed method has the advantages of simplicity, uniformity for multi dimensional function approximation, and the approximation complexity is linear with the dimensionality, which will reduce the computational cost considerably. Based on the approximation method, a novel decision making strategy learning model (Evolutionary Decision Making) has been proposed and successfully applied to the controller design task of mobile robots.