Implementing linear models in genetic programming

摘要: This paper deals with linear models of genetic programming (GP) for regression or approximation problems when given learning samples are not sufficient. The model, which is a function unknown parameters, built through extracting all possible base functions from the standard GP tree by utilizing symbolic processing algorithm. major advantage model in that its parameters can be estimated ordinary least square (OLS) method and good selected applying modern minimum description length (MDL) principle, while nonlinearity necessary to handle problem effectively maintained indirectly evolving finding various forms functions. In addition consisting mathematical functions, one variant using low-order Taylor series converted into form polynomial, considered this paper. With small samples, frequently shows abnormal behaviors such as extreme large peaks odd-looking discontinuities at points away sample points. To overcome problem, directional derivative-based smoothing (DDBS) method, incorporated OLS introduced together fitness based on MDL, reflecting effects DDBS. Also, two illustrative examples three engineering applications presented.