Nonlinear parametric regression in genetic programming

Abstract

Function approximation or regression is the problem of finding a function that best explains the relationship between independent variables and a dependent variable from the observed data. Genetic programming has been considered a promising approach for the problem since it is possible to optimize both the functional form and the coefficients. Genetic programming has been considered a promising approach for function approximation since it is possible to optimize both the functional form and the coefficients. However, it is not easy to find an optimal set of coefficients by using only non-adjustable constant nodes in genetic programming. To overcome the problem, there have been some studies on genetic programming using adjustable parameters in linear or nonlinear models. Although the nonlinear parametric model has a merit over the linear parametric model, there have been few studies on it. In this paper, we propose a nonlinear parametric genetic programming which uses a nonlinear gradient method to estimate parameters. The most notable feature in the proposed genetic programming is that we design a parameter attachment algorithm using as few redundant parameters as possible. It showed a significant performance improvement over the traditional genetic programming approaches on real-world application problems.