SC: A fuzzy approximation for nonlinear regression optimization

Abstract

Nonlinear regression is a statistical technique widely used in research which creates models that conceptualize the relation among many variables that are related in complex forms. These models are widely used in different areas such as economics, biology, finance, engineering, etc. These models are subsequently used for different processes, such as prediction, control or optimization. Many standard regression methods have proved to produce misleading results in certain data sets; this is especially true in ordinary least squares. In this paper a novel system of convergence (SC) is presented as well as its fundamentals and computing experience for some benchmark nonlinear regression optimization problems. An implementation using a novel PSO algorithm with three phases (PSO-3P): stabilization, generation with broad-ranging exploration, and generation with in-depth exploration, is presented and tested on 27 databases of the NIST collection with different degrees of difficulty. Numerical results show that the PSO algorithm provides better results when the SC criterion is used, compared to evaluate the usual objective function.