Performance of Differential Evolution Method in Least Squares Fitting of Some Typical Nonlinear Curves

Abstract

No fool-proof method exists to fit nonlinear curves to data or estimate the parameters of an intrinsically nonlinear function. Some methods succeed at solving a set of problems but fail at the others. The Differential Evolution (DE) method of global optimization is an upcoming method that has shown its power to solve difficult nonlinear optimization problems. In this study we use the DE to solve some nonlinear least squares problems given by the National Institute of Standards and Technology (NIST), US Department of Commerce, USA and some other challenge problems posed by the CPC-X Software (the makers of the AUTO2FIT software). The DE solves the test problems given by the NIST and most of the challenge problems posed by the CPC-X, doing marginally better than the AUTO2FIT software in a few cases. Further, the DE does not require the search domains of parameters to be specified too narrowly (as in case of other methods of nonlinear least squares).

Keywords: Nonlinear least squares, curve fitting, differential evolution, global optimization, AUTO2FIT, CPC-X Software, NIST, National Institute of Standards and Technology, test problems

JEL Classification: C13, C15, C16, C63