A Genetic Algorithm for Curve Fitting by Spline Regression

Abstract

Curve fitting is a computational problem in which we look for a base objective function with a set of data points. Recently, nonparametric regression has received a lot of attention from researchers. Usually, spline functions are used due to the difficulty of the curve fitting. In this regard, the choice of the number and location of knots for regression is a major issue. Therefore, in this study, a Genetic algorithm simultaneously determines the number and location of the knots based on two criteria comprise of least square error and capability process index. The proposed algorithm performance has been evaluated by some numerical examples. Simulation results and comparisons reveal that the proposed approach in curve fitting has satisfactory performance. Also, a sensitivity analysis on the number of knots has been illustrated by an example. Finally, simulation results from a real case in statistical process control show that the proposed Genetic algorithm works well in practice.

Keywords

• spline regression
• genetic algorithm
• least square error
• capability process index