Case study I: Curve fitting

Abstract

Curve fitting may be considered as one of the most traditional problems where one may benefit from optimization methods. However, its real applicability goes way beyond solving theoretical mathematical problems. Curve fitting may be used, for instance, to infer values of a function where no data are available, or obtain a mathematical function describing a physical, chemical, or biological state or process (Bishop, Pattern Recognition and Machine Learning, 2006). In this chapter, we explore the performance of the FODPSO side by side with four other alternatives, including the traditional PSO, in order to solve the same problem: find the set of parameters of a mathematical function that has the best fit to a series of data points representing the trajectory of a golf club. This is a rather interesting curve-fitting problem as it represents a real case study wherein one wants to obtain a mathematical representation of a given putting execution in order to compare process variables among different golfers (Couceiro et al. Proceedings of WACI-Workshop Applications of Computational Intelligence, 2010). In other words, the optimization algorithms are employed to obtain a kinematical analysis and a characterization of each golfer’s putting technique.