Firefly Algorithm for Explicit B-Spline Curve Fitting to Data Points. (4th November 2013)

• Record Type: Journal Article
• Authors: Gálvez, Akemi; Iglesias, Andrés
• Other Names: Xu Yang Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-11-04
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/528215
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper introduces a new method to compute the approximating explicit B-spline curve to a given set of noisy data points. The proposed method computes all parameters of the B-spline fitting curve of a given order. This requires to solve a difficult continuous, multimodal, and multivariate nonlinear least-squares optimization problem. In our approach, this optimization problem is solved by applying the firefly algorithm, a powerful metaheuristic nature-inspired algorithm well suited for optimization. The method has been applied to three illustrative real-world engineering examples from different fields. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy. Furthermore, our scheme outperforms some popular previous approaches in terms of different fitting error criteria.