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A hierarchical genetic algorithm approach for curve fitting with B-splines

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Abstract

Automatic curve fitting using splines has been widely used in data analysis and engineering applications. An important issue associated with data fitting by splines is the adequate selection of the number and location of the knots, as well as the calculation of the spline coefficients. Typically, these parameters are estimated separately with the aim of solving this non-linear problem. In this paper, we use a hierarchical genetic algorithm to tackle the B-spline curve fitting problem. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots, and the B-spline coefficients automatically and simultaneously. Our approach is able to find optimal solutions with the fewest parameters within the B-spline basis functions. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth functions and comparison with a successful method from the literature have been included.

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Notes

  1. The source files for the BARS algorithm were coded in C with wrapper to R software [21] and can be downloaded from http://www.stat.cmu.edu/~kass/bars/bars.html. See [25] for a complete description of this algorithm.

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Acknowledgments

We acknowledge the support of the Consejo Nacional de Ciencia y Tecnología de México, Centro de Investigaciones en Óptica, A.C. and Instituto Tecnológico Superior de Irapuato. This work has been partially funded by the CONACYT Project 229839 (Apoyo al Fortalecimiento y Desarrollo de la Infraestructura Científica y Tecnológica 2014) and the DAIP Project 444 (Convocatoria Institucional de Investigación Científica 2014).

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Authors and Affiliations

  1. Department of Optical Metrology, Centro de Investigaciones en Óptica, A.C., Loma del Bosque 115, Col. Lomas del Campestre, 37150, León, Guanajuato, Mexico

    C. H. Garcia-Capulin & F. J. Cuevas

  2. Department of Mechatronics, Instituto Tecnológico Superior de Irapuato, Carr. Irapuato-Silao Km. 12.5, 36821, Irapuato, Guanajuato, Mexico

    G. Trejo-Caballero

  3. Department of Electronics, DICIS - Universidad de Guanajuato, Com. Palo Blanco s/n, 36885, Salamanca, Guanajuato, Mexico

    H. Rostro-Gonzalez

Authors
  1. C. H. Garcia-Capulin
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  2. F. J. Cuevas
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  3. G. Trejo-Caballero
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  4. H. Rostro-Gonzalez
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Correspondence to C. H. Garcia-Capulin.

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Garcia-Capulin, C.H., Cuevas, F.J., Trejo-Caballero, G. et al. A hierarchical genetic algorithm approach for curve fitting with B-splines. Genet Program Evolvable Mach 16, 151–166 (2015). https://doi.org/10.1007/s10710-014-9231-3

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  • DOI: https://doi.org/10.1007/s10710-014-9231-3

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