TY - JOUR
T1 - A hierarchical genetic algorithm approach for curve fitting with B-splines
AU - Garcia-Capulin, C. H.
AU - Cuevas, F. J.
AU - Trejo-Caballero, G.
AU - Rostro-Gonzalez, H.
N1 - Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2015/4/10
Y1 - 2015/4/10
N2 - 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.
AB - 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.
KW - B-splines
KW - Curve fitting
KW - Genetic algorithm
KW - Regression
UR - http://www.scopus.com/inward/record.url?scp=84928229421&partnerID=8YFLogxK
UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=pure_univeritat_ramon_llull&SrcAuth=WosAPI&KeyUT=WOS:000352651400003&DestLinkType=FullRecord&DestApp=WOS_CPL
U2 - 10.1007/s10710-014-9231-3
DO - 10.1007/s10710-014-9231-3
M3 - Article
AN - SCOPUS:84928229421
SN - 1389-2576
VL - 16
SP - 151
EP - 166
JO - Genetic Programming and Evolvable Machines
JF - Genetic Programming and Evolvable Machines
IS - 2
ER -