Noisy data fitting with B-splines using hierarchical genetic algorithm

Data fitting by splines in noise presence, has been widely used in data analysis and engineering applications. In this regard, an important problem 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 splines coefficients. Typically, these parameters are separately estimated in the aim of solving this non-linear problem. In this paper, we use a hierarchical genetic algorithm to tackle the data fitting problem by B-splines. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, thus, allowing us to determine the number and location of the knots, and the B-spline coefficients automatically and simultaneously. 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, numerical results from tests on smooth functions have been included.