Automatic curve fairing system using visual languages
Geometric modeling
Hybridization of GA, ANN and classical optimization for B-spline curve fitting
Design and application of hybrid intelligent systems
International Journal of Hybrid Intelligent Systems
An Artificial Immune System Approach for B-Spline Surface Approximation Problem
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Automatic knot adjustment using an artificial immune system for B-spline curve approximation
Information Sciences: an International Journal
Capturing planar shapes by approximating their outlines
Journal of Computational and Applied Mathematics
Efficient particle swarm optimization approach for data fitting with free knot B-splines
Computer-Aided Design
A new iterative mutually coupled hybrid GA-PSO approach for curve fitting in manufacturing
Applied Soft Computing
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In order to obtain a good spline model from many measurement data, frequently we have to deal with knots as variables. Then the problem to be solved becomes a continuous nonlinear and multivariate optimization problem with many local optima. Therefore, it is difficult to obtain a global optimum. In this paper, we propose a new method to convert the original problem into a discrete combinatorial optimization problem and solve the converted problem by a genetic algorithm. We construct individuals by considering candidates of the locations of knots as genes, and convert the continuous problem into a discrete problem. We search for the best model among the candidate models by using Akaike's Information Criterion (AIC). Our method can determine appropriate number and locations of knots automatically and simultaneously. We don't need any subjective parameters such as error tolerance or a smoothing factor, and good initial location of knots for iterative search. Numerical examples are given to show the effectiveness of our method.