Automatic knot placement by a genetic algorithm for data fitting with a spline

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 salved 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 far 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.