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 bets 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. 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 H. Akaike´s (1974) 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