Optimal variable shape parameters using genetic algorithm for radial basis function approximation

Many radial basis function (RBF) methods contain free shape parameter or parameters that play an important role for the accuracy of the method. In most papers the authors end up choosing free shape parameter by trial and error or some other ad-hoc means. However, using variable shape parameters provides a clear potential for improved accuracy and stability of the RBF method. Already some progress has been reported to select usable variable shape parameters. In this paper, we propose applying the genetic algorithm to determine good variable shape parameters of radial basis functions for the solution of ordinary differential equations. Numerical results show that the proposed algorithm based on the genetic optimization is effective and provides reasonable shape parameters along with acceptable accuracy in linear and nonlinear case compared with other strategies to determine variable shape parameters.