Performance Evaluation of ORBIT Algorithm to Some Effective Parameters

ORBIT is a derivative-free trust-region framework that employs a radial basis function (RBF) interpolation to solve the computationally expensive optimization problems. The accuracy and stability of RBF interpolation depend on a so-called shape parameter, the type of RBF and the number of data points. So it is more appropriate to determine these parameters properly. In this paper, we evaluate the performance of the ORBIT algorithm by different types of RBF, different numbers of data points and different shape parameter values. We utilize Dolan-More performance profile and More-Wild data profile to investigate the performance of algorithms. Finally, based on this numerical study we proposed some recommendations for the type of RBF, the number of data points and the shape parameter value.