An improved hybrid-ORBIT algorithm based on point sorting and MLE technique

Abstract

Optimization using radial basis functions as an interpolation tool in trust region (ORBIT) is a derivative-free framework based on fully linear radial basis function (RBF) models. In this paper, an improved version of ORBIT algorithm based on two novel ideas is proposed. The accuracy and stability of RBFs depend on a so-called shape parameter, so it is more appropriate to determine the shape parameter according to the optimization problem. While ORBIT in all problems uses a fixed value as a shape parameter, our new version, Hybrid-ORBIT, uses a statistical technique to select an appropriate shape parameter. In addition, ORBIT uses some stored points to build a fully linear RBF model without considering their function values, while in the Hybrid-ORBIT algorithm the stored points are sorted based on their function values and the RBF model is built using the points with lower function values, and the best point in the sense of function value is defined as the trust-region center. Numerical results indicate the efficiency of the improved version compared with the original version.