A nonlinear interval number programming method based on RBF global optimization technique

In this paper, a new nonlinear interval-based programming (NIP) method based on Radial basis function (RBF) approximation models and RBF global search technique method is proposed. In NIP, searching for the extreme responses of objective and constraints are integrated with the main optimization, which leads to extremely low efficiency. Approximation models are commonly used to promote the computational efficiency. Consequently, two inevitable problems are encountered. The first one is how to obtain the global minimum and maximum in the sub-optimizations. The second one is how to diminish the approximation errors on the response bounds of system. The present method combined with RBF global search technique shows a good feature to overcome these problems. High accuracy and low computational cost can be achieved simultaneously. Two numerical examples are used to test the effectiveness of the present method.