Non parameter-filled function for global optimization

Abstract

It has been generally recognized that most of the existing parametric filled function methods used for finding the global mininizer of unconstrained global optimization problems have computational weaknesses. In this paper, a new non parameter-filled function is proposed. This type of auxiliary function behaves as a bridge that can deliver one minimizer to another local minimizer, if one exists. To prove that the proposed filled function satisfies the filling properties required by the filled function definition, the analytical properties are explored. Through several test examples, the capability of this proposed method is demonstrated and the computational weaknesses of the parametric filled function are proved to be surmounted by this new non parameter-filled function.