A new filled function method for nonlinear integer programming problem

In this paper, we develop a new filled function method to solve nonlinear integer programming problem. It is shown that any local minimizer of the new filled function constructed from a current local minimizer is either a better local minimizer of the original integer programming problem or a vertex of its constrained domain. Hence a better local minimizer can be obtained just by local search scheme for the new filled function. An algorithm based on the nice properties of the new filled function is proposed for locating the global minimizer of the original integer programming problem. Several numerical examples are presented to show the efficiency of the algorithm.