An Approximate Algorithm for the Mixed Integer Nonlinear Programming

An algorithm for global optima of general mixed integer nonlinear programming (MINLP) is proposed in this paper. The mixed local minimizer of MINLP is first defined, and then a mixed steepest descent algorithm is proposed for the mixed local minimizer. Motivated by some auxiliary function algorithm for continuous global optimization, such as the filled function algorithm, the tunnelling algorithm and so on, a kind of auxiliary function is constructed, and based on the mixed steepest descent algorithm and one of these auxiliary functions, a new algorithm for global optima of MINLP is proposed. The algorithm can find the global optima of MINLP by solving mixed local optimums of the objective function and auxiliary functions alternately. Numerical results clearly indicate the efficiency and reliability of the proposed approach.