An approximate method for local optima for nonlinear mixed integer programming problems

Abstract For a nonlinear 0–1 integer programming problem with constraint set X = (x1, …xn), we first add new constraints ∑ 1 n (x i −x i 2 )≐O and O ⩽ x i ⩽ 1 to the constraint set, thus to convert the integer problem into a nonlinear programming problem. Then we utilize a modified penalty function method to solve this nonlinear program to obtain a local optima. Running the proposed method by a widely commercialized nonlinear program software shows that this method is more convenient than current approaches as branch-and-bound method and implicit enumeration method. One issue remained for studies is to expand this method into a global method by systematically generating suitable starting points then to perform optimization processes from each of these points.