A DC Programming Approach for Mixed-Integer Linear Programs

Abstract

In this paper, we propose a new efficient algorithm for globally solving a class of Mixed Integer Program (MIP). If the objective function is linear with both continuous variables and integer variables, then the problem is called a Mixed Integer Linear Program (MILP). Researches on MILP are important in both theoretical and practical aspects. Our approach for solving a general MILP is based on DC Programming and DC Algorithms. Using a suitable penalty parameter, we can reformulate MILP as a DC programming problem. By virtue of the state of the art in DC Programming research, a very efficient local nonconvex optimization method called DC Algorithm (DCA) was used. Furthermore, a robust global optimization algorithm (GOA-DCA): A hybrid method which combines DCA with a suitable Branch-and-Bound (B&B) method for globally solving general MILP problem is investigated. Moreover, this new solution method for MILP is also applicable to the Integer Linear Program (ILP). An illustrative example and some computational results, which show the robustness, the efficiency and the globality of our algorithm, are reported.