A two-phase optimization procedure for integer programming problems

This paper presents a simple two-phase method for optimizing integer programming problems with a linear or nonlinear objective function subject to multiple linear or nonlinear constraints. The primary phase is based on a variation of the method of steepest descent in the feasible region, and a hem-stitching approach when a constraint is violated. The secondary phase zeros on the optimum solution by exploring the neighborhood of the suboptimum found in the first phase of the optimization process. The effectiveness of this method is illustrated through the optimization of several examples. The results from the proposed optimization approach are compared to those from methods developed specially for dealing with integer problems. The proposed method is simple, easy to implement yet very effective in dealing with a wide class of integer problems such as spare allocation, reliability optimization, and transportation problems.