Solving Mixed Integer Geometric Programming Problems

Abstract

Geometric Programming (GP) with integer variables is an area of active research that has drawn significant interest over the past few decades. Our approach first converts all non-convex terms of the problem into convex terms using the negative power transformation method. The convex terms are then addressed through a proposed piecewise linearization method to obtain integer solutions. Finally, the problem is solved using the nonlinear Branch and Bound algorithm. In this paper, we propose the use of the linear Branch and Bound method following piecewise linear approximation. Computational results demonstrate that our proposed method is significantly more efficient and faster than conventional methods. A numerical example is provided to illustrate the efficiency and practicality of the proposed approach.