Solving a Global-Mixed Integer Signomial Geometric Fractional Programming Problem

This article addresses mixed integer fractional signomial geometric programming (MIFSGP) problems, which have been widely used in industrial design. In this paper, first, we convert fractional signomial programming into a nonfractional problem so that it maintains its geometric structure. Then, convex relaxation is used to reach a mixed integer global solution. Although, in many cases, we obtain a better objective function value with this process, designers may still be dissatisfied with the rupture between the original objective function value and the relaxed value. Therefore, we apply a spatial branch and bound algorithm to decrease that distance to an acceptable extent and maintain the global solution. Finally, a real design problem is considered to evaluate the efficiency and accuracy of the proposed technique.