Range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems

Many global optimization approaches for solving signomial geometric programming problems are based on transformation techniques and piecewise linear approximations of the inverse transformations. Since using numerous break points in the linearization process leads to a significant increase in the computational burden for solving the reformulated problem, this study integrates the range reduction techniques in a global optimization algorithm for signomial geometric programming to improve computational efficiency. In the proposed algorithm, the non-convex geometric programming problem is first converted into a convex mixed-integer nonlinear programming problem by convexification and piecewise linearization techniques. Then, an optimization-based approach is used to reduce the range of each variable. Tightening variable bounds iteratively allows the proposed method to reach an approximate solution within an acceptable error by using fewer break points in the linearization process, therefore decreasing the required CPU time. Several numerical experiments are presented to demonstrate the advantages of the proposed method in terms of both computational efficiency and solution quality.