Global optimization of nonlinear fractional programming problems in engineering design

Abstract

This study proposes a novel method to solve nonlinear fractional programming (NFP) problems occurring frequently in engineering design and management. Fractional terms composed of signomial functions are first decomposed into convex and concave terms by convexification strategies. Then the piecewise linearization technique is used to approximate the concave terms. The NFP program is then converted into a convex program. A global optimum of the fractional program can finally be found within a tolerable error. When compared with most of the current fractional programming methods, which can only treat a problem with linear functions or a single quotient term, the proposed method can solve a more general fractional programming program with nonlinear functions and multiple quotient terms. Numerical examples are presented to demonstrate the usefulness of the proposed method.