On solving the sum-of-ratios problem

Abstract

This paper addresses the development of efficient global search methods for fractional programming problems. Such problems are, in general, nonconvex (with numerous local extremums) and belong to a class of global optimization problems. First, we reduce a rather general fractional programming problem with d.c. functions to solving an equation with a vector parameter that satisfies some nonnegativity assumption. This theorem allows the justified use of the generalized Dinkelbach’s approach for solving fractional programming problems with a d.c. goal function. Based on solving of some d.c. minimization problem, we developed a global search algorithm for fractional programming problems, which was tested on a set of low-dimensional test problems taken from the literature as well as on randomly generated problems with up to 200 variables or 200 terms in the sum.