A new vertex enumeration-based approach for bilevel linear-linear fractional programming problems

Abstract

In this paper, we focus on the bilevel linear-linear fractional programming problem (BLLFP), in which the upper level objective is linear and the lower level objective is linear fractional over a polyhedron. We provided a modified enumerative searching scheme and then incorporated the Charnes-Cooper transformation for dealing with associated lower level problems, to find the global optimal solution of this nonconvex optimization problem. The numerical example shows that our algorithm achieves the global optimal solution in finite steps with less procedures than the only one existing enumerative based algorithm in literature. As a result, our version is an improved and simplified version with some computational advantage.