Computing the Pareto frontier of a bi-objective bilevel linear problem using a multiobjective mixed-integer programming algorithm

M. J. Alves, S. Dempe and J. J. Júdice

Abstract

In this paper we study the bilevel linear programming problem with multiple objective functions at the upper level, with particular focus on the bi-objective case. We examine some properties of this problem and propose a methodological approach based on the reformulation of the problem as a multiobjective mixed 0-1 linear programming problem. The basic idea consists in applying a reference point algorithm that has been originally developed as an interactive procedure for multiobjective mixed-integer programming. This approach further enables to characterize the whole Pareto frontier in the bi-objective case. An illustrative numerical example is presented to show the viability of the proposed methodology.