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

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.