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.