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Matteo Fischetti: Bilevel Optimization

Abstract: Bilevel Optimization is a very challenging framework where two players (with different objectives) compete for the definition of the final solution. In this talk, we will address a generic Mixed-Integer Bilevel Linear Program (MIBLP), i.e., a bilevel optimization problem where all objective functions and constraints are linear, and some/all variables are required to take integer values. We will describe a general-purpose solution approach built on top of a (more familiar) Mixed-Integer Linear Programming (MILP) solver. We will first describe a minimal set of modifications needed to turn a standard MILP solver into an exact MIBLP solver. We will then describe classes of linear inequalities to be embedded in the branch-and-cut framework, some of which are intersection cuts based on feasible-free convex sets. We will finally present a computational study on various classes of benchmark instances from the literature.