Intersection Cuts for Bilevel Optimization
The exact solution of bilevel optimization problems is a very challenging task that received more and more attention in recent years, as witnessed by the flourishing recent literature on this topic. In this paper we present ideas and algorithms to solve to proven optimality generic Mixed-Integer Bilevel Linear Programs (MIBLP’s) where all constraints are linear, and some/all variables are required to take integer values. In doing so, we look for a general-purpose approach applicable to any MIBLP (under mild conditions), rather than ad-hoc methods for specific cases. Our approach concentrates on minimal additions required to convert an effective branch-and-cut MILP exact code into a valid MIBLP solver, thus inheriting the wide arsenal of MILP tools (cuts, branching rules, heuristics) available in modern solvers.
KeywordsBilevel Problem Bilevel Optimization Problem MILP Solver Leader Objective Function Suitable Normalization Factor
This research was funded by the Vienna Science and Technology Fund (WWTF) through project ICT15-014. The work of M. Fischetti and M. Monaci was also supported by the University of Padova (Progetto di Ateneo “Exploiting randomness in Mixed Integer Linear Programming”), and by MiUR, Italy (PRIN project “Mixed-Integer Nonlinear Optimization: Approaches and Applications”). The work of I. Ljubić and M. Sinnl was also supported by the Austrian Research Fund (FWF, Project P 26755-N19). The authors thank Ted Ralphs for his technical support and instructions regarding MibS, and Massimiliano Caramia for providing the instances used in .
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