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Intersection Cuts for Bilevel Optimization

  • Matteo FischettiEmail author
  • Ivana Ljubić
  • Michele Monaci
  • Markus Sinnl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9682)

Abstract

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.

Keywords

Bilevel Problem Bilevel Optimization Problem MILP Solver Leader Objective Function Suitable Normalization Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgment

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 [3].

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Matteo Fischetti
    • 1
    Email author
  • Ivana Ljubić
    • 2
  • Michele Monaci
    • 1
  • Markus Sinnl
    • 3
  1. 1.DEIUniversity of PaduaPaduaItaly
  2. 2.ESSEC Business School of ParisCergy-PontoiseFrance
  3. 3.ISORUniversity of ViennaViennaAustria

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