On the use of intersection cuts for bilevel optimization

• 成果类型: Article
• 署名作者: Fischetti, Matteo; Ljubic, Ivana; Monaci, Michele; Sinnl, Markus
• 署名单位: University of Padua; ESSEC Business School; University of Bologna; University of Vienna
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1189-5
• 发表日期: 2018
• 页码: 77-103
• 关键词: programming problem; algorithm

摘要

We 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 first propose necessary modifications needed to turn a standard branch-and-bound MILP solver into an exact and finitely-convergent MIBLP solver, also addressing MIBLP unboundedness and infeasibility. As in other approaches from the literature, our scheme is finitely-convergent in case both the leader and the follower problems are pure integer. In addition, it is capable of dealing with continuous variables both in the leader and in follower problemsprovided that the leader variables influencing follower's decisions are integer and bounded. We then introduce new classes of linear inequalities to be embedded in this branch-and-bound framework, some of which are intersection cuts based on feasible-free convex sets. We present a computational study on various classes of benchmark instances available from the literature, in which we demonstrate that our approach outperforms alternative state-of-the-art MIBLP methods.