The follower optimality cuts for mixed integer linear bilevel programming problems

We study linear bilevel programming problems, where (some of) the leader and the follower variables are restricted to be integer. A discussion on the relationships between the optimistic and the pessimistic setting is presented, providing necessary and sufficient conditions for them to be equivalent...

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Vydané v:Soft computing (Berlin, Germany) Ročník 27; číslo 16; s. 11529 - 11550
Hlavný autor: Mattia, Sara
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2023
Springer Nature B.V
Predmet:
Algorithms
Artificial Intelligence
Computational Intelligence
Control
Engineering
Inequalities
Linear programming
Mathematical Logic and Foundations
Mechatronics
Mixed integer
Optimization
Robotics
Follower optimality cuts
Bilevel optimization
Branch-and-cut
Optimistic and pessimistic problem
ISSN:1432-7643, 1433-7479
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Shrnutí:We study linear bilevel programming problems, where (some of) the leader and the follower variables are restricted to be integer. A discussion on the relationships between the optimistic and the pessimistic setting is presented, providing necessary and sufficient conditions for them to be equivalent. A new class of inequalities, the follower optimality cuts, is introduced. They are used to derive a single-level non-compact reformulation of a bilevel problem, both for the optimistic and for the pessimistic case. The same is done for a family of known inequalities, the no-good cuts, and a polyhedral comparison of the related formulations is carried out. Finally, for both the optimistic and the pessimistic approach, we present a branch-and-cut algorithm and discuss computational results.
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content type line 14
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-023-08379-3