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A Branch-and-Cut Algorithm for Mixed Integer Bilevel Linear Optimization Problems and Its Implementation

S. Tahernejad (sat214***at***lehigh.edu)
T.K. Ralphs (ted***at***lehigh.edu)
S.T. DeNegre (DeNegreS***at***hss.edu)

Abstract: In this paper, we describe an algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) by a generalized branch-and-cut approach. The framework presented merges features from existing algorithms (for both traditional mixed integer linear optimization and MIBLPs) with new techniques to produce a flexible and robust framework capable of solving a wide range of bilevel optimization problems. The framework has been fully implemented in the open source solver MibS. The paper describes the algorithmic options offered by MibS{} and presents computational results evaluating the effectiveness of the various options for the solution of a number of classes of bilevel optimization problems from the literature.

Keywords: Bilevel optimization, Mixed integer optimization, Branch-and-cut algorithm, Open-source solver

Category 1: Optimization Software and Modeling Systems

Category 2: Combinatorial Optimization (Branch and Cut Algorithms )

Category 3: Integer Programming ((Mixed) Integer Linear Programming )

Citation: COR@L Technical Report 16T-015-R3, Industrial and Systems Engineering, Lehigh University

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Entry Submitted: 04/25/2017
Entry Accepted: 04/25/2017
Entry Last Modified: 08/02/2020

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