Mathematical Programming Computation, Volume 12, Issue 4, December 2020

A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation

Sahar Tahernejad, Ted K. Ralphs, Scott T. DeNegre

In this paper, we describe a comprehensive algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) using 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.

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