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

TL;DR

This paper introduces a flexible branch-and-cut algorithmic framework for solving mixed integer bilevel linear optimization problems, implemented in the open-source solver MibS, and evaluates its effectiveness on various problem classes.

Contribution

It presents a comprehensive, generalized branch-and-cut framework for MIBLPs, integrating existing techniques with new methods, and provides an open-source implementation with computational evaluation.

Findings

Effective solution of diverse bilevel problems

Framework outperforms existing methods in certain classes

Open-source solver MibS facilitates research and application

Abstract

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.