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

arXiv: https://arxiv.org/abs/2104.09010 · HTML: https://mlsanity.com/paper/2104.09010/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2021.

## Built on by (most cited first, 6 of 6)

- [Neur2BiLO: Neural Bilevel Optimization](https://mlsanity.com/paper/2402.02552/) (2024)
- [Decentralized and Privacy-Preserving Learning of Approximate Stackelberg Solutions in Energy Trading Games with Demand Response Aggregators](https://mlsanity.com/paper/2304.02086/) (2023)
- [The Principle of Uncertain Maximum Entropy](https://mlsanity.com/paper/2305.09868/) (2023)
- [Synergistic Localization and Sensing in MIMO-OFDM Systems via Mixed-Integer Bilevel Learning](https://mlsanity.com/paper/2507.07118/) (2025)
- [Smart routes: a system for development and comparison of algorithms for solving vehicle routing problems with realistic constraints](https://mlsanity.com/paper/2608.14140/) (2026)
- [Graph4BiLO: Graph Neural Network Approximation for Bilevel Mixed-Integer Linear Optimization](https://mlsanity.com/paper/2608.30103/) (2026)

## Abstract (arXiv)

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.