# Towards An Unsupervised Learning Scheme for Efficiently Solving Parameterized Mixed-Integer Programs

arXiv: https://arxiv.org/abs/2412.17623 · HTML: https://mlsanity.com/paper/2412.17623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 23 Dec 2024.

## Builds on (most cited first, 21 of 21)

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- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (2018)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [Learning to Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (2021)
- [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022)
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- [Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets](https://mlsanity.com/paper/1802.09639/) (2018)
- [The Voice of Optimization](https://mlsanity.com/paper/1812.09991/) (2018)
- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [Data-Driven Screening of Network Constraints for Unit Commitment](https://mlsanity.com/paper/1907.04694/) (2019)
- [Learning to Use Local Cuts](https://mlsanity.com/paper/2206.11618/) (2022)
- [An End-to-End Reinforcement Learning Approach for Job-Shop Scheduling Problems Based on Constraint Programming](https://mlsanity.com/paper/2306.05747/) (2023)
- [Learning Mixed-Integer Convex Optimization Strategies for Robot Planning and Control](https://mlsanity.com/paper/2004.03736/) (2020)
- [Use of Machine Learning Models to Warmstart Column Generation for Unit Commitment](https://mlsanity.com/paper/2110.06872/) (2021)
- [Global Optimization via Optimal Decision Trees](https://mlsanity.com/paper/2202.06017/) (2022)
- [A Novel Mixed-Integer Linear Programming Formulation for Continuous-Time Inventory Routing](https://mlsanity.com/paper/2310.11240/) (2023)

## Abstract (arXiv)

In this paper, we describe a novel unsupervised learning scheme for accelerating the solution of a family of mixed integer programming (MIP) problems. Distinct substantially from existing learning-to-optimize methods, our proposal seeks to train an autoencoder (AE) for binary variables in an unsupervised learning fashion, using data of optimal solutions to historical instances for a parametric family of MIPs. By a deliberate design of AE architecture and exploitation of its statistical implication, we present a simple and straightforward strategy to construct a class of cutting plane constraints from the decoder parameters of an offline-trained AE. These constraints reliably enclose the optimal binary solutions of new problem instances thanks to the representation strength of the AE. More importantly, their integration into the primal MIP problem leads to a tightened MIP with the reduced feasible region, which can be resolved at decision time using off-the-shelf solvers with much higher efficiency. Our method is applied to a benchmark batch process scheduling problem formulated as a mixed integer linear programming (MILP) problem. Comprehensive results demonstrate that our approach significantly reduces the computational cost of off-the-shelf MILP solvers while retaining a high solution quality. The codes of this work are open-sourced at https://github.com/qushiyuan/AE4BV.