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

2024-12-23

AI Summary

To address the low computational efficiency in solving families of parametric mixed-integer programs (MIPs), this paper proposes an unsupervised learning framework: a binary-variable autoencoder (AE) is trained on historical optimal solutions to automatically extract provably valid cutting planes that tighten the feasible region of new problem instances. The method requires no labeled data, gradient information, or human intervention; instead, it learns implicit structural patterns solely from the distribution of optimal solutions. The generated cuts exhibit both statistical reliability and strong generalization across diverse instances. To the best of our knowledge, this is the first paradigm leveraging unsupervised autoencoding for cut generation in MIP. Evaluated on benchmark batch scheduling problems, the approach reduces average solution time by 57% while preserving rigorous optimality guarantees. The implementation is publicly available.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

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.

Problem

• Automated Learning Method
• Mixed Integer Programming (MIP)
• Binary Variable Pattern Recognition

Innovation

• Autoencoder Model
• Cutting Planes Generation
• Mixed Integer Programming