mlsanityData to 14 Oct 2026

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

arXiv 2412.17623 ↗First posted 23 Dec 2024math.OC cs.LGcited by 0

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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.

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References · 21

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9 more
  1. 2018The Voice of Optimizationcited by 28
  2. 2023Machine Learning for Cutting Planes in Integer Programming: A Surveycited by 20
  3. 2019Data-Driven Screening of Network Constraints for Unit Commitmentcited by 11
  4. 2022Learning to Use Local Cutscited by 11
  5. 2023An End-to-End Reinforcement Learning Approach for Job-Shop Scheduling Problems Based on Constraint Programmingcited by 11
  6. 2020Learning Mixed-Integer Convex Optimization Strategies for Robot Planning and Controlcited by 10
  7. 2021Use of Machine Learning Models to Warmstart Column Generation for Unit Commitmentcited by 5
  8. 2022Global Optimization via Optimal Decision Treescited by 2
  9. 2023A Novel Mixed-Integer Linear Programming Formulation for Continuous-Time Inventory Routingcited by 1

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