mlsanityData to 7 Oct 2026

Learning to Configure Separators in Branch-and-Cut

arXiv 2311.05650 ↗First posted 8 Nov 2023math.OC cs.LGcited by 14

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Abstract (arXiv)

Cutting planes are crucial in solving mixed integer linear programs (MILP) as they facilitate bound improvements on the optimal solution. Modern MILP solvers rely on a variety of separators to generate a diverse set of cutting planes by invoking the separators frequently during the solving process. This work identifies that MILP solvers can be drastically accelerated by appropriately selecting separators to activate. As the combinatorial separator selection space imposes challenges for machine learning, we learn to separate by proposing a novel data-driven strategy to restrict the selection space and a learning-guided algorithm on the restricted space. Our method predicts instance-aware separator configurations which can dynamically adapt during the solve, effectively accelerating the open source MILP solver SCIP by improving the relative solve time up to 72% and 37% on synthetic and real-world MILP benchmarks. Our work complements recent work on learning to select cutting planes and highlights the importance of separator management.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 23 of its 60 references that are in the map. First posted on arXiv 8 Nov 2023.

Builds on

23 of 60 references.

References · 23

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2020Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classificationcited by 500
  3. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 322
  4. 2019Exact Combinatorial Optimization with Graph Convolutional Neural Networkscited by 313
  5. 2020Solving Mixed Integer Programs Using Neural Networkscited by 178
  6. 2019Reinforcement Learning for Integer Programming: Learning to Cutcited by 108
  7. 2021Learning to Delegate for Large-scale Vehicle Routingcited by 108
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  9. 2014ParamILS: An Automatic Algorithm Configuration Frameworkcited by 88
  10. 2020Parameterizing Branch-and-Bound Search Trees to Learn Branching Policiescited by 62
  11. 2022Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learningcited by 58
  12. 2021Learning to Schedule Heuristics in Branch-and-Boundcited by 45
11 more
  1. 2022Learning to branch with Tree MDPscited by 45
  2. 2023Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Modelcited by 44
  3. 2020Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solverscited by 43
  4. 2022The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insightscited by 39
  5. 2022Learning to Compare Nodes in Branch and Bound with Graph Neural Networkscited by 30
  6. 2020Control Frequency Adaptation via Action Persistence in Batch Reinforcement Learningcited by 27
  7. 2022Adaptive Cut Selection in Mixed-Integer Linear Programmingcited by 25
  8. 2018Theoretical challenges towards cutting-plane selectioncited by 16
  9. 2018Learning to Search via Retrospective Imitationcited by 13
  10. 2022Learning to Use Local Cutscited by 11
  11. 2020Generalization in portfolio-based algorithm selectioncited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 6; 2026: 4.

14 papers.

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  1. 2024Towards Foundation Models for Mixed Integer Linear Programmingcited by 30
  2. 2024Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programmingcited by 24
  3. 2025Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programmingcited by 16
  4. 2024LLMs for Cold-Start Cutting Plane Separator Configurationcited by 8
  5. 2025EvoCut: Strengthening Integer Programs via Evolution-Guided Language Modelscited by 8
  6. 2025Learning-Guided Rolling Horizon Optimization for Long-Horizon Flexible Job-Shop Schedulingcited by 7
  7. 2025Learning to Segment for Vehicle Routing Problemscited by 5
  8. 2025CoCo-MILP: Inter-Variable Contrastive and Intra-Constraint Competitive MILP Solution Predictioncited by 4
  9. 2025RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domainscited by 3
  10. 2024Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionalitycited by 1
  11. 2026MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solverscited by 1
  12. 2026Latent Spherical Flow Policy for Reinforcement Learning with Combinatorial Actionscited by 0
2 more
  1. 2026Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networkscited by 0
  2. 2026Learning Early-to-Final Solution Consistency for MILP Accelerationcited by 0