mlsanityData to 14 Oct 2026

Optimization with Constraint Learning: A Framework and Survey

arXiv 2110.02121 ↗First posted 5 Oct 2021cs.LG math.OCcited by 28

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Abstract (arXiv)

Many real-life optimization problems frequently contain one or more constraints or objectives for which there are no explicit formulas. If data is however available, these data can be used to learn the constraints. The benefits of this approach are clearly seen, however there is a need for this process to be carried out in a structured manner. This paper therefore provides a framework for Optimization with Constraint Learning (OCL) which we believe will help to formalize and direct the process of learning constraints from data. This framework includes the following steps: (i) setup of the conceptual optimization model, (ii) data gathering and preprocessing, (iii) selection and training of predictive models, (iv) resolution of the optimization model, and (v) verification and improvement of the optimization model. We then review the recent OCL literature in light of this framework, and highlight current trends, as well as areas for future research.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). Builds on 33 of its 143 references that are in the map. First posted on arXiv 5 Oct 2021.

Builds on

33 of 143 references.

References · 33

  1. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  2. 2016Input Convex Neural Networkscited by 414
  3. 2017Smart "Predict, then Optimize"cited by 339
  4. 2020On Hyperparameter Optimization of Machine Learning Algorithms: Theory and Practicecited by 182
  5. 2021End-to-End Constrained Optimization Learning: A Surveycited by 157
  6. 2014From Predictive to Prescriptive Analyticscited by 143
  7. 2017Non-convex Optimization for Machine Learningcited by 133
  8. 2018Strong mixed-integer programming formulations for trained neural networkscited by 115
  9. 2019A Survey of Optimization Methods from a Machine Learning Perspectivecited by 91
  10. 2016Efficient softmax approximation for GPUscited by 67
  11. 2021CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraintscited by 49
  12. 2019Learning to Solve Large-Scale Security-Constrained Unit Commitment Problemscited by 40
21 more
  1. 2018Global Deterministic Optimization with Artificial Neural Networks Embeddedcited by 33
  2. 2019ReLU Networks as Surrogate Models in Mixed-Integer Linear Programscited by 33
  3. 2018Dynamic Assortment Optimization with Changing Contextual Informationcited by 28
  4. 2020Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networkscited by 28
  5. 2019JANOS: An Integrated Predictive and Prescriptive Modeling Frameworkcited by 27
  6. 2017Optimization of Tree Ensemblescited by 26
  7. 2019Verification of Neural Network Behaviour: Formal Guarantees for Power System Applicationscited by 26
  8. 2017Deep Learning Assisted Heuristic Tree Search for the Container Pre-marshalling Problemcited by 18
  9. 2015A Practical Guide to Robust Optimizationcited by 16
  10. 2018Boosting Combinatorial Problem Modeling with Machine Learningcited by 15
  11. 2019Optimization Problems for Machine Learning: A Surveycited by 15
  12. 2020Neural Networks for Encoding Dynamic Security-Constrained Optimal Power Flowcited by 15
  13. 2019Dynamic optimization with side informationcited by 14
  14. 2014Learning optimization models in the presence of unknown relationscited by 10
  15. 2020A novel embedded min-max approach for feature selection in nonlinear support vector machine classificationcited by 9
  16. 2019Designing reactive power control rules for smart inverters using support vector machinescited by 7
  17. 2020Input Convex Neural Networks for Optimal Voltage Regulationcited by 7
  18. 2018Automating Personnel Rostering by Learning Constraints Using Tensorscited by 6
  19. 2021Learning Mixed-Integer Linear Programs from Contextual Examplescited by 2
  20. 2016Towards an accurate solution of wireless network design problemscited by 1
  21. 2018Kernel-Based Learning for Smart Inverter Controlcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 3; 2024: 9; 2025: 4; 2026: 9.

28 papers.

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  1. 2023A Survey of Contextual Optimization Methods for Decision Making under Uncertaintycited by 82
  2. 2021Mixed-Integer Optimization with Constraint Learningcited by 31
  3. 2024Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Processcited by 11
  4. 2024Optimization Over Trained Neural Networks: Taking a Relaxing Walkcited by 10
  5. 2022Counterfactual Explanations Using Optimization With Constraint Learningcited by 8
  6. 2023Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networkscited by 6
  7. 2023Global Optimization: A Machine Learning Approachcited by 4
  8. 2024Neur2BiLO: Neural Bilevel Optimizationcited by 4
  9. 2024Learning Multiple Initial Solutions to Optimization Problemscited by 4
  10. 2022On data-driven chance constraint learning for mixed-integer optimization problemscited by 3
  11. 2024Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approachcited by 2
  12. 2026Relaxation-Informed Training of Neural Network Surrogate Modelscited by 2
16 more
  1. 2024Deep Reinforcement Learning for Traveling Purchaser Problemscited by 1
  2. 2024Solving 0-1 Integer Programs with Unknown Knapsack Constraints Using Membership Oraclescited by 1
  3. 2025Conformal Mixed-Integer Constraint Learning with Feasibility Guaranteescited by 1
  4. 2026Falsification-Based Verification of LLM-Generated Optimization Models: Sound Test Batteries and Their Detection Limitscited by 1
  5. 2024Output-Constrained Decision Treescited by 0
  6. 2024Mathematical Programming Algorithms for Convex Hull Approximation with a Hyperplane Budgetcited by 0
  7. 2025Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogatecited by 0
  8. 2025Optimal placement of wind farms via quantile constraint learningcited by 0
  9. 2025A study on constraint extraction and exception exclusion in care worker schedulingcited by 0
  10. 2026Efficient reformulations of ReLU deep neural networks for surrogate modelling in power system optimisationcited by 0
  11. 2026Monotone Optimisation with Learned Projectionscited by 0
  12. 2026Learning efficient representations of complex constraints for scalable optimizationcited by 0
  13. 2026Improving understanding and trust in AI: How users benefit from interval-based counterfactual explanationscited by 0
  14. 2026Optimization with Dynamic Constraint Learning (DCL)cited by 0
  15. 2026DCEmbed: Scalable Optimization over Neural Surrogatescited by 0
  16. 2026TACIT: Optimization Models that Learn from Their Mistakescited by 0