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End-to-End Constrained Optimization Learning: A Survey

arXiv 2103.16378 ↗First posted 30 Mar 2021cs.LG cs.AIcited by 154

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Abstract (arXiv)

This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning architectures. These approaches hold the promise to develop new hybrid machine learning and optimization methods to predict fast, approximate, solutions to combinatorial problems and to enable structural logical inference. This paper presents a conceptual review of the recent advancements in this emerging area.

Key facts. Cited by 154 papers in the map (data through 7 Oct 2026). Builds on 33 of its 71 references that are in the map. First posted on arXiv 30 Mar 2021.

Builds on

33 of 71 references.

References · 33

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  12. 2018Reinforcement Learning for Solving the Vehicle Routing Problemcited by 327
21 more
  1. 2019Exact Combinatorial Optimization with Graph Convolutional Neural Networkscited by 313
  2. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  3. 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 265
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  6. 2019SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solvercited by 173
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  21. 2020Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flowcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 14; 2022: 25; 2023: 29; 2024: 33; 2025: 21; 2026: 32.

154 papers.

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  1. 2021Combinatorial Optimization with Physics-Inspired Graph Neural Networkscited by 107
  2. 2022Tutorial on amortized optimizationcited by 83
  3. 2023A Survey of Contextual Optimization Methods for Decision Making under Uncertaintycited by 81
  4. 2021Decision-Focused Learning: Through the Lens of Learning to Rankcited by 61
  5. 2022Self-Supervised Primal-Dual Learning for Constrained Optimizationcited by 60
  6. 2022MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solverscited by 48
  7. 2022Modern graph neural networks do worse than classical greedy algorithms in solving combinatorial optimization problems like maximum independent setcited by 33
  8. 2024Diffusion Models as Constrained Samplers for Optimization with Unknown Constraintscited by 33
  9. 2022Graph Coloring with Physics-Inspired Graph Neural Networkscited by 29
  10. 2021Risk Bounds and Calibration for a Smart Predict-then-Optimize Methodcited by 28
  11. 2021Optimization with Constraint Learning: A Framework and Surveycited by 28
  12. 2022Learning with Combinatorial Optimization Layers: a Probabilistic Approachcited by 28
38 more
  1. 2024CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbationscited by 27
  2. 2021Integrated Conditional Estimation-Optimizationcited by 25
  3. 2021Techniques for Symbol Grounding with SATNetcited by 24
  4. 2023Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problemscited by 24
  5. 2024Scaling physics-informed hard constraints with mixture-of-expertscited by 24
  6. 2021Learning Hard Optimization Problems: A Data Generation Perspectivecited by 21
  7. 2021Fast Approximations for Job Shop Scheduling: A Lagrangian Dual Deep Learning Methodcited by 20
  8. 2023Machine Learning for Cutting Planes in Integer Programming: A Surveycited by 19
  9. 2021End-to-end Learning for Fair Ranking Systemscited by 18
  10. 2024End-to-end Conditional Robust Optimizationcited by 17
  11. 2022Flexible Differentiable Optimization via Model Transformationscited by 16
  12. 2024Learning Constrained Optimization with Deep Augmented Lagrangian Methodscited by 16
  13. 2025ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projectioncited by 15
  14. 2022Decision-Aware Learning for Optimizing Health Supply Chainscited by 14
  15. 2023Learning-based Online Optimization for Autonomous Mobility-on-Demand Fleet Controlcited by 14
  16. 2021Graph neural network initialisation of quantum approximate optimisationcited by 13
  17. 2023Backpropagation of Unrolled Solvers with Folded Optimizationcited by 13
  18. 2023A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraintscited by 12
  19. 2022Online Contextual Decision-Making with a Smart Predict-then-Optimize Methodcited by 11
  20. 2023Differentiating Through Integer Linear Programs with Quadratic Regularization and Davis-Yin Splittingcited by 11
  21. 2024Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Processcited by 11
  22. 2024Dual Lagrangian Learning for Conic Optimizationcited by 11
  23. 2021Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approachcited by 10
  24. 2023Combinatorial Optimization enriched Machine Learning to solve the Dynamic Vehicle Routing Problem with Time Windowscited by 10
  25. 2024HW-GPT-Bench: Hardware-Aware Architecture Benchmark for Language Modelscited by 10
  26. 2024First-Order Methods for Linearly Constrained Bilevel Optimizationcited by 10
  27. 2025Enforcing Hard Linear Constraints in Deep Learning Models with Decision Rulescited by 10
  28. 2022O-ViT: Orthogonal Vision Transformercited by 9
  29. 2024SupplyGraph: A Benchmark Dataset for Supply Chain Planning using Graph Neural Networkscited by 9
  30. 2022Maximum Common Subgraph Guided Graph Retrieval: Late and Early Interaction Networkscited by 8
  31. 2023Deep reinforcement learning for machine scheduling: Methodology, the state-of-the-art, and future directionscited by 8
  32. 2024Combining Constraint Programming Reasoning with Large Language Model Predictionscited by 8
  33. 2024Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guaranteescited by 8
  34. 2023Heuristics for Vehicle Routing Problem: A Survey and Recent Advancescited by 7
  35. 2023Learning Optimal Power Flow Value Functions with Input-Convex Neural Networkscited by 7
  36. 2024Graph Neural Networks in Supply Chain Analytics and Optimization: Concepts, Perspectives, Dataset and Benchmarkscited by 7
  37. 2021Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problemscited by 6
  38. 2022A Note on Task-Aware Loss via Reweighing Prediction Loss by Decision-Regretcited by 6

50 most cited of 154 All 154 (JSON)