Research map / Learning theory and algorithms / Combinatorial and search optimization
Learning branch-and-cut for MILP
Learns branching, cutting and search policies for mixed-integer programs, with generalization guarantees.
54 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Combinatorial and search optimization, keyword cluster “integer · linear · mixed”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
22 papers in 2023–24 and 16 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 6.3% to 4.4%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · The Complexity Landscape of Decompositional Parameters for ILP (AAAI 2016 · 50 citations)
- 2017 · Going Beyond Primal Treewidth for (M)ILP (AAAI 2017 · 26 citations)
- 2019 · Automatic Construction of Parallel Portfolios via Explicit Instance Grouping (AAAI 2019 · 33 citations)
- 2020 · MIPaaL: Mixed Integer Program as a Layer (AAAI 2020 · 98 citations)
- 2021 · Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies (AAAI 2021 · 60 citations)
- 2022 · Learning to Search in Local Branching (AAAI 2022 · 23 citations)
- 2023 · Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model (ICLR 2023 · 14 citations)
- 2024 · Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programming (AAAI 2024 · 4 citations)
- 2025 · Towards Foundation Models for Mixed Integer Linear Programming (ICLR 2025 · 3 citations)
- 2026 · RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programs (ICML 2026 · 1 citation)
Earliest papers here
- The Complexity Landscape of Decompositional Parameters for ILP (AAAI 2016 · 50 citations)
- Going Beyond Primal Treewidth for (M)ILP (AAAI 2017 · 26 citations)
- Automatic Construction of Parallel Portfolios via Explicit Instance Grouping (AAAI 2019 · 33 citations)
What has been tried
39 papers here report 375 measured changes (a component added, removed or swapped, compared with a baseline): helped 73%, no clear effect 3%, hurt 18%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| replace direct stop/continue decisions with an indirect learned stagnation threshold | MIK · solving time | 21.5(15.3) -> 10.9(5.4) | Helped | Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programming (AAAI 2024 · 4 citations) |
| Add the attention layer | MILP-Evolve held-out test · integrality gap correlation | 0.57 -> 0.58 | Helped | Towards Foundation Models for Mixed Integer Linear Programming (ICLR 2025 · 3 citations) |
| Lower the slack penalty from λ=1 to λ=0.1 | DNDP · MRE | Helped | Neur2BiLO: Neural Bilevel Optimization (NeurIPS 2024 · 2 citations) | |
| Increase the modification ratio from η=0.01 to η=0.10 | CA · graph similarity | 0.997 -> 0.946 | Hurt | MILP-StuDio: MILP Instance Generation via Block Structure Decomposition (NeurIPS 2024 · 1 citation) |
| Use preference-based learning instead of direct reward fitting | Fuel Cell Energy Management, T=10 to T=60 · accuracy | 95.65% vs 91.07%; 83.04% vs 72.43%; 73.88% vs 64.51%; 73.21% vs 63.62%; 56.14% vs 41.85%; 39.71% vs 32.90% | Helped | Fast and Interpretable Mixed-Integer Linear Program Solving by Learning Model Reduction (AAAI 2025 · 0 citations) |
| Use BIPNN-generated rather than original hypergraph structure | hypergraph max-cut · cuts | Helped | BIPNN: Learning to Solve Binary Integer Programming via Hypergraph Neural Networks (NeurIPS 2025 · 0 citations) | |
| replace consistency-based fixing with direct fixing of reference partial solutions | IP test · absolute primal gap | 0.00 -> 0.32 | Hurt | Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming (ICLR 2025 · 0 citations) |
| Add Single-AM to the QAP encoder | QAP20 · Gap | 12.67% -> -0.54% | Helped | Learning Solution-Aware Transformers for Efficiently Solving Quadratic Assignment Problem (ICML 2024 · 0 citations) |
| add multiple LM samples and keep the best | Mc-Sml-40 and Mc-Big-Var · GAP % | 2.10 -> 2.09; 4.79 -> 4.77 | Helped | Predicting Lagrangian Multipliers for Mixed Integer Linear Programs (ICML 2024) |
| Add constraint grouping to ACM-MILP rather than modifying one constraint at a time | MIS · solving-time relative error to training set | 24.1% -> 17.1% | Helped | ACM-MILP: Adaptive Constraint Modification via Grouping and Selection for Hardness-Preserving MILP Instance Generation (ICML 2024) |
| Use quality-weighted InfoNCE instead of unweighted InfoNCE | MVC · primal gap | 0.12% -> 0.10% | Helped | Contrastive Predict-and-Search for Mixed Integer Linear Programs (ICML 2024) |
What reviewers will expect
Datasets and baselines named in the 10 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- Predict-and-Search · 3 of 10 papers
- Gurobi · 2 of 10 papers
- Neural Diving · 2 of 10 papers
- SCIP · 2 of 10 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 38 papers; from OpenAlex and the papers' affiliations).
- University of Science and Technology of China · 6 papers
- Huawei · 6 papers
- Southeast University · 2 papers
- University of Toronto · 2 papers
- Shenzhen Research Institute of Big Data · 2 papers
- The Chinese University of Hong Kong · 2 papers
- Shanghai Jiao Tong University · 2 papers
- University of Southern California · 2 papers
- Meta · 2 papers
- Swiss Federal Institute of Technology · 2 papers
Use it
Download BibTeX of 38 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Predict-then-optimize learning (89 papers)
- Heuristics for integer programming (60 papers)
- Semidefinite relaxations for verification (47 papers)
Elsewhere in the topic
- Logic and answer set programming theory (150 papers)
- Heuristic and local search algorithms (147 papers)
- Classical and HTN planning (145 papers)
- Unsupervised neural combinatorial optimization (113 papers)
- Constrained neural network optimization (111 papers)
- Decision-focused optimization (97 papers)
- Multi-objective optimization (93 papers)
- Structure and complexity of constraint reasoning (92 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).