Research map / Learning theory and algorithms / Combinatorial and search optimization
Heuristics for integer programming
Solves large integer programs through neighborhood search, message passing and solver configuration learning.
60 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 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.
14 papers in 2023–24 and 11 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 4.0% to 3.0%.
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 · Guaranteed Outlier Removal With Mixed Integer Linear Programs (CVPR 2016 · 50 citations)
- 2017 · A Clever Elimination Strategy for Efficient Minimal Solvers (CVPR 2017 · 49 citations)
- 2018 · Deep Hashing via Discrepancy Minimization (CVPR 2018 · 61 citations)
- 2019 · Separator-Based Pruned Dynamic Programming for Steiner Tree (AAAI 2019 · 16 citations)
- 2020 · Lifted Disjoint Paths with Application in Multiple Object Tracking (ICML 2020 · 89 citations)
- 2021 · Branch and Price for Bus Driver Scheduling with Complex Break Constraints (AAAI 2021 · 7 citations)
- 2022 · An Exact Algorithm with New Upper Bounds for the Maximum k-Defective Clique Problem in Massive Sparse Graphs (AAAI 2022 · 17 citations)
- 2023 · Walkability Optimization: Formulations, Algorithms, and a Case Study of Toronto (AAAI 2023 · 7 citations)
- 2024 · An N-Point Linear Solver for Line and Motion Estimation with Event Cameras (CVPR 2024 · 9 citations)
- 2025 · Convex Relaxation for Robust Vanishing Point Estimation in Manhattan World (CVPR 2025 · 5 citations)
- 2026 · Assignment Problems in Cost Function Networks (AAAI 2026 · 4 citations)
Earliest papers here
- Guaranteed Outlier Removal With Mixed Integer Linear Programs (CVPR 2016 · 50 citations)
- Moral Lineage Tracing (CVPR 2016 · 23 citations)
- A Clever Elimination Strategy for Efficient Minimal Solvers (CVPR 2017 · 49 citations)
What has been tried
47 papers here report 371 measured changes (a component added, removed or swapped, compared with a baseline): helped 70%, no clear effect 8%, hurt 16%, 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 |
|---|---|---|---|---|
| Increase the event count from 5 to 10 | Synthetic pixel noise (0.5 px) · direction error (mean, median; °) | 5.53/1.24 -> 0.46/0.15 | Helped | An N-Point Linear Solver for Line and Motion Estimation with Event Cameras (CVPR 2024 · 9 citations) |
| Increase the maximum inlier threshold c | Synthetic dataset · F1-score | Hurt | Convex Relaxation for Robust Vanishing Point Estimation in Manhattan World (CVPR 2025 · 5 citations) | |
| Increase the proactive single-sample quantile from γ=0.5 to γ=0.9 | j10, tuning subset · feasibility ratio | 0.11 -> 0.94 | Helped | Proactive and Reactive Constraint Programming for Stochastic Project Scheduling with Maximal Time-Lags (AAAI 2025 · 3 citations) |
| Use CLUB in both preprocessing and BnB search instead of the KDBB bounds | MDCP instances across 341 graphs, k=3 and k=10 · number of instances solved over time | Helped | KD-Club: An Efficient Exact Algorithm with New Coloring-Based Upper Bound for the Maximum k-Defective Clique Problem (AAAI 2024 · 2 citations) | |
| allow indifferences in daycare priorities | Tama-21 · matched children | 560 -> 571 | Helped | Stable Matchings in Practice: A Constraint Programming Approach (AAAI 2024 · 2 citations) |
| Gather AllDifferentExcept constraints | ORLY 124, 7 days · unassigned registrations | 281 -> 253 | Helped | Check-In Desk Scheduling Optimisation at CDG International Airport (AAAI 2024 · 1 citation) |
| increase the number of current eigenvectors k_c | Spectral bundle convergence · convergence | Helped | Fast, Scalable, Warm-Start Semidefinite Programming with Spectral Bundling and Sketching (ICML 2024 · 0 citations) | |
| Add simultaneous pruning tests to standard branch-and-bound pruning | Synthetic data (varying one parameter at a time) · solving time | at least a factor 5 | Helped | A New Branch-and-Bound Pruning Framework for $\ell_0$-Regularized Problems (ICML 2024 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 25 papers; from OpenAlex and the papers' affiliations).
- Kyushu University · 2 papers
- CyberAgent Inc · 2 papers
Use it
Download BibTeX of 39 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Predict-then-optimize learning (89 papers)
- Learning branch-and-cut for MILP (54 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).