Combining Constraint Programming and Machine Learning: From Current Progress to Future Opportunities
Bibliographic record
Abstract
The integration of constraint programming (CP) together with machine learning (ML) has emerged as a promising direction for tackling complex decision-making and combinatorial optimization problems. While CP offers expressive modeling capabilities and formal guarantees, ML provides adaptive methods for learning from data and generalizing across instances. This survey presents a comprehensive overview of recent advances in combining CP and ML. We first show how ML has been used to improve the CP toolbox, both in modeling and in the efficiency of solving. Then, we examine how CP can support ML, particularly in providing structure, guarantees, and symbolic reasoning capabilities. Finally, we identify key open challenges inherent to such hybrid approaches and outline promising directions for future research. This survey provides a first conceptual and structured review of recent advancements in this emerging field, aiming to serve as a resource for practitioners and researchers in both the CP and ML communities. To keep the progress up to date, a curated list of references is hosted on an accompanying repository (https://github.com/corail-research/CPML-paper-list) and is open to community contributions.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".