Machine Learning for Optimization-Based Separation of Mixed-Integer Rounding Cuts
Bibliographic record
Abstract
Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in this family are derived by aggregating constraints then rounding coefficients, but finding the strongest MIR cuts requires optimizing a costly MIP for the aggregation step, so in practice, heuristic strategies for separating fractional points are employed. We propose to improve MIR cut generation in the context of a common scenario in applications, where constraints remain fixed but costs are varied. We present a hybrid cut generation framework in which we train a machine learning (ML) model to classify which constraints are involved in useful MIR cuts based on fractional points from relaxations of the problem. At test time, the predictions of the ML model create a reduced MIP-based generator of MIR cuts. In our experiments, we create an instance family from each of three benchmark MIP instances by performing a careful and costly perturbation of objective coefficients to build a dataset of 1,000 fractional points to be separated over the same constraint set. The results indicate that the reduced separator better strengthens the bound in each round of cut generation, particularly for instances in which the full separator failed to find strong cuts.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".