Integral simplex using decomposition with primal cutting planes
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Bibliographic record
Abstract
This paper concentrates on the addition of cutting planes to the integral simplex using decomposition (ISUD) of Zaghrouti et al. (Oper Res 62(2):435–449, 2014). This method solves the set partitioning problem by iteratively improving an existing feasible solution. We present the algorithm in a primal language and relate it to existing augmenting methods. The resulting theoretical properties, stronger than the ones already known, simplify termination proofs and deepen the geometrical insights on ISUD in particular. We show that primal cuts, that is, cutting planes that are tight at the current feasible integer solution, can be used to improve the performance of the algorithm, and further that such cutting planes are enough to solve each augmentation problem. We propose efficient separation procedures for well-known polyhedral inequalities, namely primal clique and odd-cycle cuts. Numerical results demonstrate the effectiveness of primal cutting planes; tests are performed on small and large-scale set partitioning problems from aircrew and bus-driver scheduling instances up to 1600 constraints and 570,000 variables.
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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 | 0.001 | 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 it