Primal column generation framework for vehicle and crew scheduling problems
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Bibliographic record
Abstract
Abstract The primal adjacency‐based algorithm and the multidirectional dynamic programming algorithm are two exact methods that have recently been developed to efficiently solve the shortest path problem with resource constraints (SPPRCs). These methods are primal in the sense that they are able to produce sequences of feasible solutions using iterative exploration of the search space. Since the SPPRCs often appear as a subproblem (SP) in the solution of vehicle and crew scheduling problems (VCSP) using column generation (CG), we propose a new primal column generation framework that embeds these primal methods in a CG scheme. The primal column generation solves at each iteration a sequence of appropriate restricted SP and stops solving the SP when there is no need to continue. This approach introduces a large degree of flexibility, and allows performing good cost improvements in a very limited time. Computational experiments on VCSP instances show that the proposed approach is able to find optimal solutions while reducing the time spent solving the SP by factors of up to seven compared to the standard CG algorithm. This leads to significant improvements in the overall solution times, with an average reduction factor of 3.5.
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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 | 0.000 | 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 it