Selective pricing in branch-price-and-cut algorithms for vehicle routing
Bibliographic record
Abstract
Branch-price-and-cut is a leading methodology for solving various vehicle routing problems (VRPs). For many VRPs, the pricing subproblem of a branch-price-and-cut algorithm is highly time consuming, and to alleviate this difficulty, a relaxed pricing subproblem is used. In this paper, we introduce a new paradigm, called selective pricing, that can be applied in this context to reduce the time required for solving hard-to-solve VRPs by branch-price-and-cut. This paradigm requires the development of a labeling algorithm specific to the pricing subproblem. To illustrate selective pricing, we apply it to a branch-price-and-cut algorithm for the VRP with time windows, where the relaxed pricing subproblem is a shortest ng-path problem with resource constraints. We develop a labeling algorithm for this subproblem and show through computational experiments that it can yield significant time reductions (up to 32%) to reach a good lower bound on certain very-hard-to-solve VRPTW instances with 200 customers. We also introduce a new labeling heuristic which also leads to computational time reductions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".