Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm
Bibliographic record
Abstract
In “Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm,” Uit het Broek, Schrotenboer, Jargalsaikhan, Roodbergen, and Coelho present a generic branch-and-cut framework to solve routing problems with multiple depots on directed graphs. They present new valid inequalities that eliminate subtours, enforce tours to be linked to the same depot, and enforce bounds on the number of customers in a vehicle tour. This is embedded in a branch-and-cut scheme that also contains generalized and adapted versions of valid inequalities that are well known for related routing problems. The authors show that the new inequalities tighten root node relaxations considerably. In combination with a simple but effective upper-bound procedure, only requiring a MIP solver and a smart reduction of the problem size, the authors show that the overall framework solves instances of considerably larger size to optimality than have been reported in the literature.
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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) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| 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".