New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows
Bibliographic record
Abstract
The vehicle routing problem with time windows (VRPTW) consists of finding least-cost vehicle routes to satisfy the demands of customers that can be visited within specific time windows. We introduce two enhancements for the exact solution of the VRPTW by branch-price-and-cut (BPC). First, we develop a sharper form of the limited-memory subset-row inequalities by representing the memory as an arc subset rather than a node subset. Second, from the elementary inequalities introduced by Balas in 1977, we derive a family of inequalities that dominate them. These enhancements are embedded into an exact BPC algorithm that includes state-of-the-art features such as bidirectional labeling, decremental state-space relaxation, completion bounds, variable fixing, and route enumeration. Computational results show that these enhancements are particularly effective for the most difficult instances and that our BPC algorithm can solve all 56 Solomon instances with 100 customers and 51 of 60 Gehring and Homberger instances with 200 customers.
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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 | 0.001 | 0.008 |
| 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 | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".