Exact and Heuristic Algorithms for Capacitated Vehicle Routing Problems with Quadratic Costs Structure
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Bibliographic record
Abstract
In this article we introduce the quadratic capacitated vehicle routing problem (QCVRP) motivated by two applications in engineering and logistics: the capacitated vehicle routing problem with angle penalties (angle-CVRP) and the capacitated vehicle routing problem with reload costs (CVRP-RC). We introduce a three-index vehicle-flow formulation of the problem, which is strengthened with valid inequalities, and we derive a branch-and-cut algorithm capable of providing tight lower bounds and solving small- to medium-size instances in short to moderate computing times. Furthermore, we present a hybrid metaheuristic capable of providing high quality solutions in short computing times. The two algorithms are tested on several instances from the CVRP literature modified to mimic the two problems that motivate our study.
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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 | 0.001 | 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 | 0.001 |
| 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