A Branch-Cut-and-Price Algorithm for the Energy Minimization Vehicle Routing Problem
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We study a variant of the capacitated vehicle routing problem where the cost over each arc is defined as the product of the arc length and the weight of the vehicle when it traverses that arc. We propose two new mixed-integer linear programming formulations for the problem: an arc-load formulation and a set partitioning formulation based on q-routes with additional constraints. A family of cycle elimination constraints are derived for the arc-load formulation. We then compare the linear programming (LP) relaxations of these formulations with the two-index one-commodity flow formulation proposed in the literature. In particular, we show that the arc-load formulation with the new cycle elimination constraints gives the same LP bound as the set partitioning formulation based on 2-cycle-free q-routes, which is stronger than the LP bound given by the two-index one-commodity flow formulation. We propose a branch-and-cut algorithm for the arc-load formulation, and a branch-cut-and-price algorithm for the set partitioning formulation strengthened by additional constraints. Computational results on instances from the literature demonstrate that a significant improvement can be achieved by the branch-cut-and-price algorithm over other methods.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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