Reaching the Elementary Lower Bound in the Vehicle Routing Problem with Time Windows
Bibliographic record
Abstract
In this article, we present a comparative study of several strategies that can be applied to achieve the so-called elementary lower bound in vehicle routing problems, that is, the bound obtained when all positive-valued variables in an optimal solution of the linear relaxation of the set-partitioning formulation correspond to vehicle routes without cycles. This bound can be achieved by solving the resource-constrained elementary shortest path problem-an NP-hard problem-as the pricing problem in a column generation algorithm, but several other strategies can be used to ultimately produce the same lower bound in less computational effort. State-of-the-art algorithms for vehicle routing problems rely on the quality of this lower bound to either bound the size of the search tree in a branch-and-price algorithm or the complexity of an enumeration procedure used to limit the number of variables in the set-partitioning model. We consider several strategies for imposing elementarity that involve ng-paths, strong degree constraints, and decremental state-space relaxation. We compare the performance of these strategies on some selected instances of the vehicle routing problem with time windows. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 651, 88-99. 2015
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How this classification was reachedexpand
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 | 0.002 | 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 | 0.001 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".