Tabu Search, Partial Elementarity, and Generalized <i>k</i>-Path Inequalities for the Vehicle Routing Problem with Time Windows
Why this work is in the frame
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Bibliographic record
Abstract
The vehicle routing problem with time windows consists of delivering goods at minimum cost to a set of customers using an unlimited number of capacitated vehicles assigned to a single depot. Each customer must be visited within a prescribed time window. The most recent successful solution methods for this problem are branch-and-price-and-cut algorithms where the column generation subproblem is an elementary shortest-path problem with resource constraints (ESPPRC). In this paper, we propose new ideas having the potential to improve such a methodology. First, we develop a tabu search heuristic for the ESPPRC that allows, in most iterations, the generation of negative reduced cost columns in a short computation time. Second, to further accelerate the subproblem solution process, we propose to relax the elementarity requirements for a subset of the nodes. This relaxation, however, yields weaker lower bounds. Third, we introduce a generalization of the k-path inequalities and highlight that these generalized inequalities can, in theory, be stronger than the traditional ones. Finally, combining these ideas with the most recent advances published in the literature, we present a wide variety of computational results on the Solomon's 100-customer benchmark instances. In particular, we report solving five previously unsolved instances.
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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 | 0.001 | 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