An MDD-Based Lagrangian Approach to the Multicommodity Pickup-and-Delivery TSP
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Bibliographic record
Abstract
We address the one-to-one multicommodity pickup-and-delivery traveling salesman problem, a challenging variant of the traveling salesman problem that includes the transportation of commodities between locations. The goal is to find a minimum cost tour such that each commodity is delivered to its destination and the maximum capacity of the vehicle is never exceeded. We propose an exact approach that uses a discrete relaxation based on multivalued decision diagrams (MDDs) to better represent the combinatorial structure of the problem. We enhance our relaxation by using the MDDs as a subproblem to a Lagrangian relaxation technique, leading to significant improvements in both bound quality and run-time performance. Our work extends the use of MDDs for solving routing problems by presenting new construction methods and filtering rules based on capacity restrictions. Experimental results show that our approach outperforms state-of-the-art methodologies, closing 33 open instances from the literature, with 27 of those closed by our best variant.
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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