Exact Solution of Several Families of Location-Arc Routing Problems
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Bibliographic record
Abstract
We model and solve several families of location-arc routing problems on an undirected graph. These problems extend the multidepot rural postman problem to the case where the depots are not fixed. The aim is to select the facility locations and to construct a set of routes traversing each required edge of the graph, where each route starts and ends at the same facility. The models differ from each other in their objective functions and on whether they include a capacity constraint. Alternative formulations are presented that use only binary variables, and are valid even when the input graph is not complete. This applies, in particular, to a compact two-index formulation for problems minimizing the overall routing costs, with or without facility setup costs. This formulation incorporates a new set of constraints that force the routes to be consistent and return to their original depots. A polyhedral study is presented for some of the formulations, which indicates that the main families of constraints are facet defining. All formulations are solved by branch and cut, and instances with up to 200 vertices are solved to optimality. Despite the difficulty of the problems, the numerical results demonstrate the good performance of the algorithm.
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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 | 0.001 |
| 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