The Hub Line Location Problem
Bibliographic record
Abstract
This paper presents the hub line location problem in which the location of a set of hub facilities connected by means of a path (or line) is considered. Potential applications arise in the design of public transportation and rapid transit systems, where network design costs greatly dominate routing costs and thus full interconnection of hub facilities is unrealistic. Given that service time is the predominant objective in these applications, the problem considers the minimization of the total weighted travel time between origin/destination nodes while taking into account the time spent to access and exit the hub line. An exact algorithm based on a Benders decomposition of a strong path-based formulation is proposed. The standard decomposition method is enhanced through the incorporation of several features such as a multicut strategy, an efficient algorithm to solve the subproblem and to obtain stronger optimality cuts, and a Benders branch-and-cut scheme that requires the solution of only one master problem. Computational results obtained on benchmark instances with up to 100 nodes confirm the efficiency of the proposed algorithm, which is considerably faster and able to solve larger instances than a general purpose solver.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.033 | 0.004 |
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 source (direct Gemma or distilled Codex), 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".