The uncapacitated <i>r</i>‐allocation <i>p</i>‐hub center problem
Bibliographic record
Abstract
Abstract In this paper, we propose the uncapacitated r‐allocation p‐hub center problem (UrApHCP), which represents a generalization of both single and multiple allocation variants of the p‐hub center problem. We further present two binary ‐integer linear programs for the UrApHCP and prove their equivalence for and p with respective single and multiple allocation cases. A flow formulation combining the features of the two previous models is also presented. In order to solve the UrApHCP, we develop two general variable neighborhood search (GVNS) heuristics that use nested and sequential variable neighborhood descent strategies. The proposed approaches are tested on benchmark instances from the literature with up to 423 nodes. The proposed GVNS quickly reaches all optimal or best‐known results from the literature for the single and multiple allocation variants of the problem, as well as new optimal results for r‐allocation obtained using a CPLEX 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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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 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".