Column generation and local search for the profit-oriented hub-line location problem with elastic demands
Bibliographic record
Abstract
Population growth and city sprawl have been driving increasing amounts of traffic congestion in multiple major cities worldwide. In this scenario, developing efficient public transportation networks becomes critical to ensure adequate mobility. Hub network location models address the problems of designing public transit networks to model — and to optimize — passenger mobility. More specifically, hub-line location problems (HLLP) play an essential role in the design of rapid transit corridors and subway lines. In this work we address the profit-oriented hub-line location problem (ED-HLLP) for which we introduce a column generation method to solve the linear relaxation of a mixed-integer model and matheuristic that combines column generation and local search. The proposed methodologies lead to the calculation of primal and dual bounds. We assess the performance of the proposed methods on some classic datasets from the HLLP literature. Furthermore, we conduct a study based on real-world data representing the metropolitan area of Montreal, Canada. Finally, we conduct a sensitivity analysis to assess the major attributes driving our results, both from an algorithmic point of view as well as from a planning perspective. The numerical results show that the proposed methods produce high-quality solutions, reduce computational times, and address the model’s combinatorial complexity more effectively than a commercial off-the-shelf solver, allowing for the solution of larger problems otherwise untractable for the latter. • We introduce a column generation (CG) method for the ED-HLLP. • CG allows for the computation of strong dual bounds in moderate computing times. • Introduce a hybrid matheuristic that combines CG with local search (CG+LS). • CG+LS is capable of producing strong primal bounds in short computing times. • We perform a sensitivity analysis and derive managerial insights.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".