A hybrid algorithm for the multi-depot vehicle scheduling problem arising in public transportation
Bibliographic record
Abstract
In this article, a hybrid algorithm is proposed to solve the Vehicle Scheduling Problem with Multiple Depots. The proposed methodology uses a genetic algorithm, initialized with three specialized constructive procedures. The solution generated by this first approach is then refined by means of a Set Partitioning (SP) model, whose variables (columns) correspond to the current itineraries of the final population. The SP approach possibly improves the incumbent solution which is then provided as an initial point to a well-known MDVSP model. Both the SP and MDVSP models are solved with the help of a mixed integer programming (MIP) solver. The algorithm is tested in benchmark instances consisting of 2, 3 and 5 depots, and a service load ranging from 100 to 500. The results obtained showed that the proposed algorithm was capable of finding the optimal solution in most cases when considering a time limit of 500 seconds. The methodology is also applied to solve a real-life instance that arises in the transportation system in Colombia (2 depots and 719 services), resulting in a decrease of the required fleet size and a balanced allocation of services, thus reducing deadhead trips.
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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 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".