An exact branch-and-price-and-cut algorithm for a practical and large-scale dial-a-ride problem
Bibliographic record
Abstract
Vehicle routing problems are encountered in various practical transportation scenarios. One such problem is the dial-a-ride problem (DARP), which involves transporting efficiently passengers from their origin to their destination and whose objective is to design vehicle routes minimizing total costs and accommodating all pickup-and-delivery requests. The solution must also adhere to capacity limitations, time windows, and a maximum ride time for each passenger. This paper proposes an exact branch-price-and-cut algorithm to solve a practical variant of the DARP, where both the passengers and vehicle fleet are heterogeneous, and other practical constraints such as break requirements and maximum route duration are imposed. In this algorithm, column generation which alternates between solving a master problem and subproblems, is used to compute lower bounds in the search tree. We develop a labeling algorithm to efficiently handle these subproblems. The effectiveness of the algorithm is evaluated on a real-world case study involving 849 heterogeneous passengers and more than 70 available vehicles, as well as on 10 smaller instances (with 300 to 820 trips) extracted from another very large real-world dataset. To the best of our knowledge, this 849-trip instance is the largest DARP instance reported to be solved to optimality in the literature.
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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 | 0.003 |
| 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 | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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".