An Iterated Local Search Metaheuristic for the Capacitated Demand-Driven Timetabling Problem
Bibliographic record
Abstract
In many major cities, metro lines constitute the backbone of urban public transport, providing an efficient and greener alternative to private mobility. An important feature that distinguishes metro lines from other public transport means, such as buses, is that metros are typically tightly resource constrained. The trains operating on a particular line are often specifically fitted for that line, making any capacity expansion extremely costly and time-consuming. Therefore, researchers and operators alike are seeking ways to make better use of existing resources. One possible way of doing so is by adapting timetables to forecasted demand while accounting for limited vehicle capacities. Thus, we consider a demand-driven nonperiodic timetabling problem for a two-directional metro line that minimizes the total passenger waiting time through the efficient scheduling of the available trains. Considering that passengers board trains using a well-mixed policy, we explicitly account for train capacities on a moment-to-moment basis. Last, we consider that trains are allowed to short turn. In this respect, we assume that trains must pass by a given station before short turning and are only allowed to idle after having short turned. We devise a polynomial time algorithm for assessing the total passenger waiting time generated by a given timetable and an effective lower bound that is evaluated in linear time. These are used in a variable neighborhood search algorithm, which is embedded in an iterated local search metaheuristic. Classical local search-based neighborhoods are not effective for our problem because they do not explicitly handle the vehicle scheduling decisions. To handle this challenge, we proposed three tailored neighborhoods. We validate our heuristic on the uncapacitated version of the problem. Considering a benchmark of 48 artificial instances with up to 20 stations, our heuristic achieved an average gap of 0.67% and found eight new best solutions. We also validated our heuristic on three sets of instances based on realistic lines from Milan, Madrid, and Beijing. Furthermore, we demonstrate the operational advantages of our optimized timetables in the capacitated version of the problem by comparing them with regular timetables and with exact solutions obtained for the uncapacitated case. Furthermore, we conduct a sensitivity analysis with respect to the capacity of the trains and investigate the impact of a priority boarding policy. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0271 .
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".