Estimating the Railway Network Capacity Utilization with Mixed Train Routes and Stopping Patterns: A Multiobjective Optimization Approach
Bibliographic record
Abstract
Railway capacity estimation problem is typically defined as estimating the maximum number of trains that can be operated in a railway section within a given time interval. However, trains with different speeds, routes, and stopping patterns in a railway network will likely compete for the limited capacity of network nodes and sections. As these trains may provide different services, it is ambiguous to simply indicate the network capacity by a scalar number of trains. To comprehensively estimate and interpret the railway capacity considering the capacity competition between heterogeneous trains, we propose a multiobjective perspective for the capacity estimation problem to enrich the capacity theory while handling the competition among trains with different routes and stopping patterns. Based on a time‐space network timetable saturation model, we extend the multiobjective capacity estimation approach to the detailed timetable level by optimizing the saturated timetable under capacity estimation objectives with respect to different routes and stopping patterns. With the ε‐constraint method, we can obtain the Pareto front of saturated timetables, i.e., a set of nondominated optimized timetables that no more candidate train can be additionally scheduled. The result is a more comprehensive capacity representation than a single absolute scalar number. A case study is conducted on a combined high‐speed and intercity network of Zhengzhou Railway group in China. An extensive set of Pareto‐optimal saturated timetables describing the effects on the capacity of the railway network is obtained. The results can help infrastructure managers select saturated timetables as the capacity utilization reference by considering the trade‐off between time indexes from passengers’ and operators’ perspectives.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".