Shortest Path Planning in Multimodal Metropolitan Transportation Networks Under Timetable and Label Constraints
Bibliographic record
Abstract
This study proposes a label‐setting shortest‐path algorithm with timetable and label constraints to address the path‐planning problem in multimodal urban agglomeration transportation networks. The proposed algorithm addresses the limitations of traditional shortest‐path methods, which are often challenged by complex conditions, including transfer constraints, timetable dependencies, and restrictions on the number of transfers. By analyzing the characteristics of urban agglomeration trip chains, this study constructed a multimodal network model incorporating six transportation modes: walking, buses, intercity coaches, metro, intercity railways, and private vehicles. A deterministic finite automaton was introduced to constrain feasible mode sequences, ensuring that path planning aligns with real‐world travel patterns. The algorithm incorporates time‐window constraints to simulate the effects of static timetables in scheduled transportation modes, such as railways and coaches. By improving the label‐correcting algorithm via topological sorting and applying state‐dominance rules to reduce redundant computations, it achieves optimal path planning under multiple constraints. Case studies demonstrate that the algorithm effectively balances transfer frequency and travel cost, reducing total cost by approximately 5% while ensuring feasibility, thereby validating the synergistic advantages of multimodal transportation networks. Therefore, the proposed algorithm can theoretically support multimodal traffic selection behavior or mixed traffic network modeling.
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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 | 0.000 |
| 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) | 0.002 | 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".