Vertical alignment optimization of mountain railways with terrain-driven greedy algorithm improved by Monte Carlo tree search
Bibliographic record
Abstract
Vertical alignment design is an important process for railway construction which fundamentally affects the infrastructure investment cost. Determining an optimized vertical alignment is a challenging task since the objective function is non-linear, non-differentiable, and quite unsmooth. Great efforts have been invested in solving the vertical alignment optimization problem and many methods have been proposed. However, for vertical alignment designs in complex mountainous regions, the terrain conditions impose great difficulties and, hence, many bridges and tunnels are generally required. Thus, reasonably locating bridges and tunnels along the entire alignment (EA) is a major concern that deserves further investigations. To solve this problem, this study develops a terrain-driven greedy algorithm improved by Monte Carlo tree search (T-GRA-MCTS). A terrain-driven method is proposed to determine the number and longitudinal distribution of vertical points of intersection (VPIs). In order to trade off the local section of an alignment versus the EA when optimizing each VPI along the alignment to locate bridges and tunnels reasonably, an MCTS is employed and integrated with a GRA. The basic MCTS is modified for vertical alignment optimization with a novel equation for computing the upper confidence bounds for trees and a customized termination criterion is provided. A real-world railway case is used to demonstrate the effectiveness of the proposed method. The results show that the T-GRA-MCTS performs better than a greedy search method without MCTS or a widely used nature-inspired algorithm (i.e., a particle swarm optimization). Moreover, it can find a less expensive solution than the one designed by experienced human engineers.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".