Mixed Integer Linear Programming Based Speed Profile Optimization for Heavy-Haul Trains
Bibliographic record
Abstract
Automatic heavy‐haul train (HHT) operation technology has recently received considerable attention in the field of rail transportation. In this paper, a discrete‐time‐based mathematical formulation is proposed to address the speed profile optimization problem in order to ensure the safe, efficient, and economical operation of heavy‐haul trains (HHTs). Due to the presence of long and steep downgrades (LSDs) on some heavy‐haul lines, the brake forces of the HHT are typically jointly determined by air braking and electric braking. The time characteristics of the air braking, such as the command delay and the change process caused by the air pressure, are taken into account, and then formulas are presented to calculate the air brake force. In addition, the influence of the neutral section on the control of the electric braking is considered via space‐based constraints. The resulting problem is a nonlinear optimal control problem. To achieve linearization, auxiliary 0‐1 binary variables and the big‐M approach are introduced to transform the nonlinear constraints regarding slope, curve, neutral section, air brake force, and air‐filled time into linear constraints. Moreover, piecewise affine (PWA) functions are used to approximate the basic resistance of the HHT. Finally, a mixed integer linear programming (MILP) model is developed, which can be solved by CPLEX. The experiments are carried out using data from a heavy‐haul railway line in China, and the results show that the proposed approach is effective and flexible.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".