A multiple-path gradient projection method for solving the logit-based stochastic user equilibrium model
Bibliographic record
Abstract
This paper proposes a path-based algorithm for solving the well-known logit-based stochastic user equilibrium (SUE) problem in transportation planning and management. Based on the gradient projection (GP) method, the new algorithm incorporates a novel multiple-path gradient approach to generate the descent direction in consideration of many paths existing in every single origin-destination (O-D) pair. To apply the path-based algorithm, the SUE problem is reformulated as a variational inequality (VI), and a working path set is predetermined. The numerical experiments are conducted on the Winnipeg network where a large number of paths are provided. The results show the multiple-path gradient projection algorithm outperforms the original GP method. Three different step size strategies, including the fixed step size, self-regulated averaging and self-adaptive Armijo’s strategies, are involved to draw a more general conclusion. Also, the effects of the path number on computational performance are analyzed. The multiple-path gradient projection (MGP) method converges much faster than the GP method when the path set size gets large.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".