Resilient Network Design: Disjoint Shortest Path Problem for Power Transmission Application
Bibliographic record
Abstract
Path redundancy is essential for safety and reliability in many real-world routing problems, such as the design of networks for power transmission, transportation, etc. These problems are typically posed to find the shortest path on a weighted graph. For the shortest path with path redundancy, particularly in the Disjoint Shortest 2-Path (DS2P) problem, two disjoint paths are desired such that the combined weight of the two paths is minimized while a minimum distance path separation is maintained. The conventional formulation of the above requires a large-scale mixed-integer programming (MIP) model. However, this approach is practically intractable due to the model’s complexity and extremely long run-time. We demonstrate why DS2P is NP-complete and propose an efficient heuristic to find an approximate solution to the problem in a much shorter time frame. We demonstrate the approach on a realistic dataset for power transmission routing, integrating the computational methodology with a visualization interface using Google Maps. The resulting prototype software is freely available through GitHub and can be deployed on a cloud platform, such as Amazon AWS.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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".