Lagrangean decomposition/relaxation for the routing and wavelength assignment problem
Bibliographic record
Abstract
Abstract This work deals with solving the Routing and Wavelength Assignment problem where the number of accepted connections is to be maximized. Lagrangean decomposition as well as Lagrangean relaxation are studied for both node‐arc formulations and arc‐path formulation. It is shown that relaxing the demand constraints yields an edge‐disjoint path problem with profits that is NP‐hard, while the Lagrangean problem obtained when the clash constraints are relaxed becomes a shortest path problem or a 0–1 linear knapsack problem, depending on the formulation used. Moreover, it is shown that the Lagrangean decomposition is not stronger than the Lagrangean relaxation of the demand constraints. We also propose a subgradient algorithm to solve the Lagrangean dual obtained by relaxing the clash constraints. Numerical results demonstrate a high quality of Lagrangean dual bounds with fast computation time. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012
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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 | 0.003 | 0.004 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".