A Lagrangean Relaxation and Subgradient Framework for the Routing and Wavelength Assignment Problem in WDM Networks
Bibliographic record
Abstract
Unlike traditional heuristics, we provide in this paper an optimization framework for the routing and wavelength assignment (RWA) problems with the objective of minimizing the rejection penalty of the connection demands in an all-optical wavelength-division-multiplexing (WDM) network. Our new link-based formulation takes the fairness issue and the limited wavelength conversion into consideration. The framework employs a decomposition approach to decide on the rejection/selection of the route and wavelength assignment for a semilightpath, by appropriately relaxing some of the constraints in the Lagrangean relaxation (LR) method. At the higher level, we update Lagrange multipliers iteratively with the subgradient method. At the lower level, we propose the modified minimum cost semilightpath (MMCSLP) algorithm to solve all the subproblems. A heuristic algorithm is also proposed to generate a feasible RWA scheme based on the solution to the dual problem. When compared with some latest methodology in the literature, we demonstrate that our framework can achieve better performance in terms of the computation time and the number of connection demands rejected. The much shorter computation time is due to the polynomial time complexity of our framework. In addition to achieving a very good (near-optimal) solution, the influence from the change of the number of converters is studied. Finally, we demonstrate that our framework produces fairer routing decisions by adjusting some design parameters in our framework.
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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 | 0.002 | 0.003 |
| 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 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".