Lagrangean‐based decomposition algorithms for multicommodity network design problems with penalized constraints
Bibliographic record
Abstract
Abstract This article discusses problems in the context of multicommodity network design where additional constraints (such as capacity), rather than being imposed in a strict manner, are allowed to be violated at the expense of additional penalty costs. Such penalized cost structures allow these constraints to be treated as utilization targets and provide a better modelling framework in terms of strategic or tactical level planning of network design, especially in freight transportation systems. However, due to the penalized costs, these problems are generally in the form of a nonlinear integer multicommodity network design problem. This article presents two algorithms based on Lagrangean relaxation and decomposition for the solution of such problems. The first relies upon dualizing the capacity constraints that results in a flow decomposition, and the second is through relaxing flow constraints that results in an arc decomposition. It is shown that nonlinearities in the decomposed substructures can be handled in a very efficient manner. Arc decomposition is shown, through computational experiments, to have better convergence properties. Through the proposed algorithms, reasonably good solutions can be obtained for these problems where publicly available state‐of‐the‐art nonlinear optimization codes fail to identify feasible solutions. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010
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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 | 0.005 |
| 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 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".