Progressive hedging‐based metaheuristics for stochastic network design
Bibliographic record
Abstract
Abstract We consider the stochastic fixed‐charge capacitated multicommodity network design (S‐CMND) problem with uncertain demand. We propose a two‐stage stochastic programming formulation, where design decisions make up the first stage, while recourse decisions are made in the second stage to distribute the commodities according to observed demands. The overall objective is to optimize the cost of the first‐stage design decisions plus the total expected distribution cost incurred in the second stage. To solve this formulation, we propose a metaheuristic framework inspired by the progressive hedging algorithm of Rockafellar and Wets. Following this strategy, scenario decomposition is used to separate the stochastic problem following the possible outcomes, scenarios, of the random event. Each scenario subproblem then becomes a deterministic CMND problem to be solved, which may be addressed by efficient specialized methods. We also propose and compare different strategies to gradually guide scenario subproblems to agree on the status of design arcs and aim for a good global design. These strategies are embedded into a parallel solution method, which is numerically shown to be computationally efficient and to yield high‐quality solutions under various problem characteristics and demand correlations. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".