Bibliographic record
Abstract
Solving a large batch of linear programs (LPs) with varying parameters is needed in stochastic programming and sensitivity analysis, among other modeling frameworks. Solving the LPs for all combinations of given parameter values, called the brute-force approach, can be computationally infeasible when the parameter space is high-dimensional and/or the underlying LP is computationally challenging. This paper introduces a computationally efficient approach for solving a large number of LPs that differ only in the right-hand side of the constraints ([Formula: see text] of [Formula: see text]). The computational approach builds on theoretical properties of the geometry of the space of critical regions, where a critical region is defined as the set of [Formula: see text]’s for which a basis is optimal. To formally support our computational approach we provide proofs of geometric properties of neighboring critical regions. We contribute to the existing theory of parametric programming by establishing additional results, providing deeper geometric understanding of critical regions. On the basis of the geometric properties of critical regions, we develop an algorithm that solves the LPs in batches by finding critical regions that contain multiple [Formula: see text]’s. Moreover, we suggest a data-driven version of our algorithm that uses the distribution (e.g., shape) of a sample of [Formula: see text]’s for which the LPs need to be solved. We empirically compared our approach and three other methods on various instances. The results show the efficiency of our approach in comparison with the other methods but also indicate some limitations of the algorithm. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0838 .
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 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".