A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: III. Improving the Quality of Robust Solutions
Bibliographic record
Abstract
In this paper, we study the solution quality of robust optimization problems when they are used to approximate probabilistic constraints and propose a novel method to improve the quality. Two solution frameworks are first compared: (1) the traditional robust optimization framework which only uses the a priori probability bounds and (3) the approximation framework which uses the a posteriori probability bound. We illustrate that the traditional robust optimization method is computationally efficient but its solution is in general conservative. On the other hand, the a posteriori probability bound based method provides less conservative solution but it is computationally more difficult because a nonconvex optimization problem is solved. Based on the comparative study of the two methods, we propose a novel iterative solution framework which combines the advantage of the a priori bound and the a posteriori probability bound. The proposed method can improve the solution quality of traditional robust optimization framework without significantly increasing the computational effort. The effectiveness of the proposed method is illustrated through numerical examples and applications in planning and scheduling problems.
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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 | 0.013 | 0.055 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".