Dynamic constraint and variable aggregation in column generation
Bibliographic record
Abstract
Starting from the improved primal simplex (IPS) decomposition, introduced by Elhallaoui et al. (2011) to tackle degeneracy in general linear programs, we introduce and discuss the mathematical foundations of improved column-generation decompositions (ICG) that are better than the standard column-generation decomposition when degeneracy is an issue. We also present an improved dynamic constraint aggregation (IDCA), which is a specialization of ICG to efficiently solve set partitioning problems. We show that IDCA improves the dynamic constraint aggregation (DCA) and the multiphase dynamic constraint aggregation (MPDCA) algorithms (Elhallaoui et al., 2005, 2010) that not only reduce degeneracy but also profit from it to efficiently solve set partitioning problems. IDCA solves at each iteration a complementary problem (CP) to obtain a group of variables that can be aggregated or pivoted into the basis to bypass degenerate pivots and decrease the objective value and to obtain more “central” dual solutions to generate new columns. Our numerical results show reduction factors in the solution times exceeding 10 for IDCA compared to a state-of-the-art standard column-generation solver.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".