Stabilized Column Generation Via the Dynamic Separation of Aggregated Rows
Bibliographic record
Abstract
Column generation (CG) algorithms are well known to suffer from convergence issues due, mainly, to the degenerate structure of their master problem and the instability associated with the dual variables involved in the process. In the literature, several strategies have been proposed to overcome this issue. These techniques rely either on the modification of the standard CG algorithm or on some prior information about the set of dual optimal solutions. In this paper, we propose a new stabilization framework, which relies on the dynamic generation of aggregated rows from the CG master problem. To evaluate the performance of our method and its flexibility, we consider instances of three different problems, namely, vehicle routing with time windows (VRPTW), bin packing with conflicts (BPPC), and multiperson pose estimation (MPPEP). When solving the VRPTW, the proposed stabilized CG method yields significant improvements in terms of CPU time and number of iterations with respect to a standard CG algorithm. Huge reductions in CPU time are also achieved when solving the BPPC and the MPPEP. For the latter, our method has shown to be competitive when compared with a tailored method. Summary of Contribution: Column generation (CG) algorithms are among the most important and studied solution methods in operations research. CG algorithms are suitable to cope with large-scale problems arising from several real-life applications. The present paper proposes a generic stabilization framework to address two of the main issues found in a CG method: degeneracy in the master problem and massive instability of the dual variables. The newly devised method, called dynamic separation of aggregated rows (dyn-SAR), relies on an extended master problem that contains redundant constraints obtained by aggregating constraints from the original master problem formulation. This new formulation is solved in a column/row generation fashion. The efficacy of the proposed method is tested through an extensive experimental campaign, where we solve three different problems that differ considerably in terms of their constraints and objective function. Despite being a generic framework, dyn-SAR requires the embedded CG algorithm to be tailored to the application at hand.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| 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) | 0.004 | 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".