A Geometrical Branch-and-Price (GEOM-BP) Algorithm for Big Bin Packing Problems
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Bibliographic record
Abstract
Bin packing problem examines the minimum number of identical bins needed to pack a set of items of various weights. This problem arises in various areas of the artificial intelligence demanding derivation of the exact solutions in the shortest amount of time. Employing branch-and-bound and column generation techniques to derive the exact solutions to this problem, usually requires designation of problem-specific branching rules compatible with the nature of the polluted pricing sub-problem of column generation. In this work, we present a new approach to deal with the forbidden bins which handles two-dimensional knapsack problems. Furthermore, a set of diving criteria are introduced which emphasize the importance of the geometrical features of the bins. It is further shown that efficiency of the column generation technique could significantly get improved using an implicit sectional pricing scheme. The proposed algorithm outperforms the current state-of-the-art algorithms in number of the benchmark instances solved in less than one minute.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it