Three-Dimensional Bin Packing and Mixed-Case Palletization
Why this work is in the frame
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Bibliographic record
Abstract
Despite its wide range of applications, the three-dimensional bin-packing problem is still one of the most difficult optimization problems to solve. Currently, medium- to large-size instances are only solved heuristically and remain out of reach of exact methods. This is particularly true for its practical variant, the mixed-case palletization problem, where item support is needed. This and the lack of a realistic benchmark data set are identified as major research gaps by a recent survey. In this work, we propose a novel formulation and a column-generation solution approach, where the pricing subproblem is a two-dimensional layer-generation problem. Layers are highly desirable in practical packings as they are easily packable and can accommodate important practical constraints such as item support, family groupings, isle friendliness, and load bearing. Being key to the success of the column-generation approach, the pricing subproblem is solved optimally as well as heuristically and is enhanced by using item grouping, item replacement, layer reorganization, and layer spacing. We conduct extensive computational experiments and compare against existing approaches. We also use industrial data to train and propose a realistic data set. The proposed approach outperforms the best-performing algorithm in the literature on most instances and succeeds to solve practical size instances in very reasonable computational times.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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