Three-Dimensional Bin Packing and Mixed-Case Palletization
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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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".