Optimization of two-dimensional irregular bin packing problem considering slit distance and free rotation of pieces
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Bibliographic record
Abstract
In this paper, we present a two-dimensional irregular bin packing problem (2DIBPP) that takes into account the slit distance and allows the pieces to rotate freely. The target is to arrange a specified collection of pieces with irregular shapes into a minimal number of bins. Firstly, we develop a mathematical model for the 2DIBPP that considers slit distance and free rotation of the pieces, and an equidistant edge expansion approach is then proposed to handle the slit distance. Secondly, a two-stage method is implemented to get a finite collection of promising rotation angles, effectively decreasing the search neighbourhood. Thirdly, we decompose the 2DIBPP into two sub-problems: piece assignment and packing. The Partial Bin Packing (PBP) strategy is employed in the allocation stage, and we adopt an overlap minimization method to pack the pieces into an individual bin. Finally, we use a local search (LS) algorithm to advance the quality of the solutions by adjusting the piece assignment across bins. Experimental evidence exhibits that our approach is competitive in most instances of the literature, with four better results in five benchmark instances.
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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 | 0.000 |
| 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