A method for demand-accurate one-dimensional cutting problems with pattern reduction
Bibliographic record
Abstract
The main objective in the one-dimensional cutting stock problem (1D-CSP) is to minimize material costs. In practice, it is useful to focus on auxiliary objectives, one of which is to reduce the number of different cutting patterns. This paper discusses the classical integer IDCSP, where only one type of stock object is included. Meanwhile, the demands of various items must be precisely satisfied in the constraints. In other words, no overproduction or underproduction is allowed. Therefore, to solve this issue, a variable-to-constant method based on a new mathematical model is proposed. In addition, we integrate the approach with two other representative methods to demonstrate its effectiveness. Both benchmark instances and real instances are used in the experiments, and the results show that the methodology is effective in reducing patterns. In particular, in terms of the solutions to the real-life instances, the proposed approach presents a 31.93 to 37.6% pattern reduction compared to other similar methods (including commercial software).
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".