A Greedy, Generative, Lattice Representation for Point Packing
Bibliographic record
Abstract
Point packings in the unit square are placements of n points in the unit square that maximize the minimum distance between any two of the points. Such packings are surrogates for the 2D-stock cutting problem. In this study we examine a greedy generative representation for the point packing problem and extend the problem to higher dimensions. This representation uses a greedy algorithm to select points generated as whole-number linear combinations of vectors. This means that sets of vectors are evolved. The lattice generated by the vectors, taken modulo one, yields a set of points that can be greedily filtered to a dense point packing. The focus of evolution is the choice of vector generators for the lattice. A parameter study is performed comparing two mutation operators, different rates of application for mutation, and different population sizes. The generative representation is found to efficiently locate large point packings, while using relatively few real-valued parameters. The number of real parameters used to specify a point packing may be chosen. This novel control value is shown to have a substantial impact on results. A preliminary application of point packings, as population initializers, is demonstrated. Using a point packing as an initial population for an evolutionary optimizer can yield improved performance by providing more even sampling of the optimization domain and, in this study, it is shown that use of a point packing improves performance in a higher dimensional test problem, but not in a lower dimensional one.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".