On the scalability of truss geometry and topology optimization with global stability constraints via chordal decomposition
Bibliographic record
Abstract
Abstract Geometry optimization was recently introduced to existing truss topology optimization with global stability constraints. The resulting problems are formulated as highly nonlinear semidefinite programming problems that demand extensive computational effort to solve and have been solved only for small problem instances. The main challenge for effective computation is the positive semidefinite constraints which involve large sparse matrices. In this paper, we apply several techniques to tackle the challenge. First, we use the well-known chordal decomposition approach to replace each positive semidefinite constraint on a large sparse matrix by several positive semidefinite constraints on smaller submatrices together with suitable linking constraints. Moreover, we further improve the efficiency of the decomposition by applying a graph-based clique merging strategy to combine submatrices with significant overlap. Next, we couple these techniques with an optimization algorithm that fully exploits the structure of the smaller submatrices. As a result, we can solve much larger problems, which allows us to extend the existing single-load case to the multiple-load case, and to provide a computationally tractable approach for the latter case. Finally, we employ adaptive strategies from previous studies to solve successive problem instances, enabling the joints to navigate larger regions, and ultimately obtain further improved designs. The efficiency of the overall approach is demonstrated via computational experiments on large problem instances.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| 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 | 0.000 |
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 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".