Multimodality and Global Optimization in Aerodynamic Design
Bibliographic record
Abstract
Two optimization algorithms are presented that are capable of finding a global optimum in a computationally efficient manner: a gradient-based multistart algorithm based on Sobol sampling and a hybrid optimizer combining a genetic algorithm with a gradient-based algorithm. The optimizers are used to investigate multimodality in aerodynamic-shape-optimization problems. The performance of each algorithm is tested on an analytical test function as well as several aerodynamic-shape-optimization problems in two and three dimensions. In each problem the primary objectives are to classify the problem according to the degree of multimodality and to identify the preferred optimization algorithm for the problem. The results show that multimodality should not always be assumed in aerodynamic-shape-optimization problems. Typical two-dimensional airfoil-optimization problems are unimodal. Three-dimensional shape-optimization problems may contain local optima. The number of local optima tends to increase with increasing geometric degrees of freedom and design space bounds. For problems with a modest number of local optima, which we term somewhat multimodal, the gradient-based multistart Sobol algorithm is the most efficient method.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".