Optimal Design of a Biconvex Airfoil for a Supersonic Aircraft Using the Basin-Hopping and Exhaustive Search Methods
Bibliographic record
Abstract
In this study, based on target design conditions, an airfoil is designed for a supersonic aircraft to achieve the maximum lift-to-wave drag ratio, with constraints on the lift coefficient, pitching moment, and maximum thickness. The coefficients of lift and wave drag are calculated numerically using shock/expansion wave theory. To solve the corresponding optimization problem, the Basin-Hopping algorithm—a method commonly used in computational chemical physics for determining minimum energy structures of molecules—is employed. To enhance the search for local extrema, the Sequential Least Squares Programming (SLSQP) method, known for handling constrained optimization problems, is integrated with the Basin-Hopping algorithm. For comparison and validation, the exhaustive search method, a simple technique that evaluates various combinations of design variables to find the optimal solution, is also applied. The results show that while the exhaustive search identifies the optimal design, the Basin-Hopping algorithm yields a slightly better design and requires only about 1/60 of the computation time. This work outlines the design process and demonstrates how advanced optimization algorithms can efficiently address engineering design challenges.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| 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".