Keywords
Exhaustive search
Global optimization
Lift-to-wave drag ratio
Basin-hopping Algorithm
How to Cite
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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