Parametric Optimization of Spiked Blunt Bodies in Supersonic Flow Using Surrogate-Assisted Machine Learning and Evolutionary Algorithms

This study presents a surrogate-assisted evolutionary optimization framework for parametric design under limited data conditions, integrating computational fluid dynamics (CFD), machine learning, and evolutionary algorithms to optimize spiked blunt body geometries in supersonic flow. A dataset of CFD simulations covering a range of Mach numbers and geometric ratios, including spike length () and diameter (), was used to train regression-based surrogate models.Among the evaluated models, the Gradient Boosting Regressor (GBR) achieved the highest predictive accuracy (, RMSE = 0.00775), effectively capturing the nonlinear relationship between flow conditions, geometry, and drag coefficient (). The trained surrogate model was coupled with three evolutionary algorithms—Differential Evolution (DE), Covariance Matrix Adaptation Evolution Strategy (CMA-ES), and Genetic Algorithm (GA)—to identify optimal geometric configurations across different Mach regimes. To validate the proposed framework, the optimal solutions obtained from the surrogate-based optimization were re-evaluated using CFD simulations. A strong agreement between predicted and simulated drag coefficients was observed, confirming the reliability of the surrogate model for guiding optimization within the explored design space. The results reveal consistent geometric trends, with the optimal spike length ratio decreasing as Mach number increases, while the diameter ratio converges to a narrow range around . Additionally, SHapley Additive exPlanations (SHAP) analysis identified as the most influential parameter affecting drag, followed by Mach number and , supporting the physical interpretation of the flow behavior. Overall, the proposed framework demonstrates that the integration of CFD, machine learning, and evolutionary algorithms provides an efficient and reliable approach for geometric optimization in supersonic applications, enabling accurate design exploration with a limited number of high-fidelity simulations.