Enhanced Airfoil Design Optimization Using Hybrid Geometric Neural Networks and Deep Symbiotic Genetic Algorithms

Optimal airfoil design remains a critical challenge in aerodynamic engineering, with traditional methods requiring extensive computational resources and iterative processes. This paper presents GEO-DSGA, a novel framework integrating hybrid geometric neural networks with deep symbiotic genetic algorithms for enhanced airfoil optimization. The methodology employs graph-based representations of airfoil geometries through a hybrid architecture combining graph convolutional networks with traditional deep learning, enabling precise capture of spatial geometric relationships. The parametric modeling stage utilizes CST, Bézier curves, and PARSEC methods to generate mathematically robust airfoil representations, subsequently transformed into graph structures preserving local and global shape characteristics. The optimization framework incorporates a deep symbiotic genetic algorithm enhanced with dominant feature phenotyping, applying biological symbiotic principles where design parameters achieve superior performance through mutual enhancement rather than independent optimization. This systematic exploration maintains geometric feasibility and aerodynamic validity throughout the design space. Experimental results demonstrate an 88.6% reduction in computational time while maintaining prediction accuracy within 1.5% error margin for aerodynamic coefficients across diverse operating conditions. The methodology successfully identifies airfoil geometries outperforming baseline NACA profiles by up to 12% in lift-to-drag ratio while satisfying manufacturing and structural constraints, establishing GEO-DSGA as a significant advancement in computational aerodynamic design optimization.