An Implementation of Self-Organizing Maps for Airfoil Design Exploration via Multi-Objective Optimization Technique

AbstrAct: Design candidates obtained from optimization techniques may have meaningful information, which provides not only the best solution, but also a relationship between object functions and design variables. In particular, trade-off studies for optimum airfoil shape design involving various objectives and design variables require the effective analysis tool to take into account a complexity between objectives and design variables. In this study, for the multiple-conflicting objectives that need to be simultaneously fulfilled, the real-coded Adaptive Range Multi-Objective Genetic Algorithm code, which represents the global and stochastic multi-objective evolutionary algorithm, was developed for an airfoil shape design. Furthermore, the PARSEC method reflecting geometrical properties of airfoil is adopted to generate airfoil shapes. In addition, the Self-Organizing Maps, based on the neural network, are used to visualize trade-offs of a relationship between the objective function space and the design variable space obtained by evolutionary computation. The Self-Organizing Maps that can be considered as data mining of the engineering design generate clusters of object functions and design variables as an essential role of trade-off studies. The aerodynamic data for all candidate airfoils is obtained through Computational Fluid Dynamics. Lastly, the relationship between the maximum lift coefficient and maximum lift-to-drag ratio as object functions and 12 airfoil design parameters based on the PARSEC method is investigated using the Self-Organizing Maps method.