Multi-fidelity aerodynamic design trade-off exploration using point-by-point Pareto set identification

Aerodynamic design is inherently a multi-objective optimization (MOO) problem. Determining the best possible trade-offs between conflicting aerodynamic objectives can be computationally challenging when carried out directly at the level of high-fidelity computational fluid dynamics simulations. This paper presents a computationally cheap methodology for exploration of aerodynamic design trade-offs. In particular, point-by-point identification of a set of Pareto-optimal designs is executed starting in the neighborhood of a single-objective optimal design, and using a trust-region-based, multi-fidelity optimization algorithm as well as locally constructed response surface approximations (RSAs). In this work, the RSAs are constructed using second-order polynomials without mixed terms, multi-fidelity models, and adaptive corrections. The application of the point-by-point MOO algorithm is demonstrated through MOO of transonic airfoil shapes using the Reynold-Averaged Navier Stokes equations and the Spalart-Allmaras turbulence model. The results demonstrate that the Pareto front in the neighborhood of an initial design can be obtained at a low cost when considering up to 12 design variables. The results also indicate that the computational cost of the optimization process grows slowly with the number of the design variables, and the repeatability of the algorithm is very good when starting the search from different initial points.