Multi-objective aerodynamic design with user preference using truncated expected hypervolume improvement

Multi-objective optimization in aerodynamic design plays an important role in capturing the trade-off and useful knowledge that would be useful for real-world design processes. In the preliminary design phase, aerodynamic designers usually have an interest in focusing the optimization process in a certain direction of interest. To this end, we propose the use of user preference multi-objective Bayesian global optimization (MOBGO) for aerodynamic design using truncated expected hypervolume improvement (TEHVI). Taking into account the apriori knowledge of objective functions, TEHVI acts as an infill criterion to search for the optimal solutions based on the Kriging models in MOBGO. In TEHVI-MOBGO, the first step is to obtain a coarse approximation of the Pareto front in order to capture the general trend and trade off using standard EHVI; following this step, TEHVI is then applied to focus the search on a defined region of interest. We demonstrate the capabilities and usefulness of TEHVI method on the design optimization of an inviscid transonic wing and a viscous transonic airfoil in order to minimize the drag coefficient and absolute value of pitching moment, which leads to a reduced fuel burn and easier control characteristic.