Towards a multi-fidelity & multi-objective Bayesian optimization efficient algorithm

Black-box optimization methods like Bayesian optimization are often employed in cases where the underlying objective functions and their gradient are complex, expensive to evaluate, or unavailable in closed form, making it difficult or impossible to use traditional optimization techniques. Fixed-wing drone design problems often face this kind of situations. Moreover in the literature multi-fidelity strategies allow to consistently reduce the optimization cost for mono-objective problems. The purpose of this paper is to propose a multi-fidelity Bayesian optimization method that suits to multi-objective problem solving. In this approach, low-fidelity and high-fidelity objective functions are used to build co-Kriging surrogate models which are then optimized using a Bayesian framework. By combining multiple fidelity levels and objectives, this approach efficiently explores the solution space and identifies the set of Pareto-optimal solutions. First, four analytical problems were solved to assess the methodology. The approach was then used to solve a more realistic problem involving the design of a fixed-wing drone for a specific mission. Compared to the mono-fidelity strategy, the multi-fidelity one significantly improved optimization performance. On the drone test case, using a fixed budget, it allows to divide the inverted generational distance metric by 6.87 on average.