Global Multi-Objective Optimisation utilising Surrogate Models

Kurzfassung

While global multi-objective optimization problems continue to emerge in aerospace engineering, conventional optimization methods, in particular, evolutionary algorithms such as the Non-dominated Sorting Genetic Algorithm, have shown their capability to solve such problems. However, one distinctive disadvantage of these conventional methods is that they generally require a large number of function evaluations, which makes them incompatible with computationally intensive numerical simulations that are often employed in aerospace design problems. This thesis substantiates the idea that this limitation can be overcome by using surrogate based optimization, in particular multi-objective Bayesian global optimization that utilizes Kriging as a surrogate model and Expected Hypervolume Improvement as an infill criteria. With this approach, it is possible to obtain the Pareto front with a relatively small computational budget. This is demonstrated through test cases that are conducted by solving analytical optimization problems. The results show that Bayesian optimization is able to reduce the function evaluations by 51 times for the bi-objective problem, and by 91 times for the three-objectives problem compared to genetic algorithms. Furthermore, its applicability is tested in two aerospace design problems, where function evaluations were performed through Computational Fluid Dynamics (CFD) and Computational Aeroacoustic (CAA) simulations. The proposed optimization method returns Pareto fronts which contain various design trade-offs that result in improved performance in terms of the desired objectives, with a reasonable number of function evaluations. Firstly, in the aerodynamic shape optimization, it is able to obtain the Pareto front, which contains airfoil designs with a combination of reduced drag and reduced pitching moment. Secondly, the aerodynamic-aeroacoustic shape optimization is performed where the Pareto front is obtained for airfoil designs with three objectives: reduced drag, reduced pitching moment and reduced aeroacoustic noise. This thesis demonstrates the efficiency of the Bayesian global optimization framework by showing how the Pareto front can be obtained at a relatively smaller number of function evaluations compared to some of the conventional multi-objective optimization methods. Moreover, the results obtained from the applied problems verify its capability for practical applications in aerospace design. Hence, the outcomes of this thesis highlight the potential of multi-objective Bayesian global optimization for multidisciplinary design optimization problems in the field of aerospace engineering.