Identifying Multiple Optima in Aerodynamic Design Spaces

Abstract

Parallel niching optimization algorithms are developed and applied to a multimodal aerodynamic optimization case to identify multiple optima in the design space. Previous work by the authors has presented niching optimization algorithms that use differential evolution with feasible selection as a basis that can identify multiple optima in constrained search spaces, which is necessary for aerodynamic optimization. In this paper, these algorithms are further developed for application to aerodynamic optimization by reformulating each to provide a parallel decomposition of the objective function evaluation at each iteration of the optimization process. These algorithms are tested on an analytical optimization problem. The parallel, constrained form of both local nearest-neighbourhood and local crowding are shown to be the best performing algorithms with a 99% confidence level. A variation on the AIAA ADODG case 6 multimodal wing optimization case is also studied. A multi-start gradient-based approach is used to show multimodality of the design space. The local nearest-neighbourhood-based algorithm is then applied to the aerodynamic optimization case and is able to successfully identify two minima in the design space, with one being close to the global minimum and one in a different part of the design space, which is a local minimum. * Senior Teaching Associate.

Optimisation of Multi-Modal Aerodynamic Shape and Topology Problems

“…The high level of multi-modality both in terms of flow behaviour and geometric topology makes this case ideal for niching and quality diversity [27] approaches. A recent study using a niching variant of differential evolution has succesfully been used to identify multiple minima during the optimisation of a wing [60]. These methods would allow convergence and identification of multiple minima.…”