Global Optimization of Multimodal Aerodynamic Optimization Benchmark Case

An investigation into a multimodal aerodynamic optimization benchmark case using an approximate global optimization approach is presented. A new benchmark case of the AIAA Aerodynamic Design Optimization Discussion Group that involves the drag minimization of a rectangular NACA0012 wing subject to lift and root bending moment, as well as other geometric constraints, that is currently believed to be multimodal has been suggested. In this paper, optimization of that case using a constrained population based global optimization framework is presented, with three independent runs of the
optimizer (each with different starting locations) having been performed. The runs are all coarsely-converged to give approximately converged solutions such that rapid run-times can be achieved and used to demonstrate any pitfalls that may be encountered when using a gradient-based optimizer. All three of the runs converged onto drag values close to the theoretical optimum, however with substantially different final shapes. This likely indicates the presence of a flat optimum region within the design space, where a substantial number of wing shapes are able to obtain the theoretical optimum span loading.