An investigation into an aerodynamic optimization benchmark case that exhibits multimodality is presented using a global optimization approach. The recently suggested case 6 of the AIAA Aerodynamic Design Optimization Discussion Group involves the drag minimization of a rectangular NACA0012 wing subject to lift and the root bending moment, as well as other geometric constraints. In this paper, optimization of that case using a state-of-the-art constrained population-based global optimization framework is presented. Shape control is achieved via a hierarchical application of the radial basis function domain element approach. Three different fidelities of optimization cases are performed to investigate the multimodality of various aspects of the full problem, with four independent runs of each case being performed. When considering chord optimization, the optimizer converges to two independently identifiable minima with very similar performances. When adding dihedral and sweep variation, further multimodality is introduced, although this multimodality is reasonably well defined, with minima including forward and rearward sweeps, and an upward and a downward winglet. Introducing thickness variables leads to a highly multimodal problem due to the coupling between the chord and thickness variables. The theoretical minimum drag for this case is 24.7 counts, which a number of the runs gets close to achieving.
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