This paper presents an improvement to a multi-start method for gradient based exploration of moderately multimodal design spaces in aerodynamic shape optimization problems. Free form deformation geometry control is used in conjunction with a gradient-based multistart algorithm to generalize cascading linear constraints for a sampler algorithm into a geometry-independent form. This permits large, high-quality, feasible samples of the design space to be generated and optimized quickly and e ciently. This algorithm is then used to explore multimodality in viscous aerodynamic shape optimization problems, including wings in transonic and subsonic flow, as well as a transonic blended wing-body design. Both wing cases are found to be multimodal, while the blended wing-body case is believed to be unimodal based on available evidence. A brief investigation of the e↵ect that three degrees of freedom -twist, taper, and sectional control -have on multimodality in the viscous optimization of the common research model wing is undertaken. This investigation finds little evidence of multimodality related to twist and section control, while the addition of taper design variables leads to clear indications of multimodality.

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In aerodynamic shape optimization, traditional static geometry control methods can produce suboptimal performance by introducing performance tradeoffs at various stages of optimization, enforcing arbitrary constraints on open-ended optimization, and necessitating foreknowledge of problem behavior to design an effective control scheme. These shortcomings can be mitigated through dynamic geometry control, which partly automates the geometry control design process by refining the geometry control topology throughout optimization. Such refinement can occur in a predetermined fashion (as in progressive control) or more automatically using sensitivity information to guide refinement (as in adaptive control). Both progressive control and adaptive control are implemented in the context of axial and free-form deformation geometry control, and novel contributions are made to the adaptive algorithm, including the treatment of active constraints and several novel “potential indicators” to rank candidate refinements. Application to a wide suite of aerodynamic shape optimization problems demonstrates that dynamic geometry control is effective, producing lower final drag than well-designed static schemes while reducing required iterations to convergence by 50% or more, and simultaneously reducing labor requirements on the user. These benefits are demonstrated across a wide variety of problems, representative of detailed and exploratory problems often encountered in both academia and industry.

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