Many cognitive and computational challenges accompany the design of complex engineered systems. This study proposes the many-objective visual analytics (MOVA) framework as a new approach to the design of complex engineered systems. MOVA emphasizes learning through problem reformulation, enabled by visual analytics and many-objective search. This study demonstrates insights gained by evolving the formulation of a General Aviation Aircraft (GAA) product family design problem. This problem's considerable complexity and difficulty, along with a history encompassing several formulations, make it well-suited to demonstrate the MOVA framework. The MOVA framework results compare a single objective, a two objective, and a ten objective formulation for optimizing the GAA product family. Highly interactive visual analytics are exploited to demonstrate how decision biases can arise for lower dimensional, highly aggregated problem formulations.