The recently introduced Borg multiobjective evolutionary algorithm (MOEA) framework features auto-adaptive search that tailors itself to effectively explore different problem spaces. A key auto-adaptive feature of the Borg MOEA is the dynamic allocation of search across a suite of recombination and mutation operators. This study explores the application of the Borg MOEA on a real-world product family design problem: the severely constrained, ten objective General Aviation Aircraft (GAA) problem. The GAA problem represents a promising benchmark problem that strongly highlights the importance of using auto-adaptive search to discover how to exploit multiple recombination strategies cooperatively. The auto-adaptive behavior of the Borg MOEA is rigorously compared against its ancestor algorithm, the e-MOEA, by employing global sensitivity analysis across each algorithm's feasible parameter ranges. This study provides the first Sobol' sensitivity analysis to determine the individual and interactive parameter sensitivities of MOEAs on a real-world many-objective problem.