There is a growing recognition that the design and management of complex engineered systems requires a fundamental advance in our ability to identify and exploit their inherent tradeoffs across a growing number of decisions and objectives. In support of this challenge, this study provides a rigorous evaluation of modern "many-objective" evolutionary opti- mization algorithms. The computational power of modern high-performance computing environments makes it possible to investigate optimization algorithm performance in ways that were not historically feasible. This study uses millions of algorithm runs, each per- forming hundreds of thousands of function evaluations, to do a Sobol' global sensitivity analysis on algorithm parameterization. We present this analysis for two algorithms across four formulations of a General Aviation Aircraft (GAA) conceptual product family design problem. The two algorithms are the recently introduced Borg Multi-Objective Evolu- tionary Algorithm (MOEA), a promising auto-adaptive multi-operator search algorithm, and the ε-MOEA, its algorithmic forebear. The four formulations of the GAA problem vary in their complexity and allow us to investigate the assumption that complex problem formulations are more difficult to solve.