Large-scale engineering systems require design teams to balance complex sets of considerations using a wide range of design and decision-making skills. Formal, computational approaches for optimizing complex systems offer strategies for arriving at optimal solutions in situations where system integration and design optimization are well-formulated. However, observation of design practice suggests engineers may be poorly prepared for this type of design. Four graduate student teams completed a distributed, complex system design task. Analysis of the teams' design histories suggests three categories of suboptimal approaches: global rather than local searches, optimizing individual design parameters separately, and sequential rather than concurrent optimization strategies. Teams focused strongly on individual subsystems rather than system-level optimization, and did not use the provided system gradient indicator to understand how changes in individual subsystems impacted the overall system. This suggests the need for curriculum to teach engineering students how to appropriately integrate systems as a whole.