In this paper several formulations and comparative test results are presented for problems involving the general paradigm of coupled sets of components. This paradigm is general enough to include systems of systems (SoS) and multidisciplinary design optimization (MDO). It is assumed that these systems involve a (potentially inactive) coordinating component, or "Central Authority" and one or more, potentially interacting, subordinate components. The formulations differ in the amount of control given to the central authority versus the autonomy granted to the subordinate components. Comparative test results are given for several of the formulations on a NASA-generated, public domain, aircraft conceptual design problem.