Architectural Models Enabled Dynamic Optimization for System-of-Systems Evolution

System of Systems (SoS) is designed to deliver value to participant stakeholders in a dynamic and uncertain environment where new systems are added and current systems are removed continuously and on their own volition. This requires effective evolution management at the SoS architectural level with adequate support of process, methods, and tools. This paper follows the principle of Model-Based Systems Engineering (MBSE) and develops a holistic framework integrating MBSE conceptual representations and approximate dynamic programming (ADP) to support the SoS evolution. The conceptual models provide a common architectural representation to improve communication between various decision makers while the dynamic optimization method suggests evolution planning decisions from the analytical perspective. The Department of Defense Architecture Framework (DoDAF) models using Systems Modeling Language (SysML) are used as MBSE artifacts to connect with ADP modeling elements through DoDAF metamodels to increase information traceability and reduce unnecessary information loss. Using a surface warfare SoS as an example, this paper demonstrates and explains the procedures of developing DoDAF models, mapping DoDAF models to ADP elements, formulating ADP formulation, and generating evolutionary decisions. The effectiveness of using ADP in supporting evolution to achieve a near-optimal solution that can maximize the SoS capability over time is illustrated by comparing ADP solution to other alternative solutions. The entire framework also sheds light on bridging the DoDAF-based conceptual models and other mathematical optimization methods.