Successful future surface combatants in the US Navy must embrace the growing integration and interdependency of propulsive and combat systems. Traditionally, the development of Hull, Mechanical and Electrical systems has been segregated from the development of weapons and sensors. However, with the incorporation of high energy weapons into future ship configurations, ship design processes must evolve to embrace the concept of a System of Systems being the only way to achieve affordable capability in our future fleets. This thesis bridges the gap between the physical architecture of components within a ship and the way in which they are logically connected to model the energy flow through a representative design and provide insight into sizing requirements of both system components and their connections using an Architecture Flow Optimization (AFO). This thesis presents a unique method and tool to optimize naval ship system logical and physical architecture considering necessary operational conditions and possible damage scenarios. The particular and unique contributions of this thesis are: 1) initially only energy flow is considered without explicit consideration of commodity flow (electric, mechanical, chilled water, etc.), which is calculated in post-processing; 2) AFO is applied to a large and complex naval surface combatant system of systems, demonstrating its scalability; 3) data necessary for the AFO is extracted directly from a naval ship synthesis model at a concept exploration level of detail demonstrating its value in early stage design; and 4) it uses network-based methods which make it adaptable to future knowledge-based network analysis methods and approaches. / Master of Science