The document presents a dissertation that develops a System of Systems Flexibility Framework (SoSFFram) to measure the flexibility of systems of systems and enable flexibility-based design space exploration using a combination of techniques. The framework first focuses on measuring a system of system's flexibility to evolve and adapt using network theory and discrete event simulation. It then develops a simulation environment that can also measure baseline performance. Finally, it proposes using a genetic algorithm to explore the vast design space of a system of systems. The goal is to provide a methodology for flexibility-based system of systems design.