<p dir="ltr">Managing transient heat loads has become more challenging with the increasing electrification of ground, air, and marine vehicles. Doing so requires novel designs of thermal management systems, or in some cases, novel retrofits of legacy TMSs to accommodate the addition of more electrified subsystems. However, design tools that are well suited for examining and optimizing the dynamic response of TMS over candidate operation or mission profiles are limited. In this thesis, a principled methodology and associated tools for the enumeration and dynamic optimization of all feasible architectures of an air cycle machine are presented. Graph-based modeling is pivotal for exploring and optimizing ACM architectures, providing a structured representation of system components and interactions. By modeling the ACM as a graph, with vertices and edges representing components and interactions, respectively, various component configurations and performance metrics can be systematically analyzed. This approach enables efficient exploration of design alternatives and consideration of dynamic boundary conditions (representing, for example, a complex mission profile) during optimization. Another unique contribution of this thesis is a novel application of a multi-state graph-based modeling approach for developing dynamic models of turbomachinery components. By representing multiple states within each control volume or component and connecting them through power flows, this approach accurately captures both first and second law dynamics, enabling the computation of dynamic entropy generation rates. A detailed case study demonstrates the optimization of ACM architectures based on entropy generation minimization and dynamic bleed air flow rate minimization. This study highlights the trade-offs between different optimization criteria and the potential for generalizing the tool to more complex thermofluid systems in thermal management applications. The results underscore the importance of entropy-based analysis in comparing the thermodynamic losses across various system architectures.</p>