<![CDATA[This study proposes a unified graph-based optimization model that combines shortest-path methods with Hamiltonian constraints to optimize motorsport strategy. Existing approaches address racing line optimization and pit stop decision-making as separate problems, leaving the formal integration of trajectory-level and strategy-level optimization within a single graph-theoretic architecture as an open problem. The proposed framework models racing trajectories using layered weighted graphs with edge costs derived from track curvature and vehicle dynamics, while strategic decisions are represented within a constrained state-space graph ensuring non-redundant coverage of critical race phases. Shortest-path optimization is employed to minimize the total race time under physically informed constraints. Numerical simulations show that A* reduces lap time by 0.07 seconds over Dijkstra (87.29 s vs. 87.36 s), and the two-stop pit strategy yields the shortest total race time (832.85 s), outperforming the one-stop (896.5 s) and no-stop (879.75 s) alternatives. However, the model is limited by a linear assumption of tire degradation and deterministic race conditions, which may not fully capture stochastic on-track interactions. The originality of this work lies in the formal coupling of trajectory-level edge weights with Hamiltonian-constrained strategy search within a single optimization architecture — a unification not previously established in the motorsport optimization literature. These findings demonstrate graph-based mathematical modeling as a tractable and extensible foundation for data-driven motorsport strategy.]]>
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