Developing efficient fast-charging infrastructure along highway corridors is critical for reducing range anxiety and promoting long-distance electric travel. However, traditional static location approaches often fail to account for the stochastic interactions between continuous traffic flows and the stochastic variability of remaining driving ranges. To address these methodological gaps, this study develops a demand-driven optimization framework that integrates an improved Genetic Algorithm with the flow-capturing location-allocation model (GA-FCLM). Unlike static facility location approaches, the flow-capturing location-allocation component is specifically selected to maximize the interception of continuous traffic flows under strict range constraints, while the genetic algorithm efficiently navigates the high-dimensional discrete search space of simultaneous siting and sizing decisions. By synthesizing segment-level traffic flows with Monte Carlo simulations of state of charge (SOC) trajectories, the model accurately reconstructs corridor-level charging demand. For the Beijing-Hong Kong-Macao Expressway, the optimization identifies a robust layout with twenty active stations and 204 fast chargers, requiring a capital investment of 32 million Chinese Yuan (CNY). This configuration achieves a 99% aggregate coverage ratio, effectively eliminating long uncovered segments. Sensitivity analysis reveals that while profit increases linearly with pricing, infrastructure capacity exhibits a nonlinear response to rising electric vehicle (EV) penetration, necessitating strategic spatial rebalancing. The proposed GA-FCLM framework thus provides a scalable and methodologically superior tool for balancing investment costs, coverage continuity, and spatial equity on national highway networks.