Public buses serve a vital role in urban transportation systems by alleviating traffic congestion, reducing carbon emissions, and providing cost-effective and accessible travel options. Nonetheless, a noticeable mismatch frequently exists between the supply and demand for bus services, leading to reduced passenger satisfaction in reality, especially in suburban areas. To tackle this problem, our study delves into the bus fleet allocation problem by incorporating a range of real-world operations management issues, including the uncertainty in passenger demand, the coordination of multiple bus routes, the availability of various bus types, the constraints related to parking space and staffing, as well as the maximum departure intervals. To navigate the uncertain passenger demand, a distributionally robust optimization (DRO) model that comprehensively integrates these real-world characteristics is formulated. In addition, we conduct an in-depth analysis of the DRO model and its dual problem, assessing its scalability using a general-purpose solver. We also perform sensitivity analyses within the problem domain to offer valuable managerial insights. For large-scale problems, we develop a multi -operator genetic algorithm and enhance the algorithm's efficiency by incorporating a reinforcement learning mechanism. Finally, comparative experiments based on real-world cases show that: by incorporating a reinforcement learning mechanism, the computational capability of the proposed algorithm has improved by 3.39%; compared to other heuristic algorithms, the efficiency of the proposed algorithm has increased by 5.32%.
