Modeling Metro Passenger Routing Choices with a Fully Differentiable End-to-End Simulation-Based Optimization (SBO) Approach

Metro systems in densely populated urban areas are often complicated, with some origin-destinations (OD) having multiple routes with similar travel times, leading to complex passenger routing behaviors. To improve modeling and calibration, this paper proposes a novel passenger route choice model with a metro simulator that accounts for passenger flows, queueing, congestion, and transfer delays. A novel, data-driven approach that utilizes a fully differentiable end-to-end simulation-based optimization (SBO) framework is proposed to calibrate the model, with the gradients calculated automatically and analytically using the iterative backpropagation (IB) algorithm. The SBO framework integrates data from multiple sources, including smart card data and train loadings, to calibrate the route choice parameters that best match the observed data. The full differentiability of the proposed framework enables it to calibrate for more than 20,000 passenger route choice ratios, covering every OD pair. To further improve the efficiency of the framework, a matrix-based optimization (MBO) mechanism is proposed, which provides better initial values for the SBO and ensures high efficiency with large datasets. A hybrid optimization algorithm combining MBO and SBO effectively calibrates the model, demonstrating high accuracy with synthetic data from actual passenger OD demands, where hypothesis tests are conducted for accuracies and significances. The accuracies and robustness are validated by experiments with synthetic passenger flow data, offering potential for optimizing passenger flow management in densely populated urban metro systems. Then, the SBO framework is extended for user equilibrium formulations with a crowding-aware route choice model and iterative metro simulations, calibrated by the hybrid optimization algorithm with additional matrix operations. Case studies with actual observed passenger flows are conducted to illustrate the proposed framework with multiple setups, exhibiting the heterogeneity of passenger route choice preferences and providing insights for operation management in the Hong Kong Mass Transit Railway system.