Estimation of schedule preference and crowding perception in urban rail corridor commuting: An inverse optimization method

This paper introduces an inverse optimization method to uncover commuters’ schedule preference and crowding perception based on aggregated observations from smart card data for an urban rail corridor system. The assessment of time-of-use preferences typically involves the use of econometric models of discrete choice based on detailed travel survey data. However, discrete choice models often struggle with potential endogeneity issues in behavioral observations when estimating individual samples from massive transit data with limited exogenous identifying information. This motivates us to employ an equilibrium modeling approach to capture the dynamism hidden in commuters’ departure time decision-making from aggregations. Assuming user optimality in observed choices, an inverse optimization method is proposed to find a set of preference parameters in the stochastic user equilibrium-based morning commuting model with heterogeneous commuters so that the resulting equilibrium pattern best approximates the observed departure rate distribution over time. The proposed inverse optimization problem can be formulated by a bi-level programming model and a sensitivity analysis-based solution framework is further designed for model estimation. Lastly, the smart card data and train timetable data from the rail corridor along the Beijing Subway Batong Line are synthesized for a case study to estimate commuters’ departure time choice preferences during morning peak periods, as well as to validate the robustness and practicality of the proposed method.