Optimization of Periodic Train Schedule with Flexible Train Composition during Off-Peak Periods for Urban Rail Transit

Abstract

Focusing on the insufficient passenger demand during off-peak periods in urban rail transit, a new train operation mode with flexible train composition considering trains couple/decouple at intermediate stations is proposed. An optimized two-phase nonlinear model is formulated in order to design a periodic train schedule, where train headways remain constant over a specific period. This model takes into account the flexible train composition. The objective function aims to minimize total passenger waiting time and train operating costs while considering constraints such as maximum line passing capacity, passenger flow demand, and the number of train units in the composition. Linearization techniques are applied to convert nonlinear constraints into linear equivalents, and the CPLEX solver is employed to solve the model. An illustrative real-case example is presented to validate the effectiveness of the proposed model. The results demonstrate that the operation mode with flexible train composition during off-peak periods offers significant advantages over traditional train composition modes, including single train routes, long-short train routes, and multiple train compositions. This mode enables better alignment between passenger demand and capacity, reduces operating costs, and enhances passenger service levels. The proposed operation mode is particularly suitable for urban rail transit lines with low passenger demand but requiring high passenger service, such as suburban lines or common lines during off-peak periods.