A simulation-based metro train scheduling optimization incorporating multimodal coordination and flexible routing plans

Document Type

Journal Article

Publication Date


Subject Area

mode - subway/metro, infrastructure - interchange/transfer, operations - coordination, operations - scheduling, place - urban, economics - operating costs, technology - intelligent transport systems


Metro train schedule, Multimodal coordination, Flexible routing plans, Passenger simulation, Variable neighborhood search algorithm


The promotion of multimodal coordination is of great significance to the joint development of diversified urban transportation systems. Focusing on an urban comprehensive passenger transport hub (UCPTH) that converges both inter-city modes and multiple inner-city modes, this study aims to customize a bridging metro train operation plan with the utilization of multimodal passenger simulation. A bi-objective integer nonlinear programming model (INLP) incorporating train schedule and flexible routing plan is proposed to minimize passenger waiting time and operating costs simultaneously. Notably, a real-time flow prediction method based on Monte Carlo simulation and queuing network system is proposed and embedded in the optimization model framework to reflect the difference of individual passengers’ transfer walking time and thereby provide detailed passenger distribution on the platform for metro hub stations connecting UCPTH. Compared with the estimation using historical data, this method can particularly support the scheduling coordination of metro and other modes during an abrupt change of arrival flows. Moreover, to solve the collaborative optimization model tractably, the -constraint method based on a tailored variable neighborhood search algorithm is developed to generate approximate Pareto optimal solutions, including the number of effective trains, demand-sensitive headway, the route pattern of each effective train, and train dwell time. Finally, two sets of numerical experiments, including a small-scale case and a real-world hub-metro network instance are conducted to demonstrate the effectiveness of the proposed approaches. The study associated with the findings can benefit both metro providers and users especially those who need to transfer to the metro system at hubs by achieving the best match between passenger and train flows in temporal and spatial domains.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


Transportation Research Part C Home Page: