Optimization of Metro Train Schedules With a Dwell Time Model Using the Lagrangian Duality Theory

This paper proposes an optimization method of train scheduling for metro lines with a train dwell time model according to passenger demand. An optimization problem of train scheduling is established with constraints of a headway equation, passenger equation, and train dwell time equation, where the train dwell time is modeled as a function of boarding and alighting passenger volumes. The aim of the optimization problem is to minimize the waiting time of passengers and train operation cost. Lagrangian duality theory is adopted to solve this optimization problem with high dimensionality. Finally, simulation results illustrate that this method is efficient to generate the train schedule, which meets the passengers' exchanging requirements between trains and platforms. The contribution of this paper is that a dwell time model is introduced in train schedule optimization, which provides the possibility of reducing the operation cost in the precondition that the exchanging time of passengers between platforms and trains is assured.