Integrated optimization for train operation zone and stop plan with passenger distributions

With the aim of generating system-optimal operation strategies, this paper proposes a new integrated optimization method for train operation zone, stop plan and passenger distribution optimization problems on the basis of a train stop planning model. Through the introduction of a set of critical system constraints, the problem is rigorously formulated as a two-objective mixed-integer linear programming problem with the objectives of minimizing the total running distance of unoccupied seats and the total number of stops for all involved trains. Finally, two sets of numerical experiments are implemented using GAMS to demonstrate the performance of the proposed approach.