Objective function value statistics.

Urban rail transit train operation plan is a comprehensive production plan encompassing line planning, timetabling, and rolling stock scheduling. In order to solve the problem of infeasibility of the line plan and timetable because the number of rolling stocks could be only precisely considered in the rolling stock scheduling. An integrated optimization solution is proposed which considers the line plan, timetable, and rolling stock schedule. Candidate service routes are generated according to the layout of the turn-back stations. Considering the constraints of operation and passenger flow demand, an integer nonlinear programming model is established to minimize the cost of operation and passenger waiting time. The model complexity is analyzed and based on its decomposability a deterministic search algorithm is designed. Taking Chongqing Metro Line 3 in China as an example to verify the effectiveness of the proposed model and algorithm. Compared with the train operation plan based on manual experience and compiled by stages, the integrated optimization model can better improve the quality of train operation plan.