Energy-efficient timetabling and rolling stock circulation planning based on automatic train operation levels for metro lines

Abstract We investigate the energy-efficient train timetabling and rolling stock circulation planning problem for metro lines based on flexible selections of train operation levels, which involve running levels (various running times and speed profiles) and dwell levels (various dwell times at stations). The travel demand of passengers is involved in the energy-efficient train timetabling problem via service patterns, i.e., different operation headways are used in peak and off-peak hours to satisfy the passenger demand. A mixed integer nonlinear programming (MINLP) formulation is presented to optimize train timetables and circulation plans of rolling stocks simultaneously with the aim of minimizing the headway deviations relating to service patterns, the headway variations among neighboring train services, the needed depot movements for rolling stocks, and the overall energy consumption. To increase the regularity (i.e., the consistency of operation level selections of train services) of train timetables and to improve the computational efficiency, two extensions of the energy-efficient timetabling formulation are proposed, i.e. the energy-efficient train timetabling models with pre-fixed selections and optimal identical (or consistent) selections of the operation levels. The proposed MINLP formulations are transformed into mixed integer linear programming formulations, which could be effectively solved, e.g., by Cplex and Gurobi solvers. To investigate the effectiveness of the proposed models, we perform computational experiments based on the real-world data of the Beijing Yizhuang line. The numerical results illustrate that the energy consumption of the daily train timetable obtained by the proposed energy-efficient train timetabling model with flexible selection of operation levels is reduced by 9.90% when compared with that of the train timetables without operation level selections. Moreover, the energy savings of the energy-efficient train timetables with optimal identical selection and pre-fixed selection of operation levels are 7.67% and 5.75%, respectively. However, the computation time of the energy-efficient train timetabling models with operation level selections is significantly longer than that without operation level selections.