Integrated optimization of energy-efficient train timetable and rolling stock circulation plan with regenerative energy utilization

With the running and dwell levels considered, we investigate the integrated energy-efficient train timetabling and rolling stock circulation planning problem for a metro line, where the passenger demand is considered via the service pattern. A mixed integer non-linear programming model is proposed to minimize the headway variations, headway deviations, the number of required rolling stocks, and the net energy consumption. Specifically, the regenerative energy utilization is considered by the brake-traction overlapping times. After linearization, the energy-efficient timetabling problem can be solved by existing solvers. A two-step method is presented to enhance the computational efficiency. In the first step, the arrival times of train services at the first station are determined. In the second step, the timetable and rolling stock circulation plan are optimized according to the given arrival times at the first station. Two case studies with different service patterns are conducted based on the data of Beijing Yizhuang metro line. The computational results demonstrate that the two-step method can reduce the optimality gap sharply. Compared with the energy-efficient model without the consideration of regenerative energy utilization, the regenerative energy utilization of the model with regenerative energy utilization considered increases 25.64% and 35.95% in the two test cases, respectively.