In this paper we propose a sparse optimization approach to maximize the utilization of regenerative energy produced by baking trains for energy-efficient timetabling in metro railway systems. By introducing the cardinality function and the square of the Euclidean norm function as the objective function, the resulting sparse optimization model can characterize the utilization of the regenerative energy appropriately. A two-stage alternating direction method of multipliers is designed to efficiently solve the convex relaxation counterpart of the original NP-hard problem and then to produce an energy-efficient timetable of trains. The resulting approach is applied to Beijing Metro Yizhuang Line with different instances of service for case study. Comparison with the approach proposed by Das Gupta et al. [Transportation Research Part B 93 (2016): 57-74] is also conducted which illustrates the effectiveness of our proposed sparse optimization model and the efficiency of our numerical optimization algorithm.
Beijing Jiaotong University, June 9, 2018