Mean-variance model for optimization of the timetable in urban rail transit systems

Regenerative braking is an energy-efficient technology that converts kinetic energy to electrical energy during braking phases. For more efficient recovered energy utilization, the stochastic cooperative scheduling approach has been proposed for determining the dwell times at stations, wherein the accelerating trains can use the energy recovered from the adjacent braking trains as much as possible. Here, running times at the sections are considered as random variables with given probability functions. In this paper, the authors develop a data-driven stochastic cooperative scheduling approach in which the real data of the speed of trains are recorded and used in the place of motion equations. First, the authors formulate a stochastic mean-variance model, which maximizes the expected utilization and minimizes the variance of the quantity of the recovered energy. Second, a genetic algorithm that utilizes particle swarm optimization has been designed to find the optimal dwell times at stations. Finally, numerical examples are presented based on the real-life operational data from Beijing Yizhuang urban rail transit line in China. The results illustrate that the real-life operational data in the data-driven stochastic cooperative scheduling approach can provide a more accurate description about the movement of trains, which would result in more efficient energy saving, i.e. by 1.66%, in comparison with the stochastic cooperative scheduling approach. Most importantly, the data-driven stochastic cooperative scheduling approach results in lower variance by 68.69% and higher robustness.