Robust optimization of train timetable and energy efficiency in urban rail transit: A two-stage approach

With the rapid development of urban rail transit systems in large cities, the travel demand of urban rail transit has increased and the total energy consumption has risen sharply. These situations will result in a huge operating cost, especially the energy consuming. In urban rail transit operations, some uncertain or stochastic factors frequently occur, which will lead to trains deviating from the schedule train timetable. Therefore, it is of great significance to study the optimal strategy to reduce the energy consumption and enhance the flexibility. Providing a robust train timetable is able to reduce operating costs and improve service quality. This paper proposes a two-stage robust optimization model for finding an optimal train timetable to save energy-efficient and reduce passenger waiting time. In the stage-one model, the objective is to reduce passenger waiting time, and the decision variable is the train departure time interval. In the stage-two model, the objective is to minimize the total energy consumption of all trains, and the decision variable is the train departure and arrival time at each station. Due to the complexity of the mathematical model, this paper proposed a nested heuristic genetic algorithm to solve it. An adaptive generation operator and a nested chromosome set generation strategy are included to solve the two-stage robust optimization model. The proposed model and algorithm is then validated by the practical data of Beijing Subway Yizhuang line. The proposed approach can be potentially applied to metro operation optimization of urban rail transit system.