Collaborative optimization of energy-efficient train schedule and train circulation plan for urban rail

It is of great practical significance to save train traction energy for reducing the operation cost of urban rail transit. The energy-efficient train scheduling without combining with train circulation planning may inadvertently increase the other cost of rolling stocks, and finally lead to an increment of the total operation cost. This paper studies the integrated problem of energy-efficient train scheduling and train circulation planning for urban rail, and aims to reduce the total operation cost of rolling stocks including energy consumption. Its main challenge is to simultaneously solve three subproblems, namely the saving of train's traction energy in each rail section, the utilizing of regenerative braking energy and the optimizing of train circulation plan. We construct an optimization model to simultaneously optimize schedule and train circulation plan. Based on the designing of a strategy to create the train circulation plan for each train schedule, an efficient particle swarm algorithm is formed to solve our proposed model. The numerical experiments based on Guangzhou Metro Line 9 of China illustrate that the collaborative optimization can reduce the total operation cost of trains by 4.48% compared with the initial train schedule.