Robust stochastic optimization model and branch and bound algorithm for train scheduling using regenerative braking energy

An energy-efficient timetable provides the condition that the regenerative energy produced by the trains in braking mode is used by the trains in accelerating mode running at the same power supply section. In this paper, it is intended to propose a train timetable which synchronize the accelerating and braking actions of trains to maximize the utilization of regenerative energy in urban railway lines. To that end, a mathematical model and a Branch and Bound (B&B) algorithm are proposed. As the train departures and arrivals are always contaminated with unwilling uncertainties, a robust method based on the stochastic optimization is introduced. The results are investigated considering an Iranian case study. The results show 17.5% improvement in time synchronization by the introduced approach.