Robust energy-efficient train speed profile optimization in a scenario-based position-time-speed network

Train speed profile optimization is an efficient approach to reducing energy consumption in urban rail transit systems.Different from most existing studies that assume deterministic parameters as model inputs,this paper proposes a robust energy-efficient train speed profile optimization approach by considering the uncertainty of train modeling parameters.Specifically,we first construct a scenario-based position-time-speed(PTS)network by considering resistance parameters as discrete scenariobased random variables.Then,a percentile reliability model is proposed to generate a robust train speed profile,by which the scenario-based energy consumption is less than the model objective value at a confidence level.To solve the model efficiently,we present several algorithms to eliminate the infeasible nodes and arcs in the PTS network and propose a model reformulation strategy to transform the original model into an equivalent linear programming model.Lastly,on the basis of our field test data collected in Beijing metro Yizhuang line,a series of experiments are conducted to verify the effectiveness of the model and analyze the influences of parameter uncertainties on the generated train speed profile.