Robust Optimization of Energy-Saving Train Trajectories under Passenger Load Uncertainty Based on p-NSGA-II

Railway electrification has attracted substantial interests in recent years as a key part of the global effort to achieve transport decarbonisation. To improve the energy efficiency of train operations, of particular interest is the optimization of train speed trajectories. However, most studies formulate the problem as a single-objective optimization model and do not take into account train mass uncertainty associated with the passenger load variations. This paper formulates a bi-objective robust optimization model to minimize both the energy consumption and journey time, in which the robustness against the uncertain train mass is considered and viewed as a decision-maker preference. A novel multi-objective optimization algorithm namely p-NSGA-II is proposed, incorporating the original NSGA-II and a proposed preference dominance criterion to handle the DM preference. With the proposed p-NSGA-II, not only all solutions will converge to the optimal Pareto front but also solutions with better robustness in the Pareto front will be automatically selected and retained, meanwhile the spread of the selected solutions is maintained. The effectiveness of the p-NSGA-II to generate a set of performance-robust driving schemes is verified by numerical case studies. The results show that the p-NSGA-II can achieve up to 40.59% robustness improvement compared to the original NSGA-II.