Energy-Efficient Timetable Optimization Empowered by Time-Energy Pareto Solution Under Actual Line Conditions

Considering the high complexity of actual railway line conditions, this paper proposes a two-level energy-efficient timetable optimization method empowered by time-energy Pareto solution to reduce energy consumption while maintaining the existing infrastructure unchanged. At the train-level, an efficient equivalence method for actual line conditions, including varying slopes, curves, and tunnels is proposed to formulate the train driving process as a multi-objective optimization model to balance the time cost and energy consumption. An improved non-dominated sorting genetic algorithm II (INSGA-II) enhanced by differential evolution (DE) and a new crowding distance (NCD) operator is further proposed to access the time-energy Pareto solution of the potential speed profile for a single train by comparing different control strategies. At the timetable-level, an integer linear programming (ILP) model is designed with the computed train-level Pareto solution to optimize the energy-efficient timetable by restricting the headway between trains, in which a novel operation time-based branch-and-bound (BBOT) method is proposed to enable quick search of optimal control strategy and thus allows for accurate output of the optimal timetable while retaining real simulation results. A case study on the actual operation data of the Beijing-Jinan section of the Beijing-Shanghai high-speed railway shows that the optimized timetable can save up to 18.69% of energy when the train is on time. In cases of train delays, the total savings under 8-min, 9-min, and 14-min delay scenarios are 4.69%, 9.93%, and 8.05%, respectively compared to the method using time-oriented strategies, which have demonstrated the effectiveness of the proposed two-level optimization formulation.