A bi-objective timetable optimization model incorporating energy allocation and passenger assignment in an energy-regenerative metro system

Complex passenger demand and electricity transmission processes in metro systems cause difficulties in formulating optimal timetables and train speed profiles, often leading to inefficiency in energy consumption and passenger service. Based on energy-regenerative technologies and smart-card data, this study formulates an optimization model incorporating energy allocation and passenger assignment to balance energy use and passenger travel time. The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is applied and the core components are redesigned to obtain an efficient Pareto frontier of irregular timetables for maximizing the use of regenerative energy and minimizing total travel time. Particularly, a parallelogram-based method is developed to generate random feasible timetables; crossover and local-search-driven mutation operators are proposed relying on the graphic representations of the domain knowledge. The suggested approach is illustrated using real-world data of a bi-directional metro line in Beijing. The results show that the approach significantly improves regenerative energy use and reduces total travel time compared to the fixed regular timetable.