Regenerating braking energy is one major pathway to make rail traffic energy-efficient. It is therefore desirable to design timetables that exploit this feature. However, timetables that allow to regenerate energy are often bad for the passengers. We hence formulate and analyze a bicriteria optimization problem (PESP-Passenger-Energy) to find periodic railway timetables that maximize the regenerated energy in terms of the brake-traction overlap time and minimize the travel time of the passengers. Our model extends the Periodic Event Scheduling Problem (PESP) and offers a rich combinatorial theory. We investigate its computational complexity on one-station networks, building on matchings and Hamiltonian paths. Besides showing its NP-hardness even for a single objective, we identify several polynomial-time solvable special cases. Finally, we provide two case studies, underlining the practicability of our model, and analyzing the Pareto front.

翻译：再生制动能量是实现铁路交通节能的主要途径之一。因此，设计能够利用这一特性的时刻表具有重要价值。然而，允许能量再生的时刻表往往对乘客不利。为此，我们提出并分析了一个双目标优化问题（PESP-乘客-能量），旨在寻找能够最大化制动-牵引重叠时间所对应的再生能量，同时最小化乘客旅行时间的周期性铁路时刻表。我们的模型扩展了周期性事件调度问题（PESP），并提供了丰富的组合理论。我们基于匹配与哈密顿路径，研究了该问题在单车站网络上的计算复杂性。除了证明即使仅考虑单一目标该问题也是NP难的，我们还识别出了若干多项式时间可解的特例。最后，我们提供了两个案例研究，以强调模型的可实践性，并分析了帕累托前沿。