This paper proposes a value-based deep reinforcement learning approach that is capable of handling train timetable rescheduling under both disturbed and disrupted situations. A railway environment is constructed to simulate the problem as a Markov decision process, where the optimization objective is integrated into the reward module and various constraints are incorporated into the conflict detection and avoidance module. To address the challenges of sparse rewards and large action space with limited legal actions, a value-based algorithm framework is proposed to efficiently select and effectively evaluate actions. Through the designed simulation and training procedures, the proposed approach is tested on several disturbance and disruption cases based on a real-world instance (i.e. a Chinese high-speed railway corridor). Experimental results show that the proposed method can obtain high-quality solutions within a reasonable computing time, and also outperforms handcrafted rules in terms of the optimality of solutions. Furthermore, the proposed method exhibits promising generalization capabilities in homogeneous perturbation scenarios (disturbance scenarios and disruption scenarios that share either the same affected location and start time or the same affected location and disrupted duration).

We address the problem of simultaneously scheduling trains and planning preventive maintenance time slots (PMTSs) on a general railway network. Based on network cumulative flow variables, a novel integrated mixed-integer linear programming (MILP) model is proposed to simultaneously optimize train routes, orders and passing times at each station, as well as work-time of preventive maintenance tasks (PMTSs). In order to provide an easy decomposition mechanism, the limited capacity of complex tracks is modelled as side constraints and a PMTS is modelled as a virtual train. A Lagrangian relaxation solution framework is proposed, in which the difficult track capacity constraints are relaxed, to decompose the original complex integrated train scheduling and PMTSs planning problem into a sequence of single train-based sub-problems. For each sub-problem, a standard label correcting algorithm is employed for finding the time-dependent least cost path on a time-space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted on a small artificial network and a real-world network adapted from a Chinese railway network, to evaluate the effectiveness and computational efficiency of the integrated optimization model and the proposed Lagrangian relaxation solution framework. The benefits of simultaneously scheduling trains and planning PMTSs are demonstrated, compared with a commonly-used sequential scheduling method.