## 2 Related Works
They used several datasets to train the agent and then finally tested it with a real single-track line in Slovenia. Other or problem-specific heuristics: [PERSON] and [PERSON] [7] studied a complex railway line that serves both passenger and freight traffic. They combined group-based decomposition (decomposing the traffic into passenger trains and freight trains) and train-based decomposition (treating each freight train separately to generate the feasible schedule). [PERSON] et al. [8] studied the Lagrangian dual problem of the train timetabling problem. They claimed that this kind of dual problem traditionally had been solved using an aggregate approach in which all train requests had been involved in the dual problem. However, in this study, the dual information from all requested train paths were treated individually, which was called by the authors \"disaggregate bundling\". [PERSON] et al. [9] exploredthe potential of parallel programming applications to train scheduling and succeeded in applying it. They developed tree-based depth-first search heuristics to be implemented in parallel in a multicore computer. [PERSON] and [PERSON] [10] worked on the scheduling problem for a mixed-traffic high-speed rail line where overtaking is allowed. They sought ways to extend the typically short time windows found in the train scheduling literature. In order to overcome the computational complexity generated by this problem while working on Lagrangian-based decomposition algorithms, they proposed an improved alternating direction method of multipliers. [PERSON] et al. [11] focused on generating feasible scheduling solutions with less computational time and workload. The authors considered a railway network without central control. They also worked on a two-level control approach in which low-level controllers prepare solutions for their area of responsibility and their high-level supervisors evaluate the solutions. Authors proposed greedy heuristics to improve this implementation. [PERSON] et al. [12] developed greedy heuristics to solve the conflicts that arise from a distorted timetable. They scheduled the trains one at a time, thus resolving the conflicts arising on the run. Their algorithm is also suitable for parallel computing. [PERSON] [13] developed two heuristic methods for the single-line rescheduling problem. One was a greedy heuristic method imitating the decision behavior of train dispatchers in the Turkish State Railways network. The other one was a heuristic with a look-ahead component to give improved results. [PERSON] et al. [14] studied the rescheduling problem in case of closed tracks for maintenance tasks. They developed a hierarchical heuristic algorithm that treats line closures and train runs together and reconstructs a feasible schedule within a short duration. [PERSON] et al. [15] studied improving dispatching decisions related to overtakes in double-track sections. They demonstrated the use of an \"odds ratio\" as an aiding tool to dispatchers. Hybrid Methods: [PERSON] and [PERSON] [16] considered the periodic and symmetric train timetabling problems and utilized a time-space graph formulation to solve them. They aimed to minimize the total travel times of passengers rather than trains. They named their solution method the \"dive-and-cut-and-price\" method, and it made use of different heuristics, such as neighborhood search, Bender's cuts and column generation. [PERSON] et al. [17] used a multiobjective approach because timetable robustness and minimization of the planned running times in the timetable are indeed contradictory objectives. They proposed a timetable model for a single unidirectional track and applied some enhancement procedures based on a microscopic simulation fed and calibrated with random delay data. [PERSON] and [PERSON] [18] considered a periodic timetable for a network with unidirectional lines. Their MILP model determines the order of the trains so that the minimum possible cycle period is minimized, and it then generates a feasible timetable for that order.