## 2 Related Works  
A very large number of studies about train scheduling and rescheduling have been published for decades. This may be attributed to continuously increasing railway traffic volumes and failure to improve their infrastructures through investment to cope with this situation. When it is not possible to have higher-capacity infrastructure, the natural response is to seek ways to utilize the existing infrastructure more efficiently. Generatingmore efficient timetables (called timetabling or scheduling) and improving dispatching decisions in case of disturbances (called rescheduling) is an applicable strategy to achieve this, hence the wide interest towards these topics [1]. In the literature, there are a variety of topics considered under the generic concept of train scheduling. These include timetable optimization, energy-efficient timetable generation, rolling stock planning, crew planning, etc. This study is focused on rescheduling; hence, we limited the literature review with studies on or closely related to train rescheduling. In addition, because this study is intended for conventional single-track intercity railway lines, studies related to high-speed lines and urban transit lines are not included in the review. Train rescheduling is an NP-complete (nondeterministic polynomial-time complete) problem [1]. In this kind of problem, the major concern is computational workload because it exhibits a huge boost as the problem size (i.e., number of trains, number of stations, number of tracks, etc.) enlarges. Computational workload becomes even more crucial when the problem has to be solved in a very short period of time. This is the principal focus of this paper, which can be considered \"a still open problem\" in the literature because the approaches to the solution based on mathematical programming still need improvements in terms of computational efficiency. For train rescheduling, as any other NP-complete problem, it is no surprise that researchers attack the problem with three main solution types: exact solutions (mostly optimizing over some criteria with a mixed integer linear programming model), metaheuristic solutions (like genetic algorithms, tabu search, simulated annealing, etc.) and other heuristics (either tailor-made or problem-specific heuristics or standard heuristics such as relaxations or branch-and-bound techniques) and simulation-based solutions. There are also a number of hybrid solution approaches, which make use of a combination of two or three of the above solution types. This will form the basis for classification in the literature review part. We will focus on the studies about rescheduling trains over the main lines. Exact Methods: [PERSON] et al. [2] developed a mixed integer linear programming (MILP) model to improve the robustness of a timetable to reduce delay propagation in case of disturbances. They optimized the buffer times. [PERSON] et al. [3] developed a MILP model for rescheduling in case of disruptions with some additional binary variables that introduce the options of cancelling or rerouting some of the trains. They concluded that these options are required for switching between the original timetable and the newly constructed schedule. [PERSON] et al. [4] aimed to minimize the expected total travel time of passengers (rather than trains) in practice with a MILP model. Their MILP also includes a lot of constraints and valid inequalities to speed up the solution process. [PERSON] et al. [5] focused on the train scheduling problem to estimate the arrival (or travel) times of freight trains. Their proposed model is basically a MILP model for the train rescheduling problem. Similar to our study, this study also makes use of the lazy constraint attribute to speed up the run. Metaheuristics: [PERSON] et al. [6] solved the train rescheduling and rerouting problem. They developed an ant colony optimization model for this purpose. [PERSON] et al. [6] utilized a reinforced learning approach, Q-learning, for rescheduling a single-track line in case of large disruptions.