# Real-Time Path Planning of Driverless Mining Trains with Time-Dependent Physical Constraints
## 2 Related Works  
An enormous number of studies have been conducted on railway scheduling and train timetabling problems [7; 8; 9; 10; 11; 12]. The research work can be classified into three main categories: the train scheduling and rescheduling problem, the periodic and nonperiodic timetabling problem, and the passenger train and freight train timetabling problem [13]. Train scheduling is an offline problem that determines the arrival and departure times for trains at each station before the schedule is executed, e.g., [14; 15; 16; 17; 18]. With a planned schedule, rescheduling is a real-time problem that aims to determine detailed train movements and timetables to minimize train deviations, e.g., [19; 20; 21; 22]. [PERSON] et al. [17] studied a train scheduling problem in a large national railway network, and presented two flexible heuristics based on a mixed integer program formulation for local optimisation to improve infrastructure utilization. [PERSON] et al. [18] studied the integration of train scheduling and rolling stock circulation planning under time-varying passenger demand for an urban rail transit line and proposed three approaches to solve the resulting multiobjective mixed-integer nonlinear programming problem to deliver both an irregular train schedule (i.e., departure and arrival times of all train services) and a rolling stock circulation plan (including entering/exiting depot operations of rolling stocks and connections between train services) simultaneously. [PERSON] et al. [14] formalized demand-oriented scheduling and rescheduling models in order to propose a dynamic timetable, and proposed a min-max method with which to address operational constraints related to train capacity, train speed limits, train transfers, possible conflict in the track section use, with the main objective to minimize the travel time. [PERSON] et al. [20] proposed a train rescheduling optimisation model in the case of the vehicle breakdown on a metro line. Efficient rescheduling strategies including flexible short-turning and adding backup trains in particular are formulated into the model. [PERSON] and [PERSON] [22] proposed a timetable rescheduling model to handle unexpected disruptions, where flexible stopping (i.e. skipping stops and adding stops) and flexible short-turning (i.e. full choice of short-turn stations) are innovatively integrated with three other dispatching measures: retiming, reordering, and cancelling. Periodic timetabling requires that most or all train paths repeat in time with a certain period (e.g., 12 h), e.g., [23; 24; 25; 26; 27]. However, as it becomes difficult to obtain effective periodic schedules when dealing with interruptions or conflicts (e.g., track maintenance), a nonperiodic timetable becomes more appropriate, e.g., [28; 29]. [PERSON] et al. [23] integrated stop planning, service planning, and scheduling in a periodic timetabling problem and modelled it as a mixed integer linear programming formulation to minimize the average travel delay of passengers. They then developed a genetic algorithm supported by a scheduling heuristic to solve the problem for better scalability and efficiency. [PERSON] et al. [24] considered a robust periodic timetabling problem--the problem of designing a periodic timetable that can easily be adjusted in case of small periodic disturbances--and developed a solution method for a parameterised class of uncertainty regions. [PERSON] et al. [25]used the minimum cycle time of the periodic timetable as an indicator for stability, and defined an optimization problem with this minimum cycle time as the objective function to be minimized. They then proposed an optimization method to find a feasible periodic timetable that also ensures maximum stability for heterogeneous railway networks, which is capable of handling flexible train orders, running and dwell times, and overtaking locations. [PERSON] et al.