عنوان مقاله [English]
The train timetabling in a railway network is one of the most critical problems in passenger or freight transportation systems. With uncontrollable noises affecting the system, finding a schedule whose performance does not significantly reduce under various disturbances is vital. A train timetable is considered robust when it has the ability to absorb small disturbances, and its performance does not reduce under the situation of recurring disturbances.
The integer programming problem of robust train timetabling problem with a decision variable and constraint for every train and every block in a railway network takes one an unreasonably long time to solve, and this may be possible after adopting numerous simplifying assumptions. To move around these disadvantages, discrete event simulation is a more appropriate approach. The methodology that combines simulation modeling and optimization techniques for solving optimization problems is commonly referred to as simulation optimization.
In this paper, we introduce a new simulation optimization method to solve the robust optimization of train timetabling problem in metro lines. We aim to minimize the expected value of the passenger's waiting time with a satisfactory rate of carriage fullness. Headways, which are the time intervals between arrivals of two consecutive trains into one station, are considered as the
decision variables. It is assumed that the rate of passenger arrival to stations and travel times is stochastic. We first develop the simulation model in a way that the constraints, such as the train waiting times in stations, station capacities, overtaking, and the safe distance between trains, are satisfied. Then, using the inputs/outputs combination of simulation model, two stochastic Kriging metamodels are fitted as one for the objective function and one for the constraint. To write the robust counterpart problem, we use the Bertsimas and Sim methodology for the resulting mathematical model. The final mathematical programming model is solved by PSO metaheuristic. This methodology is applied to a particular line within Tehran railway system. Our approach generates satisfactory solutions to different levels of conservatism factor at moderately few number of experiments.