The Train Timetabling Problem (TTP) is the problem of finding the timetable that utilizes the infrastructure as efficient as possible, while satisfying market demands and operational constraints. As reliability is important to passengers it is important that timetables are robust. In this paper we propose a method that combines optimization and simulation to find the timetable that minimizes the travel times and maximizes the expected punctuality. The core method consists of iteratively re-optimizing a bi-objective mixed integer sequencing timetable model, where both planned travel time and simulated delays are taken into account. Each generated timetable is validated and re-evaluated using the micro-simulation tool RailSys. The advantage of the method is that it captures both the uncertainty of a timetable at the planning stage and the validity of the generated timetable. The method is evaluated on a unidirectional track section of the Western Main Line in Sweden and shows promising results for future research.

Minimal travel time and maximal reliability are two of the most important properties of a railway transportation service. This paper considers the problem of finding a timetable for a given set of departures that minimizes the weighted sum of scheduled travel time and expected delay, thereby capturing these two important socio-economic properties of a timetable. To accurately represent the complex secondary delays in operational railway traffic, an approach combining microscopic simulation and macroscopic timetable optimization is proposed. To predict the expected delay in the macroscopic timetable, a surrogate function is formulated, as well as a subproblem to calibrate the parameters in the model. In a set of computational experiments, the approach increased the socio-economic benefit by 2-5% and improved the punctuality by 8-25%.

This paper considers the problem of minimizing travel times and maximizing travel time reliability, which are important socio-economic properties of a railway transport service, for a given set of departures on a double-track line. In this paper travel time reliability is measured as the average delay, and a delay prediction model for MILP timetable optimization is presented. The average delay prediction model takes into consideration time supplements, buffer times and propagation of delays in the railway network and is not restricted to a fixed order of the trains. Validation of the average delay prediction model, and an evaluation of the approach with combined simulation-optimization for improving railway timetables, are conducted by a simulation study on a part of the Swedish Southern Main Line. Results from the simulation study show that the average delays are reduced by up to approximately 40% and that the punctuality is improved by up to approximately 8%.

Performance aspects such as travel time, punctuality and robustness are conflicting goals of utmost importance for railway transports. To successfully plan railway traffic, it is therefore important to strike a balance between planned travel times and expected delays. In railway operations research, a lot of attention has been given to construct models and methods to generate robust timetables—that is, timetables with the potential to withstand design errors, incorrect data, and minor everyday disturbances. Despite this, the current state-of-practice in railway planning is to construct timetables manually, possibly with support of microsimulation for robustness evaluation. This paper aims to narrow the gap between the state-of-the-art optimization-based research approaches, and the current state-of-practice to construct timetables by combining simulation and optimization. The paper proposes a combined simulation-optimization approach for double-track lines, which generalizes previous work to allow full flexibility in the order of trains by including a new and more generic model to predict delays. By utilizing delay data from simulation, the approach can make socio-economically optimal modifications of a given timetable by minimizing predicted disutility—the weighted sum of scheduled travel time and total predicted delay.  In a large simulation experiment on the heavily congested Swedish Western Main Line, it is demonstrated that compared with a real-life, manually constructed, timetable large reductions of delays as well as improvements in punctuality could be obtained to a small cost of marginally longer travel times. The cost of scheduled in-vehicle travel time and mean delay was reduced by 5% on average, representing a large improvement for a highly utilized railway line. Furthermore, a separate scaling experiment indicate that the approach can be suitable also for larger problems. 

Punctuality of railway traffic is one of the most important quality indicators for passenger traffic. In previous research it has been shown that the timetable has substantial impact on punctuality. Despite this, surprisingly few scientific approaches for explicitly maximizing the punctuality exists in the literature. The only two methods with this purpose, that we are aware of, also seems to be too computationally expensive to be applicable in practice. In this paper, we therefore propose a combined simulation-optimization method for improving the punctuality of a given main line timetable. The intended use case for this method is in tactical timetabling, for improving daily graphs in the annual timetabling process through small adjustments of the time supplements in the timetable. Throughout Europe and the world, this step is commonly done based on ad-hoc simulations or experience only. We evaluated the proposed method in a simulation experiment on the Swedish Western Main Line and compared its impact on punctuality and robustness with five other methods---three state-of-the-art methods and two more basic approaches. The most important result from the simulation experiment was that in terms of total punctuality, the proposed method was better than all other methods, and significantly so except in one case. Scalability was evaluated by solving a scenario with 10 replications of the original timetable within a little more than 2 hours, on average.