Black-Box Optimization in Railway Simulations

In railway timetabling one objective is that the timetable is robust against minor delays. One way to compute the robustness of a timetable is to simulate it with some predefined delays that occur and are propagated within the simulation. These simulations typically are complex and do not provide any information on the derivative of an objective function such as the punctuality. Therefore, we propose black-box optimization techniques that adjust a given timetable so that the expected punctuality is maximized while other objectives such as the number of operating trains or the travel times are fixed. As an example method for simulation, we propose a simple Markov chain model directly derived from real-world data. Since every run in any simulation framework is computationally expensive, we focus on optimization techniques that find good solutions with only few evaluations of the objective function. We study different black-box optimization techniques, some including expert knowledge and some are self-learning, and provide convergence results.