Analysing stability and investments in railway networks using advanced evolutionary algorithms

We consider a network of periodically running railway lines. Investments are possible to increase the speed and to improve the synchronisation of trains. The model also includes random delays of trains and the propagation of delays across the network. We derive a cost-benefit analysis of investments, where the benefit is measured in reduced waiting time for passengers changing lines. We also estimate the actual mean waiting time simulating the train delays. This allows us to analyse the impact that an increasing synchronisation of the timetable has on its stability. Simulation is based on an analytical model obtained from queueing theory. We use sophisticated adaptive evolutionary algorithms, which send off avant-garde solutions from time to time to speed up the optimisation process. As there is a high correlation between scheduled and estimated waiting times for badly synchronised timetables, we are even able to include the time consuming simulation into our optimisation runs.