Timetabling optimization of a mixed double- and single-tracked railway network

The paper deals with the timetabling problem of a mixed multiple- and single-tracked railway network. Out of all the solutions minimizing the maximum relative travel time, the one minimizing the sum of the relative travel times is selected. User preferences are taken into account in the optimization problems, that is, the desired departure times of travellers are used instead of artificially planned departure times. To find the global optimum of the optimization problem, an algorithm based on the bisection rule is used to provide sharp upper bounds of the objective function together with one trick that allows us to drastically reduce the number of binary variables to be evaluated by considering only those which really matter. These two strategies together permit the memory requirements and the computation time to be reduced, the latter exponentially with the number of trains (several orders of magnitude for existing networks), when compared with other methods. Several examples of applications are presented to illustrate the possibilities and excellences of the proposed method. The model is applied to the case of the existing Madrid–Sevilla high-speed line (double track), together with several extensions to Toledo, Valencia, Albacete, and Málaga, which are contemplated in the future plans of the high-speed train Spanish network. The results show that the computation time is reduced drastically, and that in some corridors single-tracked lines would suffice instead of double-tracked lines.