Mixed-integer linear programming and pseudospectral methods are among the new methods proposed for single- and multi-train systems for the solution of the nonlinear trajectory planning problem which involves constraints such as varying speed restrictions and maximum traction/braking force. Signaling systems and their effects are also accounted for in the trajectory planning model.

Origin-destination passenger demand is included in the model formulation for train scheduling. Iterative convex programming and efficient bi-level approaches are utilized in the solution of the train-scheduling problem. In addition, the splitting rates and route choices of passengers are also optimized from the system point of view.

The problems and solutions described in Optimal Trajectory Planning and Train Scheduling for Urban Rail Transit Systems will interest researchers studying public transport systems and logistics whether from an academic or practitioner background as well as providing a real application for anybody studying optimization theory and predictive control.