A framework for real-time near-optimal train run-curve computation with dynamic travel time and speed limits

This paper studies the problem to generate the most energy efficient run-curves subject to given travel time requirements. The target is to provide a train with the ability to quickly adjust its run curve according to different travel time requirements and speed limits along the track before departing a terminal. Using a train model considering train length, varying track gradient and speed limit profile, the optimal run-curve problem is formulated into a bi-criteria optimization problem that minimizes weighted energy consumption and weighted travel time. By selecting appropriate weight values, the optimization problem would generate a run-curve with near-optimal energy consumption. We propose a two stage procedure framework, which includes an off-line stage and a real-time stage. A series of geometric relation between weight in the objective function and travel time are derived. The actual run-curves are generated in the real-time stage using approximate dynamic programming. For the first time, a framework provides trains with the ability to fast response to dynamic travel time requirement using complex physical models.