Scheduling distributed locomotives for optimal train handling

This paper deals with an open loop control problem of planning the split of tractive and braking efforts amongst locomotives distributed along a heavy-haul freight train with the objective of managing the forces experienced by couplers between railcars (i.e. in-train forces). An optimization problem is formulated to solve this train handling problem with the magnitude of the largest forces experienced by the couplers as the cost function, which is to be minimized subject to real-world operational constraints on what tractive effort splits are permissible and temporal restrictions thereof. While the formulated problem contains continuous and discrete-valued variables, the structure of the problem is used to decompose it into a convex program with continuous variables and a purely discrete variable decision making problem. The latter is solved using dynamic programming by mapping it to a variant of the shortest path on a graph problem. Simulation results are presented to verify the efficacy of the approach.