Reducing energy consumption through trajectory optimization for a metro network

The techniques of optimal control and optimization are applied to a practical problem of reducing energy consumed by the Montreal Metro (subway) system. The problem considered is the determination of tunnel trajectories in the "equivalent" vertical plane when trains traveling in both directions must follow the same trajectory. The problem is first formulated as a control problem with control and state constraints. Then, under certain simplifying assumptions, an heuristic method employing a direct search algorithm is presented and used in the trajectory optimization. The trajectories are optimized to reduce the sum of the energy consumed by the trains traveling in both directions on the trajectory. The results show an average reduction of 7.73 percent in energy consumption as compared with existing trajectories. The trajectories found using the method presented here will be followed in future tunnel construction.