Deterministic vs heuristic algorithms for eco-driving application in metro network

In this paper, we investigate the performances of two different algorithms for calculating the metro vehicles speed profiles minimizing the energy consumption of a given path. The optimization problem, formulated as a Mixed-Integer Nonlinear Programming (MINLP) problem, take into account constraints related to the trip (time-table, distances, acceleration limits, etc.) and constraints related to the electric feeding system (line voltage, substations supplied power, etc.). We implement a deterministic algorithm based on Dynamic Programming Optimization (DPO) method, and a heuristic one based on Particle Swarm Optimization (PSO) method, and we evaluate the performances in terms of the time spent on search of a feasible solution and the goodness of the obtained solution. The resulting speed profiles are tested in a metro network simulation tool, based on the `quasi static' backwards looking method, and taking into account the track topology, the characteristics of the metro system. The results in terms of energy saved, current supplied by the electric substations and line voltage stabilization are evaluated and discussed.