Optimization Techniques Applied to Railway Systems
We study the problem of minimizing the usage of electrical energy in railway systems. The objective is to determine a train speed profile that minimizes energy consumption given a time schedule. In collaboration with an industrial partner, we propose a new model that is more complete than the ones existing in the literature, in particular the model takes into account several non-linearities that emerge in a real setting. First, we formulate our problem within the framework of optimal control where our solution approach consists in discretizing the control problem and solving numerically the finite-dimensional optimization problem that is obtained out of the discretization. To do so we develop a platform based on AMPL and Ipopt that allows a fast and accurate solution. We then reformulate the problem within the framework of Dynamic Programming which allows to get the optimal action for any initial point. Solving the Dynamic Programming is very time consuming and we develop a C++ code to solve some simple examples. We finally implement our solution in a train simulator in order to estimate the energy reduction obtained in several real examples provided by INGETEAM S.A. The results obtained by the simulator indicate that the energy reduction is between 8% and 25%. We thus conclude that our first approach represents a scheme that could be implemented by industry to solve real-life cases.