Mixed Integer Programming Formulation for the Energy-Efficient Train Timetables Problem
Railway traffic is the biggest individual electricity consumer in Germany, amounting to 2% of the country’s total electricity usage. However, up to 20% of the annual electricity cost depends on the highest power value drawn within the billing period. In this paper, we optimize the timetables of railway traffic in order to avoid high peaks in power consumption, while preserving at the same time some usability and safety considerations. We propose an exact mixed integer programming model together with a systematic way of simplifying the model in order to obtain feasible solutions that are not far from the optimum. We also discuss two possible dynamic programming approaches that may be used for solving small instances with a specific structure. Our approach became Team Optimixtli’s winning entry in the Discrete Optimization Challenge: Energy-Efficient Train Timetables. This competition was part of the Open Research Challenge 2015 organized by the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) in Germany.
We thank the Mexican National Council on Science and Technology (CONACyT) for providing scholarships to most students in our graduate program (including two team members) and also for providing a scholarship to another team member through the National System of Researchers (SNI). We thank the Mexiquense Council on Science and Technology (COMECyT) for providing a scholarship to our last team member. We thank Universidad Autónoma Metropolitana Azcapotzalco for funding Research Project SI004-13 (Algorithms and Models for Network Optimization Problems) and also for allowing us the use of some computing facilities through the Systems Department. We thank Gurobi Optimization for giving us free licenses to their software. We thank the Friedrich-Alexander-Universität Erlangen-Nürnberg for organizing the Discrete Optimization Challenge and the participating teams for their great effort. Last, but not least, we thank honorary team member Gabrijela Zaragoza for proposing a nice team name, a portmanteau of optimization and the nahuatl word mixtli (cloud).
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