A Two-Step Linear Programming Model for Energy-Efficient Timetables in Metro Railway Networks

TL;DR

This paper introduces a new two-step linear programming model that efficiently generates energy-saving train timetables for metro networks, significantly reducing energy use and enabling quick computation.

Contribution

The paper presents a linear optimization model for metro timetable planning that is computationally tractable and outperforms existing NP-hard models in efficiency and energy savings.

Findings

Model finds optimal timetables within 13 seconds

Achieves up to 19.27% energy reduction

Successfully applied to Shanghai Metro network data

Abstract

In this paper we propose a novel two-step linear optimization model to calculate energy-efficient timetables in metro railway networks. The resultant timetable minimizes the total energy consumed by all trains and maximizes the utilization of regenerative energy produced by braking trains, subject to the constraints in the railway network. In contrast to other existing models, which are NP-hard, our model is computationally the most tractable one being a linear program. We apply our optimization model to different instances of service PES2-SFM2 of line 8 of Shanghai Metro network spanning a full service period of one day (18 hours) with thousands of active trains. For every instance, our model finds an optimal timetable very quickly (largest runtime being less than 13s) with significant reduction in effective energy consumption (the worst case being 19.27%). Code based on the model has been integrated with Thales Timetable Compiler - the industrial timetable compiler of Thales Inc that has the largest installed base of communication-based train control systems worldwide.