A Two-Objective Timetable Optimization Model in Subway Systems

The train timetable optimization problem in subway systems is to determine arrival and departure times for trains at stations so that the resources can be effectively utilized and the trains can be efficiently operated. Because the energy saving and the service quality are paid more attention, this paper proposes a timetable optimization model to increase the utilization of regenerative energy and, simultaneously, to shorten the passenger waiting time. First, we formulate a two-objective integer programming model with headway time and dwell time control. Second, we design a genetic algorithm with binary encoding to find the optimal solution. Finally, we conduct numerical examples based on the operation data from the Beijing Yizhuang subway line of China. The results illustrate that the proposed model can save energy by 8.86% and reduce passenger waiting time by 3.22% in comparison with the current timetable.