Metro timetable optimisation for minimising carbon emission and passenger time: a bi-objective integer programming approach

Timetable optimisation in metro systems is typically a multi-objective decision problem involving both social and passengers' benefits. Based on the train operation and passenger demand data, this study develops a bi-objective timetable optimisation model to reduce both passenger time and carbon emission of train operation. Firstly, the cooperative scheduling rule of multiple trains within the same electricity supply section is analysed. The tractive energy consumption and utilisation of regenerative braking energy are calculated with a set of kinematical equations. The carbon emission is formulated according to the calculations of energy consumption. Meanwhile, a passenger time calculation function is established by analysing the real-world passenger demand data. Secondly, a bi-objective integer programming model with dwell time control is formulated, and a linearly weighted compromise algorithm and a heuristic algorithm are designed to find the optimal solution. Finally, a numerical example is presented based on the passenger and operation data from the Beijing Metro Yizhuang Line. The results show that the best found timetable can achieve a good performance on both carbon emission and passenger time in comparison with the currently used timetable.