A Multi-objective Programming Model for Subway Last Train Timetabling

Subway last train timetabling focuses more on train coordination to make passengers transfer smoothly. Aiming to find an optimal balanced timetabling, a multi-objectives programming model is proposed with speed profile control for finding the optimal train velocity on sections and train dwell time at stations. Our work makes two contributions. First, this paper analyzes train movements in a line and provides an energy flow transferring method. Second, based on the analysis of train velocity and energy flow, an optimization model, in which passenger satisfaction, train trip time and network energy consumption are model objectives, is brought into the last train timetabling. Finally, to obtain an approximately optimal scheduling strategy, an artificial intelligence algorithm is proposed in particular to effectively solve the proposed model. The results of numerical experiments demonstrate the efficiency and effectiveness of the proposed method.