Optimizing vertical alignment of underground metro for energy saving of train operation

Existing studies on saving energy consumption of train movement (ECTM) have focused mainly on optimizing train operation and service timetable. However, the ECTM is also significantly affected by metro vertical alignment. This paper presents a mathematical model for optimizing the vertical alignment between any two adjacent underground metro stations, with the objective of minimizing the total ECTM in both train-running directions. The model takes into account train operation with variable speed limits and gradients in the calculations of the ECTM, and a number of constraints involving local geographical conditions and design criteria set by the Code for Design of Metro in China. To solve the proposed model, a customized genetic algorithm (GA) with an indirect coding method is developed. Case studies on a real-world metro line show that the vertical alignments optimized by the model outperform that designed by experienced consultants in the ECTM savings; and the average energy saving rate on the total ECTM in a train's round trip exceeds 5%. In addition, the principles of designing metro vertical alignment with particular consideration of saving ECTM are summarized, which can be of great reference value to future vertical alignment design.