地铁列车运行常采用巡航模式来保证运营的安全、舒适和准点，而人工纵断面线形设计较难契合列车的巡航状态、不适应设计条件的多变，无法做到有效节能。本文以变坡点里程和高程为变量，以列车双向运行牵引能耗为目标建立纵断面线形节能优化模型，采用差分进化算法进行模型求解。优化策略包括初始方案搜索和整正两个阶段，初始方案搜索阶段依据区间长度假定适当多的变坡点进行优化，方案整正阶段将删除初始方案上坡度代数差极小的变坡点得到优化方案。优化结果表明：巡航模式下，节能坡坡度值越大，中间坡度越缓，列车双向能耗越小。灵敏性分析表明：惰行距离较长时，宜设置较长的节能坡；车站高差增大时，宜缩小低位车站节能坡的长度和坡度值，增长高位车站节能坡的长度。

Cruising mode is a common method used by metro trains for safety, comfort, and punctual operation. However, the manual design of vertical alignment is hard to fit with the cruising state and the variation of design conditions, which means ineffective energy saving. This paper defines mileages and elevations of the gradient change points, sets up a vertical alignment optimization model based on the objective of minimum traction energy consumption of double directions, and utilizes a differential evolution algorithm to solve the optimization model. The optimization strategy includes two stages named initial alignment search and adjustment. The appropriate number of gradient change points are set according to the interval length in the stage of initial alignment search, and the gradient change points with small gradient differences on the initial alignment are deleted in order to get the finial optimal alignment. The optimization result reveals that the energy saving of double directions could be small while the energy-saving slopes are steep and the middle slopes are gentle. The sensitive analysis reveals that the length of the energy-saving slop should be large if the coasting length is large. If the elevation difference of stations is large, the gradient and length of energy-saving slop adjacent lower station should be small, and the length of energy-saving slop adjacent higher station should be larger.

蜀道投资集团有限责任公司企业基金:环境敏感区生态选线研究(2020SR001)，广州地铁设计研究院股份有限公司企业项目:城市轨道交通智慧选线系统