基于过饱和条件的市域铁路与地铁运行图协同优化

Collaborative optimization of suburban railway and metro timetables based on oversaturation condition

随着城镇一体化的快速发展,通勤客流需求逐渐增大,市域铁路与地铁的衔接为通勤旅客的出行提供了便利,但大量的通勤客流给市域铁路与地铁衔接的换乘站带来了巨大的压力。为了满足市域客流和地铁客流的出行需求,同时降低通勤旅客在换乘站的等待时间,缓解换乘站的客流压力,需要进行市域铁路与地铁列车运行图的协同优化。引入动态、过饱和OD客流概念,在过饱和条件下,考虑非均匀车头时距、灵活停站时间和旅客换乘条件等约束,从滞留旅客数量和换乘等待时间2个方面构建双目标非线性整数规划模型。结合模型特点,采用ε-约束法将其转化为单目标优化模型,设计具有双阈值和记忆功能的改进模拟退火算法。为验证所提方法的可行性和有效性,将模型及算法应用于金山铁路与上海地铁3号线上海南—中山公园进行案例研究。计算结果表明:优化后的市域铁路与地铁列车运行图,滞留旅客总数增加了9.28%,协同列车数增加了50%,旅客换乘总等待时间降低了60.79%,不断更新容忍度ε能够得到一组综合考虑旅客服务水平和换乘效率的近似Pareto方案,改进的模拟退火算法相较于传统模拟退火算法具有更好的收敛效果和求解效率。研究结果为市域铁路与地铁运行图的协同优化,进一步提升通勤客流的换乘效率提供了理论参考。

The demand for commuter flow has become a major concern due to the rapid development of urban integration.The connection between suburban railway and metro provides convenience for commuters.However,a large number of commuters bring great pressure to the transfer stations where suburban railway and metro are connected.In order to meet the travel demand of both suburban railway and metro passenger flows,reduce waiting time for the commuters at transfer stations and alleviate the passenger flow pressure at transfer stations,it is necessary to conduct collaborative optimization of timetables for suburban railway and metro train.By introducing the concept of dynamic and oversaturated origin-destination(OD)passenger flow and considering constraints under oversaturation condition such as non-uniform headway,flexible stopping time,and passenger transfer conditions,a dual-objective nonlinear integer programming model was constructed in terms of the number of detained passengers and transfer waiting time.By taking the characteristics of the model into account,the model was transformed into a single-objective optimization model using theε-constraint method,and an improved simulated annealing algorithm with dual thresholds and memory function was designed.To verify feasibility and effectiveness of the proposed method,the model and algorithm were applied to a case study on the Jinshan Railway and the Shanghai South-Zhongshan Park segment of Shanghai Metro Line 3.The results demonstrate that the timetables for suburban railway and metro trains after optimization can increase by 9.28%in total number of detained passengers,increase by 50%in collaborative train numbers,and reduce by 60.79%in total waiting time for passenger transfer.Continuous updating of the tolerance levelεcan obtain a set of approximate Pareto solutions that take the level of passenger service and the transferring efficiency into account simultaneously.The improved simulated annealing algorithm has a better convergence effect and solution efficiency as compared to the traditional one.The results could provide theoretical guidance for the collaborative optimization of suburban railway and metro timetables and further improvement for transfer efficiency of commuting passenger flow.