考虑乘客时间成本的城市公交发车间隔优化模型

Optimization model for urban bus departure intervals considering passenger time costs

针对城市公交发车间隔优化时对公交运行过程描述不够全面、未充分考虑乘客时间成本的问题,提出了考虑乘客时间成本的城市公交发车间隔优化模型.首先,在详细分析能够体现公交车辆运行特征的不同时段与站间的运行速度、站点停站时间、上车人数、下车人数、滞留人数以及新增候车人数等变量或参数基础上,建立车辆运行约束和乘客人数约束,将包含等候时间和在车时间的乘客平均出行时间作为出行成本、车辆平均满载率作为公交企业载客成本,以乘客出行成本与公交企业载客成本之和最小为目标建立发车间隔优化模型.然后,使用软件Pycharm中scikit-opt代码库调用遗传算法求解模型.最后,以北京市848路公交上行线路早高峰8:00—9:00时段为例,求解其理论最优发车间隔,结合运营实际确定实际最优发车间隔及总成本.研究结果表明:考虑乘客时间成本后的发车间隔较实际发车间隔,乘客平均出行成本降低9.09%,公交企业载客成本上涨0.57%,乘客与企业总成本下降约3.01%,提出的模型可行有效.

To address the problem of incomplete descriptions of the urban bus operation process and insufficient consideration of passenger time costs during the optimization of urban bus departure inter-vals,optimization model for urban bus departure intervals considering passenger time costs is pro-posed.This study first establishes constraints for bus operation and passenger numbers.These con-straints are based on a detailed analysis of variables and parameters that reflect the characteristics of bus operations at different times and between stations.These variables include travel speeds,station dwell times,passenger boarding and alighting counts,the number of new waiting passengers,and new waiting passenger counts.The paper incorporates the average passenger travel time,which ac-counts for both waiting and on-board time,as the travel cost and the average vehicle load rate as the passenger cost for the bus company.The objective is to minimize the sum of passenger travel costs and bus company passenger unit costs,resulting in an optimization model for urban bus departure inter-vals.Next,the paper employs the scikit-opt library in software Pycharm to implement a genetic algo-rithm for solving this model.Subsequently,the theoretical optimal urban bus departure intervals is illustrated for the Beijing Route 848 during the morning peak hours of 8:00—9:00 as an example.This is followed by determining the practical optimal urban bus departure intervals,which takes actual op erational considerations into account,along with the corresponding total cost.The results show that,compared to the actual departure intervals,optimizing urban bus departure intervals leads to a 9.09%reduction in the average travel costs for passengers,a 0.57%increase in passenger unit costs for the bus company,and an overall 3.01%decrease in combined costs for passengers and enterprises.These findings highlight the feasibility and effectiveness of the proposed model.