Abstract: Reducing the deadhead time of electric bus (EB) from terminals to charging stations can effectively reduce hidden costs such as additional driver staffing and improve charging efficiency. In light of this, firstly, the deadhead time was minimized based on the cost objectives of existing research, balancing both cost and efficiency requirements. Secondly, based on the analysis of the charging time characteristics of EB under slow and fast charging modes, two charging time slot parameters were set for slow and fast charging, addressing the shortcomings of existing studies that considered only a single charging method and treating it as an unbalanced assignment problem at the meanwhile. Then, by fully considering constraints such as uncertainty in vehicle speed and the latest charging time limit for vehicles, a joint optimization study on charging facility layout and scheduling was conducted, and a multi-objective optimization model was constructed. Finally, the genetic algorithm was improved with the first come first served (FCFS) strategy and the Metropolis criterion, which was applied to a case study to validate the effectiveness of the model and algorithm. The results show that considering only the cost objective causes the drawback of excessively long deadhead time, whereas the established multi-objective model can effectively reduce the maximum deadhead time per EB and improve charging efficiency. Shortening charging time slots can reduce the costs of EB charging facility layout and scheduling. Increasing EB driving speed can effectively reduce deadhead time. In the initial stage of bus system operation, a higher weight should be given to the cost objective to address the issue of financial constraints, while in the middle and later stages, a higher weight can be given to the deadhead time objective to improve charging efficiency. Compared to a single slow/fast charging method, considering both slow and fast charging methods simultaneously yields the best overall effect.

Key words: traffic engineering; electric bus; deadhead time; charging time slot; joint optimization

摘要： 减少电动公交车(electric bus, EB)从终点站前往充电站的空驶时间，可有效降低额外司机人员配置等隐性成本，提升充电效率。鉴于此，首先，在已有研究的成本目标上最小化空驶时间，兼顾成本与效率需求；其次，基于EB慢/快速充电时间特性分析，设定慢速与快速两个充电时隙参数，在弥补已有研究仅考虑单一充电方式不足的同时将其视作不平衡指派问题；然后，充分考虑车速不确定性、车辆最晚充电时间限制等约束，对充电设施布局与调度问题进行联合优化研究，构建多目标优化模型；最后，运用先来先服务(first come first served, FCFS)策略和Metropolis准则改进遗传算法，并应用于实例检验模型与算法的有效性。结果表明：仅考虑成本目标会产生空驶时间过长的弊端，而所建多目标模型能有效降低EB的单车最大空驶时间，提升充电效率；充电时隙的缩短能降低EB充电设施布局与调度成本；EB行驶速度的提高可有效减少空驶时间；公交系统运营初期应给予成本目标较高权重以解决资金紧张问题，而中后期则可给予空驶时间目标较高权重以提高充电效率；与单一慢/快速充电方式相比，同时考虑慢/快速充电方式的总体效果最优。

关键词: 交通工程；电动公交车；空驶时间；充电时隙；联合优化