考虑行程时间波动的电动公交可变行车计划

为解决因运行时间不确定性导致的公交到发时间不准点问题，本文基于公交线路双方向发车趟次和运营时间的不对称特征，提出一种可变行车计划优化问题。以最小化车辆使用数和乘客等待时间为目标，考虑车次链的行程接续和电动公交车辆电量等约束，构建公交时刻表和车辆排班一体化优化模型。根据可变行车计划优化问题特性设计改进的粒子群算法(Modified Particle Swarm Optimization for Timetabling and Scheduling, MPSO-TS)进行求解，定制粒子编码和子代更新方式。采用“基于优势车次链”的子代更新机制，以“车次链”为纽带最大程度地保留父代被继承信息中时刻表与车辆调度方案之间的关联性。使用连云港市某公交线路验证模型和算法，案例结果表明：可变行车计划能够有效保证车辆到发准点性，通过更紧密的排班计划将使用车数由35辆减少至31辆，车辆使用效率提升了28.1%；所提出的MPSO-TS算法求解效率较高，具有较好的稳定性，可有效避免计算结果陷入“局部最优”。

Optimization of Variable Electric Bus Schedule Considering Volatility in Trip Travel Time

A variable bus schedule optimization model based on asymmetric characteristics in two directions, including the number of frequencies and operating time, was proposed to cope with the inaccurate timetable caused by random fluctuations in trip travel time. The model combined bus timetabling and vehicle scheduling under the constraints of trip connectivity and battery state of charge to minimize the number of vehicles and passengers' waiting time. A modified particle swarm optimization algorithm, called modified particle swarm optimization for timetabling and scheduling (MPSO-TS), was tailored to tackle the integrated optimization problem of bus timetabling and vehicle scheduling. Besides, a customized particle encoding and offspring update method was provided. The offspring update method was built on the "dominant vehicle chain", wherein the "vehicle chain" can help to inherit the relevance between the timetable and vehicle scheduling from the parent generation. A bus line in Lianyungang, China, was taken to verify the proposed model and algorithm. The results show that the proposed method can ensure the punctuality of timetable. Moreover, the proposed method generates a tighter vehicle schedule and reduces the number of vehicles used from 35 to 31. The vehicles' utilization is effectively increased by 28.1%. The proposed MPSO-TS has a high level of efficiency and stability, as well as a powerful capacity to avoid from being trapped in the local optimum.