Abstract: This paper investigates the optimization of dynamic formation plan for bus unit road operation based on modular public transport system. A two-stage joint optimization model for the direction assignment and formation permutation of platoon was proposed. In the first stage, an integer linear programming model was developed with the objective of minimizing the number of passengers in-motion transfer. The model enables the direction assignment of bus units and the calculation of replenishment bus units. Based on this, a second-stage bi-objective optimization mixed integer nonlinear programming model was constructed, with the objectives of minimizing formation permutation time and in-motion transfer time, to optimize the efficiency of dynamic formation of bus units. Furthermore, the algorithms was designed to solve the proposed models. The CPLEX solver was used to solve the first-stage direction assignment model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm was used to solve the second-stage formation permutation model. At last, the study verified the effectiveness of the proposed model and its solution algorithms. It also included an analysis of the optimization of bus unit formation efficiency and change in bus occupancy rate in a modular public transport system under different passenger demands and bus unit capacities. The results indicate that within a certain increase in modular bus unit capacity, the formation efficiency of modular bus units improves with the increase in bus unit capacity. When the increase in bus unit capacity is too big, the dynamic formation efficiency cannot be improved effectively, and the bus occupancy rate will be reduced, which would lead to overcapacity of modular bus platoon.

Key words: urban traffic, modular bus unit formation, two-stage joint optimization model, modular bus unit, NSGA-II; in-motion transfer

摘要： 为研究基于模块化公交系统的车辆单元路段运行动态编组方案优化问题，首先，构建车辆单元方向分配与位置调整的两阶段联合优化模型。第1阶段，构建以乘客换乘次数最少为目标的整数线性规划模型，实现车辆单元最佳方向分配与增补车辆单元数计算；第2阶段，构建以位置调整时间最小和车内换乘时间最小的双目标混合整数非线性规划模型，实现车辆单元动态编组方案优化。其次，构建模型的求解算法，利用CPLEX求解器求解第1阶段车辆单元分配模型，设计非支配排序遗传算法(NSGA-II)求解第2阶段车辆编队位置调整模型。最后，算例验证构建模型及求解算法的有效性，并定量探究不同车辆单元容量下的车辆单元动态编组效率与公交载客率变化。算例结果表明：在模块化公交车辆单元容量一定增幅内，模块化公交车辆单元动态编组效率会随着车辆单元容量的增加而提高；而车辆单元容量增幅太大，不仅不会提高动态编组效率，反而会降低车辆编队的载客率，造成模块化公交车辆编队运力过剩。

关键词: 城市交通, 动态编组方案优化, 两阶段联合优化模型, 模块化公交车辆单元, NSGA-II, 车内换乘