城市公交区域调度双层优化方法研究

为了实现区域公交行车计划编制优化，构建了一个以区域内乘客候车时间为上层目标、以车队规模为下层目标的双层规划模型。由于上、下层目标之间存在的互相影响关系，导致模型难以获取最优解，选择将下层目标转化为模型的约束条件从而实现对模型的简便求解。对于车队规模的取值，提出了一种基于逆差函数的车队规模搜寻算法。进一步地，为了建立车队规模的约束条件，提出了3类核算时间点，并引入逻辑变量表征发车方案的选择，通过对核算时间点所对应的逆差函数值进行约束从而保证当前的发车方案能够满足既定的车队规模要求。在车队规模取值及约束条件确定的基础上，对模型进行求解即可得到不同车队规模取值情况下所对应的换乘时间表现最佳的发车方案。为了验证模型及求解思路的可行性，以哈尔滨市部分公交线路为例进行验证。结果表明：候车时间最优方案较初始方案能减少换乘时间10.3%，车队规模最优方案能减少初始车队规模15.2%；模型计算结果相当于为公交运营企业提供了可选择方案的效果边界，公交运营方可以通过结合预期的运营目标和实际公交规模选取最佳的发车方案，从而提高实际调度水平和运营效果。

Bi-level Optimization Method for Urban Public Transport Regional Dispatching

To optimize regional bus scheduling, a bi-level model, in which the upper goal was waiting time and the lower goal was fleet size, was constructed. However, obtaining the optimal solution of the model was difficult because of the interaction between the upper and lower targets. Therefore, an algorithm was introduced that transformed the lower level target into the constraints of the model to achieve a simple solution. For the given value of fleet size, a fleet size search algorithm was proposed based on a deficit function. Furthermore, to establish the constraints of fleet size, three types of time points were put forward, and logical variables were introduced to represent the selection of departure scheme. By constraining the value of the deficit function corresponding to the accounting time point, the current departure scheme can meet the requirements of the established fleet size. On the basis of the determination of the fleet size and the constraints, the best departure scheme can be obtained by solving the model. To verify the feasibility of the model, bus lines in Harbin were taken as an example. The best transfer time scheme was found to reduce the range of waiting time by 10.3% compared with that of the initial scheme, and the best fleet size scheme was found to reduce the range of initial fleet size by 15.2%. The model calculation results provide alternatives for bus operation enterprises at the boundary of the scheme, enabling bus operators to select the best departure scheme by combining the expected operation objectives and the actual bus scale, thereby improving the actual operation level.