The emerging modular autonomous vehicle (MAV) provides new opportunities to address the imbalance between supply and demand in the public transportation system. The continuous approximation (CA) model can efficiently solve the optimal time-varying headway of bus corridors, but the current CA model for MAV corridors does not consider the demand uncertainty, and its vehicle formation method still has limitations. To solve these gaps, this paper proposes collaborative optimization of vehicle formation and timetable for modular autonomous bus considering demand uncertainty based on a data-driven continuous approximate method. First, a time-dependent passenger flow disturbance parameter is introduced to capture the uncertainty demand, and the CA model is extended under demand uncertainty. Second, data-driven stochastic optimization methods (i.e., stochastic programming and distributed robust optimization) are developed to address the loss function term with the random passenger flow in the CA model. Then, based on the proposed CA model, a mixed integer linear programming (MILP) model is developed to obtain the optimal vehicle formation. Finally, two numerical experiments were conducted to verify the effectiveness and superiority of the proposed model. Results show that, (1) the proposed vehicle formation model achieves up to a 9.8% reduction in average total system cost compared to the benchmark model. (2) stochastic programming and distributed robust optimization do not significantly reduce the average system total cost when demand is uncertain, but can significantly improve the robustness of timetables and vehicle formation. Compared to the deterministic model, the proposed method achieves a reduction of over 90% in both the sample standard deviation and the interquartile range on the test dataset. In summary, the proposed method can provide theoretical support for modular bus operation and scheduling under passenger flow uncertainty.

中文翻译：

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考虑需求不确定性的模块化自动驾驶公交车编队与时间表协同优化——一种数据驱动的连续近似方法

新兴的模块化自动驾驶汽车 （MAV） 为解决公共交通系统中的供需失衡问题提供了新的机会。连续逼近 （CA） 模型可以有效地求解公交走廊的最优时变车距，但目前的 MAV 走廊 CA 模型没有考虑需求不确定性，其车辆编队方法仍然存在局限性。为了解决这些差距，本文提出了基于数据驱动的连续近似方法，对考虑需求不确定性的模块化自动驾驶公交车的车辆编队和时间表进行协同优化。首先，引入随时间变化的客流扰动参数来捕获不确定性需求，并在需求不确定性下扩展 CA 模型。其次，开发了数据驱动的随机优化方法（即随机规划和分布式鲁棒优化）来解决 CA 模型中随机客流的损失函数项。然后，基于所提出的 CA 模型，开发了混合整数线性规划 （MILP） 模型以获得最优车辆编队。最后，进行了两次数值实验，验证了所提模型的有效性和优越性。结果表明，（1） 与基准模型相比，所提出的车辆编队模型的平均总系统成本降低了 9.8%。（2） 当需求不确定时，随机规划和分布式鲁棒优化不会显著降低平均系统总成本，但可以显著提高时间表和车辆编队的鲁棒性。 与确定性模型相比，所提出的方法在测试数据集上的样本标准差和四分位数范围上都减少了 90% 以上。综上所述，所提方法可以为客流不确定性下的模块化公交运行和调度提供理论支持。