通过上学时间调度缓解区域交通拥堵：一种双层交替优化方法
Mitigating Regional Traffic Congestion via School Start Time Scheduling: A Bilevel Alternating Optimization Approach
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中文总结 AI 辅助
本文针对城市中学校相关集中出行引发的早高峰拥堵，提出结合宏观基本图的双层交替优化框架，通过调节上学时间缓解拥堵，明确了上学时间灵活性与交通效率的权衡关系。
中文摘要 AI 辅助
本文针对城市网络中与学校相关的集中出行导致的早高峰通勤拥堵问题展开研究。我们提出一种双层优化框架，用于调节采用宏观基本图（Macroscopic Fundamental Diagrams, MFDs）的多区域城市网络的上学时间，明确将系统级调控与基于多类别用户均衡的出发时间选择相结合。上层问题联合最小化总出行时间和与当前学校作息的偏差，下层问题通过确定性动态多类别用户均衡模型对通勤者行为进行建模，该模型纳入了针对出行时间、早到和迟到成本的α-β-γ偏好。为应对双层结构、非凸交通动态和内生需求响应带来的计算挑战，我们开发了一种在上层与下层问题之间交替的迭代算法；上层问题通过可由标准数学规划求解器求解的公式进行近似，而下层均衡问题则由迭代算法提供近似解。数值结果表明，该方法可大幅缓解拥堵，并明确了上学时间灵活性与交通效率之间的权衡关系；敏感性分析进一步考察了MFD不确定性和调度偏好的影响。
英文摘要
This paper addresses morning commute congestion caused by concentrated school-related trips in urban networks. We propose a bi-level optimization framework for regulating school start times in a multi-region urban network characterized by Macroscopic Fundamental Diagrams (MFDs), explicitly coupling system-level regulation with multi-class user-equilibrium-based departure-time choices. The Upper-Level problem jointly minimizes total time spent and deviations from current school schedules, while the Lower-Level problem models commuter behavior through a deterministic dynamic multi-class user equilibrium formulation incorporating alpha-beta-gamma preferences for travel time, earliness, and lateness costs. To address the computational challenges arising from the bilevel structure, non-convex traffic dynamics, and endogenous demand responses, an iterative algorithm alternating between the Upper- and Lower-Level problems is developed. The Upper-Level problem is approximated through a formulation solvable with standard mathematical programming solvers, while an iterative algorithm provides an approximate solution to the Lower-Level equilibrium problem. Numerical results demonstrate substantial congestion reductions and characterize the trade-off between school start-time flexibility and traffic efficiency. Sensitivity analyses further examine the effects of MFD uncertainty and scheduling preferences.
