Contextual Bayesian optimization of congestion pricing with day-to-day dynamics
Contextual Bayesian optimization of congestion pricing with day-to-day dynamics
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DOI：
10.1016/j.tra.2023.103927
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发表时间：
2024-01
期刊：
影响因子：
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通讯作者：
Renming Liu;Yu Jiang;Ravi Seshadri;M. Ben-Akiva;C. L. Azevedo
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作者：
Renming Liu;Yu Jiang;Ravi Seshadri;M. Ben-Akiva;C. L. Azevedo
拥挤收费是缓解城市交通拥挤的常用手段。次优拥挤收费方案的设计通常被表述为非线性规划和双层优化问题，其中下层问题涉及静态或动态网络均衡模型。这些双层收费优化问题的复杂性大大增加时，将日常的动态模型的旅行行为和网络拥塞的动态模型。这些模型通常使用模拟来操作，因此，收费设计问题是一个具有计算挑战性的基于模拟的优化问题，其中单个候选定价方案的评估涉及模拟日常模型直到收敛。为了规避这个问题，我们提出了一个上下文贝叶斯优化（BO）框架，BO计划是嵌入在日常的动态模型，通过使用时间上下文信息。该框架隐含地纳入了跨天的目标函数之间的关系，并使用过去几天的观察（功能评估）作为弱先验时，构建高斯过程的基础BO算法为当前一天的通行费优化问题，从而在计算效率的收益。上下文BO方法适用于设计的基于距离的定价方案的早晨通勤问题。我们数值证明，该计划收敛到系统的最优，而且，利用一个显着更少的模拟评估（减少十倍）比标准的方法，其中每个功能的评估涉及到模拟的日常模型，直到收敛。从政策的角度来看，我们发现，基于距离的计划产生显着的福利收益相对于基于区域的计划，并表明，基于距离的关税计划的设计可以显着影响分配的影响。合理设计的两部制运价结构可以部分抵消通勤距离较长的出行者相对较大的福利损失，同时保持总体福利。拟议的上下文BO方案还进行了扩展，以纳入特定于上下文的需求和供应信息，这对于政策制定者在以可计算的方式评估各种场景下的最佳收费设计方案时可能具有价值。
Congestion pricing is a common approach to alleviate urban traffic congestion. The design of second-best congestion pricing schemes is typically formulated as non-linear programming and bi-level optimization problems, where the lower-level problem involves either a static or dynamic network equilibrium model. The complexity of these bi-level toll optimization problems increases considerably when incorporating day-to-day dynamic models of travel behavior and dynamic models of network congestion. These models are often operationalized using simulation, and consequently, the toll design problem is a computationally challenging simulation-based optimization problem where the evaluation of a single candidate pricing scheme involves simulating the day-to-day model until convergence. In order to circumvent this issue, we propose a contextual Bayesian optimization (BO) framework, where the BO scheme is embedded within the day-to-day dynamic model by using temporal contextual information. The framework implicitly incorporates the relationship between the objective function across days and uses past days’ observations (function evaluations) as weak priors when constructing the Gaussian process underlying the BO algorithm for the current day’s toll optimization problem, resulting in gains in computational efficiency.The contextual BO approach is applied to the design of distance-based pricing schemes for the morning commute problem. We demonstrate numerically that the scheme converges to the system optimum, and moreover, utilizes a significantly smaller number of simulation evaluations (ten-fold reduction) than the standard approach wherein each function evaluation involves simulating the day-to-day model until convergence. From a policy perspective, we find that the distance-based schemes yield significant welfare gains relative to area-based schemes and show that the design of the distance-based tariff scheme can significantly affect distributional impacts. A suitably designed two-part tariff structure can partially offset the relatively large welfare losses of travelers with longer commute distances while maintaining overall welfare. The proposed contextual BO scheme is also extended to incorporate context specific demand and supply information, which can be of value to policy-makers when evaluating optimal toll design schemes under a wide range of scenarios in a computational tractable manner.