Optimal multi-step toll design under general user heterogeneity

Chen Hongyu; Nie Yu (Marco); Yin Yafeng

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Optimal multi-step toll design under general user heterogeneity

机译：一般用户异质性下的最优多步骤收费设计

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This paper studies the optimal multi-step toll design problem for the bottleneck model with general user heterogeneity. The design model is formulated as a mathematical program with equilibrium constraints (MPEC), which is NP-hard due to non-convexity in both the objective function and the feasible set. An analytical method is proposed to solve the MPEC by decomposing it into smaller and easier quadratic programs, each corresponding to a unique departure order of different user classes. The quadratic programs are defined on a polyhedral set, which makes it easier to identify a local optimum. Importantly, each quadratic program is constrained by a set of linear feasibility cuts that define the presence of each user class in the arrival window. We prove that the proposed method ensures global optimality provided that each quadratic program can be solved globally. To obviate enumerating all departure orders, a heuristic method is developed to navigate through the solution space by using the multipliers associated with the feasibility cuts. Numerical experiments are conducted on several small examples to validate the proposed methodology. These experiments show that the proposed heuristic method is effective in finding near-optimal solutions within a relatively small number of iterations. (C) 2015 Elsevier Ltd. All rights reserved.

机译：该文研究了具有一般用户异质性的瓶颈模型的最优多步收费设计问题。该设计模型被表述为具有平衡约束（MPEC）的数学程序，由于目标函数和可行集的非凸性，该平衡约束是NP难的。该文提出一种解析方法，将MPEC分解为更小、更简单的二次程序，每个程序对应于不同用户类别的唯一离去顺序。二次规划是在多面体集上定义的，这使得识别局部最优值变得更加容易。重要的是，每个二次程序都受到一组线性可行性削减的约束，这些可行性削减定义了到达窗口中每个用户类的存在。我们证明了所提出的方法确保了全局最优性，前提是每个二次程都可以全局求解。为了避免枚举所有离境订单，开发了一种启发式方法，通过使用与可行性削减相关的乘数来浏览解决方案空间。在几个小实例上进行了数值实验，以验证所提出的方法。这些实验表明，所提出的启发式方法可以有效地在相对较少的迭代次数内找到接近最优的解。（C） 2015 爱思唯尔有限公司保留所有权利。

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来源
《Transportation research, Part B. Methodological》 |2015年第3期|775-793|共19页
作者
Chen Hongyu; Nie Yu (Marco); Yin Yafeng;
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作者单位

Northwestern Univ, Dept Civil & Environm Engn, Evanston, IL 60208 USA;

Univ Florida, Dept Civil & Coastal Engn, Gainesville, FL 32611 USA;

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原文格式 PDF
正文语种英语
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关键词
Step toll; General user heterogeneity; Mathematical program with equilibrium constraint; Quadratic program; Bottleneck model;

机译：步数收费;一般用户异构性;具有平衡约束的数学程序;二次程序;瓶颈模型;

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Optimal multi-step toll design under general user heterogeneity

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