Budget-Constrained Rail Electrification Modeling Using Symmetric Traffic Assignment: A North American Case Study
Budget-Constrained Rail Electrification Modeling Using Symmetric Traffic Assignment: A North American Case Study
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DOI：
10.1061/(asce)is.1943-555x.0000682
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发表时间：
2021-10
影响因子：
3.3
通讯作者：
Priyadarshan N. Patil;Rydell Walthall;S. Boyles
中科院分区：
文献类型：
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作者：
Priyadarshan N. Patil;Rydell Walthall;S. Boyles
我们考虑预算受限的铁路网络电气化问题以及能源使用成本（通过路径梯度和曲率）、运营和长期维护的相关变化。特别是，我们认为这样一个网络上的货运流量形成了用户均衡。同一走廊上的电动和柴油列车之间的相互作用用不可分离的链路性能函数表示，但其具有对称的雅可比行列式。使用遗传算法 (GA) 解决北美铁路网络的双层公式，结合特定领域的见解来减少必须考虑的解决方案的数量。我们分析解决方案的特征和决策影响。结果表明，广泛的连通性将有利于大多数影响。不断增长的需求将电气化走廊转向人口较多的东部和墨西哥湾沿岸，而运营成本的增加导致穿越山区的路线电气化。简介 铁路网络在地方和国家经济结构中发挥着至关重要的作用。在日本和瑞士等许多国家，它们在客运交通方式中占有相当大的份额。铁路货运也占货运总量的很大一部分，在加拿大和俄罗斯等大型经济体中，铁路货运所占的份额超过 50%。因此，政府政策存在着一个重大机会，可以激励铁路网络的改善，以提供更大的经济、环境和社会回报。铁路网络电气化以及随之而来的从柴电机车到全电力机车的过渡，是美国迈向可持续系统和可再生燃料来源的重要步骤。关于 1 Patil，2021 年 10 月 26 日 ar X iv :2 11 0. 03 83 2v 2 [ m at h. 有很多研究。 O C ] 2 4 Oct 2 02 1 铁路电气化的影响和成本效益分析（美国交通部联邦铁路管理局 2015；美国交通部联邦铁路管理局 2019）。电力机车的优点包括较低的长期能源和机车维护成本、较低的噪音和空气污染水平、更快的加速以及主电源的灵活性更大，从而减少燃料价格波动的波动。这些好处必须与基础设施升级的大量前期投资、更高的基础设施维护成本、架空建筑的脆弱性、私营铁路公司更高的财产税义务以及投资的普遍不确定性相平衡（Walthall 2019）。我们考虑铁路网络设计问题（RNDP），其中部分货运铁路网络可以实现电气化，主要受预算限制。 RNDP 被表述为双层问题：上层问题决定电气化链路的最佳子集，下层问题计算链路流量以及相关的网络指标。我们的上层制定以最小化私人成本为目标，为提高净社会效益奠定基础，并反映补贴应该投向何处。鉴于有许多铁路运营商，托运人可以选择使用哪个运营商（不一定与净社会效益一致），我们将较低级别的问题建模为用户均衡交通分配问题（TAP）。遗传算法（GA）解决了寻找最佳电气化链路的更高层次的问题。在这种情况下，功利主义模式不是将电气化预算独立分配给每个铁路运营商，而是为特定线路的电气化分配电气化预算，以最大程度地降低整个网络的成本。然后，铁路运营商和托运人通过改变其调度和流动模式来应对这些变化，以最大限度地降低其个人成本。考虑到多个运营商，较低级别的问题是“自私”地引导流量的设置，以最大限度地降低运输成本。对于较低水平的问题，我们假设这些活动会导致均衡，即运输成本不能单方面降低。由于装运流量以吨为单位，作为长期连续的数量，该问题满足流量分配用户均衡假设。鉴于很少有自我优化的车队所有者，我们有一个纳什-古诺均衡，这在极限情况下导致用户均衡流量模式。 Van Vuren 和 Watling (1991) 表明，两个机队的纳什古诺均衡导致平均差异小于 5%。大型网络的旅行时间（以及扩展的总系统旅行时间）。随着机队数量的增加，这种差异会减小并接近于零。因此，我们在研究中使用用户均衡假设。这一假设与该主题的先前文献一致（Uddin 和 Huynh 2015；Wang 等人 2018）。贡献和概述 NDP 在道路网络中得到了广泛的研究。铁路新发展计划有两个重要方面的差异。首先，大部分货运铁路网都是用户私有或外包使用，这导致了非社会最优的使用限制。当未考虑外部效益时，铁路电气化具有高度不确定性，甚至可能为负回报率 2 Patil, October 26, 2021。本文为未来分析美国的政策干预提供了一个框架，以将拥有铁路并负责实施电气化的私营公司的利益内部化。其次，单个网络连接的特征（轨道曲率和坡度）对维护和运营成本的影响比道路网络更大。考虑到这些区别，本文的主要贡献如下： • 我们将铁路电气化 NDP 表述为包含电气化成本的双层优化问题。燃料、机车和运营成本；列车阻力（轴承、法兰、空气、坡度、曲线、制动和惯性）成本。 • 我们为算法 B 推导了适当的流量转移公式，用于解决我们的公式（具有对称链路交互的流量分配），并表明它满足收敛所需的最优条件。 • 我们使用基于特定问题见解的通用元启发式算法（遗传算法）来生成高质量的解决方案，并在大型北美铁路网络上解决此问题。 • 我们进行敏感性分析并分析由此产生的解决方案，以得出见解和政策结论。本文的其余部分组织如下。我们首先提供铁路电气化的背景信息，并讨论交通分配、NDP 和这两个问题的解决方法方面的进展。然后，我们描述铁路电气化 NDP 的公式和相关模型组件。然后，我们描述了我们使用的北美铁路网络数据集和需求数据，并概述了我们的实验设计。接下来我们总结了我们的实验结果并得出了实际的见解。最后，我们总结了我们的发现并提出了未来工作的途径。
We consider a budget constrained rail network electrification problem with associated changes in costs of energy usage (via path gradient and curvature), operations, and longterm maintenance. In particular, we consider that freight flows on such a network form a user equilibrium. Interactions between electric and diesel trains on the same corridor are represented with nonseparable link performance functions, which nevertheless have a symmetric Jacobian. This bi-level formulation is solved for the North American railroad network using a genetic algorithm (GA), incorporating domain-specific insights to reduce the number of solutions which must be considered. We analyze solution characteristics and decision-making implications. Results show that broad connectivity would be beneficial for most impact. Increasing demand shifts electrified corridors towards the more populous east and gulf coasts, while increased operational costs results in electrification of routes through mountainous terrains. INTRODUCTION Rail networks play a vital role in local and national economic structures. In many countries such as Japan and Switzerland, they constitute a significant share of passenger transport mode share. Rail freight transit also accounts for a large portion of total freight transit, exceeding 50% modal share in large economies like Canada and Russia. Therefore, a significant opportunity exists for government policies incentivizing rail network improvements to provide for larger economic, environmental and social returns. Rail network electrification, and the accompanying transition from diesel-electric to fully electric locomotives, are important steps towards sustainable systems and renewable fuel sources for the United States of America. There are many studies on 1 Patil, October 26, 2021 ar X iv :2 11 0. 03 83 2v 2 [ m at h. O C ] 2 4 O ct 2 02 1 the impact and cost-benefit analysis of rail electrification (United States Department of Transportation Federal Railroad Administration 2015; U.S. Department of Transportation Federal Railroad Administration 2019). Advantages of electric locomotion include lower long-term energy and locomotive maintenance costs, lower noise and air pollution levels, faster acceleration, and more flexibility in the primary power source, leading to less volatility from fuel price fluctuations. These benefits must be balanced with significant upfront investment for infrastructure upgrades, higher infrastructure maintenance costs, vulnerability of overhead architecture, higher property tax obligations for private rail companies, and the general uncertainty in the investment (Walthall 2019). We consider a rail network design problem (RNDP) where parts of a freight rail network can be electrified, subject primarily to budget constraints. The RNDP is formulated as a bi-level problem: the upper level problem deciding optimal subset of links for electrification, and the lower level problem calculating link flows as well as associated network metrics. Our upper-level formulation uses the objective of minimizing private costs, laying a foundation that can be adapted to improve net social benefit and reflect where subsidies ought to be directed. Given that there are many rail operators, and shippers can choose which operator to use (not necessarily aligning with net social benefit), we model the lower level problem as a user-equilibrium traffic assignment problem (TAP). Genetic algorithms (GA) solve the higher level problem of finding the optimal links to electrify. In this setting, rather than apportioning an electrification budget to each rail operator independently, a utilitarian schema allocates the electrification budget for specific link electrification in order to bring about the greatest possible cost reductions across the network. The rail operators and shippers then respond to these changes by altering their scheduling and flow patterns to minimize their individual costs. Given multiple operators, the lower level problem is a setting where flow is directed “selfishly,” to minimize shipment costs. For the lower level problem, we assume that these activities lead to an equilibrium, where the costs of shipment flows cannot be lowered unilaterally. With shipment flow expressed in tons, as a continuous quantity over the long term, this problem satisfies the traffic assignment user equilibrium assumptions. Given few selfoptimizing fleet owners, we have a Nash-Cournot equilibrium, which in the limit results in user equilibrium flow pattern. Van Vuren and Watling (1991) show that a NashCournot equilibrium for two fleets results in less than 5% difference in avg. travel times (and by extension, total system travel time) for large networks. As the number of fleets increase, this difference decreases and approaches zero. Therefore, we use the user equilibrium assumption in our study. This assumption is consistent with prior literature on the topic (Uddin and Huynh 2015; Wang et al. 2018). Contributions and overview NDPs are widely studied in road networks. Rail NDPs vary in two significant ways. First, most of the freight rail network is privately owned by the user or contracted out for usage, which leads to non-socially-optimal usage restrictions. Rail electrification has highly uncertain, and possibly negative, rates of return when external benefits are 2 Patil, October 26, 2021 not accounted for. This paper provides a framework for future analysis of policy interventions in the US to internalize the benefits to the private companies that own the rails and would be responsible for implementing electrification. Second, the characteristics of individual network links (track curvature and gradient) affect maintenance and operating costs more so than in road networks. With these distinctions in mind, the main contributions of this article are as follows: • We formulate the rail electrification NDP as a bi-level optimization problem incorporating electrification costs; fuel, locomotive, and operational costs; and train resistance (bearing, flange, air, grade, curve, braking, and inertia) costs. • We derive the appropriate flow shift formula for Algorithm B for solving our formulation (traffic assignment with symmetric link interactions) and show that it meets the optimality conditions required for convergence • Weuse a general-purposemetaheuristic (a genetic algorithm) based on problemspecific insights to generate high-quality solutions, and solve this problem on a large-scale North American rail network. • We conduct sensitivity analysis and analyze the resulting solutions to draw insights and policy conclusions. The rest of this article is organized as follows. We first provide background information on rail electrification and discuss advances in traffic assignment, NDPs, and solution methods for both problems. We then describe the formulation for the rail electrification NDP and associated model components. We then describe the North American rail network dataset and demand data we use, and outline our experiment design. We follow this with a summary of the results from our experiments and draw practical insights. We conclude by summarizing our findings and suggest avenues for future work.