Budget-constrained rail network electrification problem

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 (MLIT Ministry of Land, Infrastructure, Transport and Tourism 2018; Statistics Bureau,Ministry of InternalAffairs andCommunications 2018; Federal Statistical Office Section Mobility 2019). Rail freight transit also accounts for a large portion of total freight transit, exceeding 50% modal share in large economies like Canada and Russia (Organisation for Economic Co-operation and Development 2013; Business Standard 2019; Eurostat 2020). Therefore, a significant opportunity exists for government policies incentivizing rail network improvements to provide for larger economic, environmental and social returns. 1 Patil, October 11, 2021 ar X iv :2 11 0. 03 83 2v 1 [ m at h. O C ] 8 O ct 2 02 1 Rail network electrification, and the accompanying transition from diesel-electric to fully electric locomotives, are important steps towards sustainable systems and renewable fuel sources. There are many studies on 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. For readers unfamiliar with the bi-level optimization problem known as a network design problem (NDP), the literature review provides background reading. The RNDP we formulate aims to find the optimal subset of rail links for infrastructure upgrade with a given objective. In this paper, the 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 that 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 (GAs) 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. This assumption is consistent with prior literature on the topic (Uddin and Huynh 2015; Wang et al. 2018). Rail electrification and policy planning The oil crisis of the 1970’s spurred research into the economics of rail electrification. In 1977, Schwarm (1977) examined the detailed costs associatedwith rail electrification infrastructure. Schwarm found three primary categories: power delivery, public works compatibility, and signaling systems compatibility. The power delivery category itself can be divided into the contact systems and the traction substations, the latter helping to determine each link’s electrified capacity. Nearly ten years later, Kneschke (1986) 2 Patil, October 11, 2021 detailed the design requirements of the traction substations, which affect the electrified lines’ capacities. In the midst of these studies looking at the costs of electrification, and the trade-offs with regards to capacity, other researchers began looking at electrification’s benefits. Whitford (1981) examined the energy savings from electrifying the high-density portions of the rail network, and Ditmeyer et al. (1985) would incorporate ancillary benefits and costs, such as those accruing to maintenance, reliability, and fuel handling. At the time, emissions were not a major concern. Additionally, computational costs and the relative youth of network optimization techniques meant that these analyses primarily used traffic density as a heuristic for link selection. As computational resources and optimization algorithms progressed, the oil crisis abated and deregulation led to a decrease in rail network mileage. Interest in freight rail electrification only returned relatively recently. In 2012, Cambridge Systematics (2012) conducted an extensive study on electrification for the Southern California Association of Governments. RailTEC (2016) conducted a similar study for the California Air Resource Board in 2016. Both studies were primarily motivated by reducing rail emissions, particularly in dense urban areas. The latter study highlighted the problem of network connectivity: because rail freight routes are particularly long, and the costs of switching from electric to diesel-electric locomotives en route are high (in terms of delay and logistical costs of ensuring locomotives are available), confining electrification to relatively small regions is not an efficient way to limit emissions. Outside of regulatory constraints or internalized emissions costs, rail companies would likely send large numbers of diesel-electric trains through electrified portions of the rail network in order to limit overall route costs. We thus face an optimization problem impacted by policy: how should the initial links be selected for electrification, given budget constraints and a desire to reduce emissions from the rail network? While there is not an extensive literature applying the traffic assignment problem to rail electrification, there are studies to draw on for link improvement under a budget constraint, such as Mishra et al. (2016), which applied numerical methods towards “[making] optimal investment decisions. in moderate and large transportation networks. ” Mishra utilized travel costs to road users, primarily consisting of temporal costs. Applying a similar framework to a rail network considers similar costs, although fuel costs for rail constitute a relatively larger portion, and time costs a relatively smaller one. 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 not accounted for. This paper provides a framework for future analysis of policy interventions 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) affectmaintenance and operating costs more so than in road networks. 3 Patil, October 11, 2021 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 present a heuristic for solving our formulation, using a general-purpose metaheuristic (a genetic algorithm) based on problem-specific insights. • We solve this problemon a large-scale network representing theNorthAmerican rail system, and analyze the resulting solutions to draw insights and policy conclusions. The rest of this article is organized as follows. We first describe the formulation for the rail electrification NDP and associated model components. We then provide background information and reading on NDPs and solution methods. 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 resul