Routing and charging locations for electric vehicles for intercity trips

This study addresses two problems in the context of battery electric vehicles (EVs) for intercity trips: the EV routing problem and the EV optimal charging station location problem (CSLP). The paper shows that EV routing on the shortest path subject to range feasibility for one origin–destination (O–D) pair, called the shortest walk problem (SWP), as well as a stronger version of the problem – the p-stop limited SWP – can be reduced to solving the shortest path problem on an auxiliary network. The paper then addresses optimal CSLPs in which EVs are range feasible with and without p-stops. We formulate the models as mixed-integer multi-commodity flow problems on the same auxiliary network without path and relay pattern enumeration. Benders decomposition is used to propose an exact solution approach. Numerical experiments are conducted using the Indiana state network.     

Computing 4D near-optimal trajectories for dynamic air traffic flow management with column generation and branch-and-price

Abstract

The current air traffic system faces recurrent saturation problems. Numerous studies are dedicated to this issue, including the present research on a new dynamic regulation filter holding frequent trajectory optimisations in a real-time sliding horizon loop process. We consider a trajectory optimisation problem arising in this context, where a feasible four-dimensional (4D) trajectory is to be built and assigned to each regulated flight to suppress sector overloads while minimising the cost of the chosen policy. We model this problem with a mixed integer linear programme and solve it with a branch-and-price approach. The pricing sub-problem looks for feasible trajectories in a dynamic three-dimensional (3D) network and is solved with a specific algorithm based on shortest path labelling algorithms and on dynamic programming. Each algorithm is tested on real-world data corresponding to a complete traffic day in the European air traffic system; experimental results, including computing times measurement, validate the solution process.     

The design of single allocation incomplete hub networks

The hub location problem deals with finding the location of hub facilities and allocating the demand nodes to these hub facilities so as to effectively route the demand between any origin–destination pair. In the extensive literature on this challenging network design problem, it has widely been assumed that the subgraph induced by the hub nodes is complete. Relaxation of this basic assumption constitutes the starting point of the present work. In this study, we provide a uniform modeling treatment to all the single allocation variants of the existing hub location problems, under the incomplete hub network design. No network structure other than connectivity is imposed on the induced hub network. Within this context, the single allocation incomplete p-hub median, the incomplete hub location with fixed costs, the incomplete hub covering, and the incomplete p-hub center network design problems are defined, and efficient mathematical formulations for these problems with O(n³) variables are introduced. Computational analyses with these formulations are presented on the various instances of the CAB data set and on the Turkish network.     

A discrete-convex programming approach to the simultaneous optimization of land use and transportation

Three design problems are discussed in this article. First, it is shown that the network design problem with congestion reduces to an all-or nothing traffic assignment problem under some assumptions on the congestion function and the investment cost function. Second, the land use design problem is formulated as an extension of the Koopmans-Beckmann problem and a heuristic is proposed to solve this problem. Third, it is shown that the seemingly more complex problem of designing jointly a land-use plan and a transportation network reduces to a pure land-use design problem. All that is needed to solve the joint optimization problem is a shortest path algorithm and a heuristic to solve the land use design problem. Computational experience is reported for each algorithm.     

Preferences for travel time under risk and ambiguity: Implications in path selection and network equilibrium

In this paper, we study the preferences for uncertain travel times in which probability distributions may not be fully characterized. In evaluating an uncertain travel time, we explicitly distinguish between risk, where the probability distribution is precisely known, and ambiguity, where it is not. In particular, we propose a new criterion called ambiguity-aware CARA travel time (ACT) for evaluating uncertain travel times under various attitudes of risk and ambiguity, which is a preference based on blending the Hurwicz criterion and Constant Absolute Risk Aversion (CARA). More importantly, we show that when the uncertain link travel times are independently distributed, finding the path that minimizes travel time under the ACT criterion is essentially a shortest path problem. We also study the implications on Network Equilibrium (NE) model where travelers on the traffic network are characterized by their knowledge of the network uncertainty as well as their risk and ambiguity attitudes under the ACT. We derive and analyze the existence and uniqueness of solutions under NE. Finally, we obtain the Price of Anarchy that characterizes the inefficiency of this new equilibrium. The computational study suggests that as uncertainty increases, the influence of selfishness on inefficiency diminishes.     

The electric vehicle touring problem

The increasing concern over global warming has led to the rapid development of the electric vehicle industry. Electric vehicles (EVs) have the potential to reduce the greenhouse effect and facilitate more efficient use of energy resources. In this paper, we study several EV route planning problems that take into consideration possible battery charging or swapping operations. Given a road network, the objective is to determine the shortest (travel time) route that a vehicle with a given battery capacity can take to travel between a pair of vertices or to visit a set of vertices with several stops, if necessary, at battery switch stations. We present polynomial time algorithms for the EV shortest travel time path problem and the fixed tour EV touring problem, where the fixed tour problem requires visiting a set of vertices in a given order. Based on the result, we also propose constant factor approximation algorithms for the EV touring problem, which is a generalization of the traveling salesman problem.     

Finding the k reliable shortest paths under travel time uncertainty

This paper investigates the problem of finding the K reliable shortest paths (KRSP) in stochastic networks under travel time uncertainty. The KRSP problem extends the classical K loopless shortest paths problem to the stochastic networks by explicitly considering travel time reliability. In this study, a deviation path approach is established for finding K α-reliable paths in stochastic networks. A deviation path algorithm is proposed to exactly solve the KRSP problem in large-scale networks. The A^* technique is introduced to further improve the KRSP finding performance. A case study using real traffic information is performed to validate the proposed algorithm. The results indicate that the proposed algorithm can determine KRSP under various travel time reliability values within reasonable computational times. The introduced A^* technique can significantly improve KRSP finding performance.     

Solving the bicriterion routing and scheduling problem for hazardous materials distribution

Hazardous materials routing and scheduling decisions involve the determination of the minimum cost and/or risk routes for servicing the demand of a given set of customers. This paper addresses the bicriterion routing and scheduling problem arising in hazardous materials distribution planning. Under the assumption that the cost and risk attributes of each arc of the underlying transportation network are time-dependent, the proposed routing and scheduling problem pertains to the determination of the non-dominated time-dependent paths for servicing a given and fixed sequence of customers (intermediate stops) within specified time windows. Due to the heavy computational burden for solving this bicriterion problem, an alternative algorithm is proposed that determines the k-shortest time-dependent paths. Moreover an algorithm is provided for solving the bicriterion problem. The proximity of the solutions of the k-shortest time-dependent path problem with the non-dominated solutions is assessed on a set of problems developed by the authors.     

Application of the support vector machine and heuristic k-shortest path algorithm to determine the most eco-friendly path with a travel time constraint

This study aims to determine an eco-friendly path that results in minimum CO₂ emissions while satisfying a specified budget for travel time. First, an aggregated CO₂ emission model for light-duty cars is developed in a link-based level using a support vector machine. Second, a heuristic k-shortest path algorithm is proposed to solve the constrained shortest path problem. Finally, the CO₂ emission model and the proposed eco-routing model are validated in a real-world network. Specifically, the benefit of the trade-off between CO₂ emission reduction and the travel time budget is discussed by carrying out sensitivity analysis on a network-wide scale. A greater spare time budget may enable the eco-routing to search for the most eco-friendly path with higher probability. Compared to the original routes selected by travelers, the eco-friendly routes can save an average of 11% of CO₂ emissions for the trip OD pairs with a straight distance between 6 km and 9 km when the travel time budget is set to 10% above the least travel time. The CO₂ emission can also be reduced to some degree for other OD pairs by using eco-routing. Furthermore, the impact of market penetration of eco-routing users is quantified on the potential benefit for the environment and travel-time saving.     

Distributed computing approaches for large‐scale probit‐based stochastic user equilibrium problems

Applications of probit‐based stochastic user equilibrium (SUE) principle on large‐scale networks have been largely limited because of the overwhelming computational burden in solving its stochastic network loading problem. A two‐stage Monte Carlo simulation method is recognized to have satisfactory accuracy level when solving this stochastic network loading. This paper thus works on the acceleration of the Monte Carlo simulation method via using distributed computing system. Three distributed computing approaches are then adopted on the workload partition of the Monte Carlo simulation method. Wherein, the first approach allocates each processor in the distributed computing system to solve each trial of the simulation in parallel and in turns, and the second approach assigns all the processors to solve the shortest‐path problems in one trial of the Monte Carlo simulation concurrently. The third approach is a combination of the first two, wherein both different trials of the Monte Carlo simulation as well as the shortest path problems in one trial are solved simultaneously. Performances of the three approaches are comprehensively tested by the Sioux‐Falls network and then a randomly generated network example. It shows that computational time for the probit‐based SUE problem can be largely reduced by any of these three approaches, and the first approach is found out to be superior to the other two. The first approach is then selected to calculate the probit‐based SUE problem on a large‐scale network example. Copyright © 2011 John Wiley & Sons, Ltd.     

A probabilistic framework for weather-based rerouting and delay estimations within an Airspace Planning model

In this paper, we develop a novel severe weather-modeling paradigm to be applied within the context of a large-scale Airspace Planning and collaborative decision-making model in order to reroute flights with respect to a specified probability threshold of encountering severe weather, subject to collision safety, airline equity, and sector workload considerations. This approach serves as an alternative to the current practice adopted by the Federal Aviation Administration (FAA) of adjusting flight routes in accordance with the guidelines specified in the National Playbook. Our innovative contributions in this paper include (a) the concept of “Probability-Nets” and the development of discretized representations of various weather phenomena that affect aviation operations; (b) the integration of readily accessible severe weather probabilities from existing weather forecast data provided by the National Weather Service; (c) the generation of flight plans that circumvent severe weather phenomena with specified probability threshold levels, and (d) a probabilistic delay assessment methodology for evaluating planned flight routes that might encounter potentially disruptive weather along its trajectory. Additionally, we conduct an economic benefit analysis using a k-means clustering mechanism in concert with our delay assessment methodology in order to evaluate delay costs and system disruptions associated with variations in probability-net refinement-based information. Computational results and insights are presented based on flight test cases derived from the Enhanced Traffic Management System data provided by the FAA and using weather scenarios derived from the Model Output Statistics forecast data provided by the National Weather Service.     

Assessing network vulnerability of heavy rail systems with the impact of partial node failures

Much of the literature in recent years has examined the vulnerability of transportation networks. To identify appropriate and operational measures of nodal centrality using connectivity in the case of heavy rail systems, this paper presents a set of comprehensive measures in the form of a Degree of Nodal Connection (DNC) index. The DNC index facilitates a reevaluation of nodal criticality among distinct types of transfer stations in heavy rail networks that present a number of multiple lines between stations. Specifically, a new classification of transfer stations—mandatory transfer, non-mandatory transfer, and end transfer—and a new measure for linkages—link degree and total link degree—introduces the characteristics of heavy rail networks when we accurately expose the vulnerability of a node. The concept of partial node failure is also introduced and compare the results of complete node failure scenarios. Four local and global indicators of network vulnerability are derived from the DNC index to assess the vulnerability of major heavy rail networks in the United States. Results indicate that the proposed DNC indexes can inform decision makers or network planners as they explore and compare the resilience of multi-hubs and multi-line networks in a comprehensive but accurate manner regardless of their network sizes.

     

Joint travel problem in space–time multi-state supernetworks

Joint travel problem (JTP) is an extension of the classic shortest path problem and relevant to shared mobility. A pioneering endeavor via supernetwork framework has been put forward to model two-person JTP. However, it was only addressed in the static context and with the assumption of zero waiting disutility, which resulted in no or weak synchronization among the travelers. This paper proposes a space–time multi-state supernetwork framework to address JTP for conducting one joint activity in the time-dependent context. Space–time synchronization and various choice facets related to joint travel are captured systematically. Two-person JTP is first discussed in a uni-modal transport network, and further extended to incorporate multi-modal and multi-person respectively. Stage-wise recursive formulations are proposed to find the optimal joint paths. It is found that JTP is a variant of Steiner tree problem by reduction and the number of meeting/departing points has no impact on the run-time complexity in space–time multi-state supernetworks.

     

Airline competition and network structure

This paper studies airline networks and their welfare implications in an unregulated environment. Competing airlines may adopt either fully-connected (FC) or hub-and-spoke (HS) network structures; and passengers exhibiting low brand loyalty to their preferred carrier choose an outside option to travel so that markets are partially served by airlines. In this context, carriers adopt hubbing strategies when costs are sufficiently low, and asymmetric equilibria where one carrier chooses a FC strategy and the other chooses a HS strategy may arise. Quite interestingly, flight frequency can become excessive under HS network configurations.     

Future electricity demand from battery‐powered vehicles

An important decision faced by airline schedulers is how to adapt the flight schedule and aircraft assignment to unforeseen perturbations in an established schedule. In the face of unforeseen aircraft delays, schedulers have to decide which flights to delay, and when delays become excessive, which to cancel. Current scheduling models deal with simple decision problems of delay or cancellation, but not with both simultaneously. But in practice the optimal decision may involve results from the integration of both flight cancellations and delays. In Part I of this paper, a quadratic programming model for the integration decision problem is given. The model can formulate the integration of flight cancellations and delays as well as some special cases, such as the ferrying of surplus aircraft and the possibility of swapping different types of aircraft. In this paper, based on the special structure of the model, an effective algorithm is presented, sufficient computational experiments are conducted and some results are reported. These show that we can expect to obtain a sufficiently good solution in terms of reasonable CPU time.     

A math-heuristic algorithm for the integrated air service recovery

A sophisticated flight schedule might be easily disrupted due to adverse weather, aircraft mechanical failures, crew absences, etc. Airlines incur huge costs stemming from such flight schedule disruptions in addition to the serious inconveniences experienced by passengers. Therefore, an efficient recovery solution that simultaneously decreases an airline's recovery cost while simultaneously mitigating passenger dissatisfaction is of great importance to the airline industry. In this paper, we study the integrated airline service recovery problem in which the aircraft and passenger schedule recovery problems are simultaneously addressed, with the objective of minimizing aircraft recovery and operating costs, passenger itinerary delay cost, and passenger itinerary cancellation cost.Recognizing the inherent difficulty in modeling the integrated airline service recovery problem within a single formulation (due to its huge solution space and quick response requirement), we propose a three-stage sequential math-heuristic framework to efficiently solve this problem, wherein the flight schedules and aircraft rotations are recovered in the first stage, Then, a flight rescheduling problem and passenger schedule recovery problems are iteratively solved in the next two stages. Time-space network flow representations, along with mixed-integer programming formulations, and algorithms that take advantages of the underlying problem structures, are proposed for each of three stages. This algorithm was tested on realistic data provided by the ROADEF 2009 challenge and the computational results reveal that our algorithm generated the best solution in nearly 72% of the test instances, and a near-optimal solution was achieved in the remaining instances within an acceptable timeframe. Furthermore, we also ran additional computational runs to explore the underlying characteristics of the proposed algorithm, and the recorded insights can serve as a useful guide during practical implementations of this algorithm.     

Finding the most reliable path with and without link travel time correlation: A Lagrangian substitution based approach

Path travel time reliability is an essential measure of the quality of service for transportation systems and an important attribute in travelers’ route and departure time scheduling. This paper investigates a fundamental problem of finding the most reliable path under different spatial correlation assumptions, where the path travel time variability is represented by its standard deviation. To handle the non-linear and non-additive cost functions introduced by the quadratic forms of the standard deviation term, a Lagrangian substitution approach is adopted to estimate the lower bound of the most reliable path solution through solving a sequence of standard shortest path problems. A subgradient algorithm is used to iteratively improve the solution quality by reducing the optimality gap. To characterize the link travel time correlation structure associated with the end-to-end trip time reliability measure, this research develops a sampling-based method to dynamically construct a proxy objective function in terms of travel time observations from multiple days. The proposed algorithms are evaluated under a large-scale Bay Area, California network with real-world measurements.     

Critical Review of Time-Dependent Shortest Path Algorithms: A Multimodal Trip Planner Perspective

Abstract

A multimodal trip planner that produces optimal journeys involving both public transport and private vehicle legs has to solve a number of shortest path problems, both on the road network and the public transport network. The algorithms that are used to solve these shortest path problems have been researched since the late 1950s. However, in order to provide accurate journey plans that can be trusted by the user, the variability of travel times caused by traffic congestion must be taken into consideration. This requires the use of more sophisticated time-dependent shortest path algorithms, which have only been researched in depth over the last two decades, from the mid-1990s. This paper will review and compare nine algorithms that have been proposed in the literature, discussing the advantages and disadvantages of each algorithm on the basis of five important criteria that must be considered when choosing one or more of them to implement in a multimodal trip planner.     

International experience with speed limits during and prior to the energy crisis of 1973–4

This paper presents an artificial neural network (ANN) based method for estimating route travel times between individual locations in an urban traffic network. Fast and accurate estimation of route travel times is required by the vehicle routing and scheduling process involved in many fleet vehicle operation systems such as dial‐a‐ride paratransit, school bus, and private delivery services. The methodology developed in this paper assumes that route travel times are time‐dependent and stochastic and their means and standard deviations need to be estimated. Three feed‐forward neural networks are developed to model the travel time behaviour during different time periods of the day‐the AM peak, the PM peak, and the off‐peak. These models are subsequently trained and tested using data simulated on the road network for the City of Edmonton, Alberta. A comparison of the ANN model with a traditional distance‐based model and a shortest path algorithm is then presented. The practical implication of the ANN method is subsequently demonstrated within a dial‐a‐ride paratransit vehicle routing and scheduling problem. The computational results show that the ANN‐based route travel time estimation model is appropriate, with respect to accuracy and speed, for use in real applications.     

Minimal-revenue congestion pricing Part II: An efficient algorithm for the general case

The second of a two-part series, this paper derives an efficient solution to the minimal-revenue tolls problem. As introduced in Part I, this problem can be defined as follows: Assuming each trip uses only a path whose generalized cost is smallest, find a set of arc tolls that simultaneously minimizes both average travel time and out-of-pocket cost. As a point of departure, this paper first re-solves the single-origin problem of Part I, modeling it as a linear program. Then with a change of variable, it transforms the LP's dual into a simple longest-path problem on an acyclic network. The multiple-origin problem – where one toll for each arc applies to all origins – solves analogously. In this case, however, the dual becomes an elementary linear multi-commodity max-cost flow problem with an easy bundling constraint and infinite arc capacities. After a minor reformulation that simplifies the model's input to better accommodate output from common traffic assignment software, a solution algorithm is exemplified with a numerical example.