A toll-based bi-level programming approach to managing hazardous materials shipments over an intermodal transportation network

This research proposes a bi-level bi-objective model to regulate the usage of rail intermodal terminals for hazardous materials (hazmat) shipments, where government imposes tolls to deter carriers from using certain terminals. The complexity of the resulting mathematical program motivates the development of a hybrid speed-constrained multi-objective particle swarm optimization algorithm, which is then integrated with CPLEX, to solve the model. Through a real problem instance based on the intermodal service chain of Norfolk Southern in US, the toll-setting model is examined and further compared with a regular network design approach, in which certain terminals are closed to hazmat containers. The computational results show that the toll-setting policy is more practical and efficient, and the two models can be combined as a two-stage strategy in long-term hazmat transportation regulations. Additional managerial insights are derived for different stakeholders.     

A cost and expected consequence approach to planning and managing railroad transportation of hazardous materials

Although hazardous materials (hazmat) account for around 140 million tons of all railroad freight traffic in the US, it has not received much attention from academic researchers. This is surprising especially when one considers the volume of hazmat moved by railroads in both North America and Europe. In this paper we develop a bi-objective optimization model, where cost is determined based on the characteristics of railroad industry and the determination of transport risk incorporates the dynamics of railroad accident. The optimization model and the solution framework is used to solve a realistic-size problem instance based in south-east US, which is then analyzed to gain managerial insights. In addition, a risk-cost frontier depicting non-dominated solutions is developed, followed by conclusion.     

Regulating hazardous materials transportation by dual toll pricing

We investigate dual-toll setting as a policy tool to mitigate the risk of hazardous material (hazmat) shipment in road networks. We formulate the dual-toll problem as a bi-level program wherein the upper level aims at minimizing the risk, and the lower level explores the user equilibrium decision of the regular vehicles and hazmat carriers given the toll. When the upper level objective is to minimize the risk and all links are tollable, we decompose the formulation into first-stage and second-stage, and suggest a computational method to solve each stage. Our two-stage solution methodology guarantees nonnegative valid dual tolls regardless of the solution accuracy of the first-stage problem. We also consider a general dual-toll setting problem where the regulator rather wishes to minimize a combination of risk and the paid tolls and/or some links are untollable. To solve this truly bilevel problem, we provide heuristic algorithms that decompose the problem into subproblems each being solved by a line search. Case studies based on the Sioux Falls network illustrate the insights on the dual-toll policies.     

A bilevel flow model for hazmat transportation network design

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.     

A bi-objective user equilibrium model of travel time reliability in a road network

Travel time, travel time reliability and monetary cost have been empirically identified as the most important criteria influencing route choice behaviour. We concentrate on travel time and travel time reliability and review two prominent user equilibrium models incorporating these two factors. We discuss some shortcomings of these models and propose alternative bi-objective user equilibrium models that overcome the shortcomings. Finally, based on the observation that both models use standard deviation of travel time within their measure of travel time reliability, we propose a general travel time reliability bi-objective user equilibrium model. We prove that this model encompasses those discussed previously and hence forms a general framework for the study of reliability related user equilibrium. We demonstrate and validate our concepts on a small three-link example.     

A bi-level model for single-line rail timetable design with consideration of demand and capacity

This paper proposes a bi-level model to solve the timetable design problem for an urban rail line. The upper level model aims at determining the headways between trains to minimize total passenger cost, which includes not only the usual perceived travel time cost, but also penalties during travel. With the headways given by the upper level model, passengers’ arrival times at their origin stops are determined by the lower level model, in which the cost-minimizing behavior of each passenger is taken into account. To make the model more realistic, explicit capacity constraints of individual trains are considered. With these constraints, passengers cannot board a full train, but wait in queues for the next coming train. A two-stage genetic algorithm incorporating the method of successive averages is introduced to solve the bi-level model. Two hypothetical examples and a real world case are employed to evaluate the effectiveness of the proposed bi-level model and algorithm. Results show that the bi-level model performs well in reducing total passenger cost, especially in reducing waiting time cost and penalties. And the section loading-rates of trains in the optimized timetable are more balanced than the even-headway timetable. The sensitivity analyses show that passenger’s desired arrival time interval at destination and crowding penalty factor have a high influence on the optimal solution. And with the dispersing of passengers' desired arrival time intervals or the increase of crowding penalty factor, the section loading-rates of trains become more balanced.     

Deploying public charging stations for electric vehicles on urban road networks

This paper explores how to optimally locate public charging stations for electric vehicles on a road network, considering drivers’ spontaneous adjustments and interactions of travel and recharging decisions. The proposed approach captures the interdependency of different trips conducted by the same driver by examining the complete tour of the driver. Given the limited driving range and recharging needs of battery electric vehicles, drivers of electric vehicles are assumed to simultaneously determine tour paths and recharging plans to minimize their travel and recharging time while guaranteeing not running out of charge before completing their tours. Moreover, different initial states of charge of batteries and risk-taking attitudes of drivers toward the uncertainty of energy consumption are considered. The resulting multi-class network equilibrium flow pattern is described by a mathematical program, which is solved by an iterative procedure. Based on the proposed equilibrium framework, the charging station location problem is then formulated as a bi-level mathematical program and solved by a genetic-algorithm-based procedure. Numerical examples are presented to demonstrate the models and provide insights on public charging infrastructure deployment and behaviors of electric vehicles.     

Pareto-improving transportation network design and ownership regimes

Private provision of public roads signifies co-existence of free, public-tolled and private-tolled roads. This paper investigates the Pareto-improving transportation network design problem under various ownership regimes by allowing joint choice of road pricing and capacity enhancement on free links. The problem of interest is formulated as a bi-objective mathematical programming model that considers the travel cost of road users in each origin-destination pair and the investment return of the whole network. The non-dominated Pareto-improving solutions of toll and/or capacity enhancement schemes are sought for achieving a win-win situation. A sufficient condition is provided for the existence of the non-dominated Pareto-improving schemes and then the properties of those schemes are analyzed. It is found that, under some mild assumptions, the optimal capacity enhancement is uniquely determined by the link flow under any non-dominated Pareto-improving scheme. As a result, the joint road pricing and capacity enhancement problem reduces to a bi-objective second-best road pricing problem. A revenue distribution mechanism with return rate guarantee is proposed to implement the non-dominated Pareto-improving schemes.     

A bi-level model of dynamic traffic signal control with continuum approximation

This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure.     

Traveler delay costs and value of time with trip chains, flexible activity scheduling and information

The delay costs of traffic disruptions and congestion and the value of travel time reliability are typically evaluated using single trip scheduling models, which treat the trip in isolation of previous and subsequent trips and activities. In practice, however, when activity scheduling to some extent is flexible, the impact of delay on one trip will depend on the actual and predicted travel time on itself as well as other trips, which is important to consider for long-lasting disturbances and when assessing the value of travel information. In this paper we extend the single trip approach into a two trips chain and activity scheduling model. Preferences are represented as marginal activity utility functions that take scheduling flexibility into account. We analytically derive trip timing optimality conditions, the value of travel time and schedule adjustments in response to travel time increases. We show how the single trip models are special cases of the present model and can be generalized to a setting with trip chains and flexible scheduling. We investigate numerically how the delay cost depends on the delay duration and its distribution on different trips during the day, the accuracy of delay prediction and travel information, and the scheduling flexibility of work hours. The extension of the model framework to more complex schedules is discussed.     

Second best toll pricing within the framework of bounded rationality

The network design problem is usually formulated as a bi-level program, assuming the user equilibrium is attained in the lower level program. Given boundedly rational route choice behavior, the lower-level program is replaced with the boundedly rational user equilibria (BRUE). The network design problem with boundedly rational route choice behavior is understudied due to non-uniqueness of the BRUE. In this study, thus, we mainly focus on boundedly rational toll pricing (BR-TP) with affine link cost functions. The topological properties of the lower level BRUE set are first explored. As the BRUE solution is generally non-unique, urban planners cannot predict exactly which equilibrium flow pattern the transportation network will operate after a planning strategy is implemented. Due to the risk caused by uncertainty of people’s reaction, two extreme scenarios are considered: the traffic flow patterns with either the minimum system travel cost or the maximum, which is the “risk-prone” (BR-TP-RP) or the “risk-averse” (BR-TP-RA) scenario respectively. The upper level BR-TP is to find an optimal toll minimizing the total system travel cost, while the lower level is to find the best or the worst scenario. Accordingly BR-TP can be formulated as either a min –min or a min –max program. Solution existence is discussed based on the topological properties of the BRUE and algorithms are proposed. Two examples are accompanied to illustrate the proposed methodology.     

Spatial decision support system for hazardous material truck routing

Shipping hazardous material (hazmat) places the public at risk. People who live or work near roads commonly traveled by hazmat trucks endure the greatest risk. Careful selection of roads used for a hazmat shipment can reduce the population at risk. On the other hand, a least time route will often consist of urban interstate, thus placing many people in harms way. Route selection is therefore the process of resolving the conflict between population at risk and efficiency considerations. To assist in resolving this conflict, a working spatial decision support system (SDSS) called Hazmat Path is developed. The proposed hazmat routing SDSS overcomes three significant challenges, namely handling a realistic network, offering sophisticated route generating heuristics and functioning on a desktop personal computer. The paper discusses creative approaches to data manipulation, data and solution visualization, user interfaces, and optimization heuristics implemented in Hazmat Path to meet these challenges.     

Adaptive traffic signal control with equilibrium constraints under stochastic demand

This study develops a methodology to model transportation network design with signal settings in the presence of demand uncertainty. It is assumed that the total travel demand consists of commuters and infrequent travellers. The commuter travel demand is deterministic, whereas the demand of infrequent travellers is stochastic. Variations in demand contribute to travel time uncertainty and affect commuters’ route choice behaviour. In this paper, we first introduce an equilibrium flow model that takes account of uncertain demand. A two-stage stochastic program is then proposed to formulate the network signal design under demand uncertainty. The optimal control policy derived under the two-stage stochastic program is able to (1) optimize the steady-state network performance in the long run, and (2) respond to short-term demand variations. In the first stage, a base signal control plan with a buffer against variability is introduced to control the equilibrium flow pattern and the resulting steady-state performance. In the second stage, after realizations of the random demand, recourse decisions of adaptive signal settings are determined to address the occasional demand overflows, so as to avoid transient congestion. The overall objective is to minimize the expected total travel time. To solve the two-stage stochastic program, a concept of service reliability associated with the control buffer is introduced. A reliability-based gradient projection algorithm is then developed. Numerical examples are performed to illustrate the properties of the proposed control method as well as its capability of optimizing steady-state performance while adaptively responding to changing traffic flows. Comparison results show that the proposed method exhibits advantages over the traditional mean-value approach in improving network expected total travel times.     

Large-scale evacuation network optimization: a bi-level control method with uncertain arterial demand

To improve the efficiency of large-scale evacuations, a network aggregation method and a bi-level optimization control method are proposed in this paper. The network aggregation method indicates the uncertain evacuation demand on the arterial sub-network and balances accuracy and efficiency by refining local road sub-networks. The bi-level optimization control method is developed to reconfigure the aggregated network from both supply and demand sides with contraflow and conflict elimination. The main purpose of this control method is to make the arterial sub-network to be served without congestion and interruption. Then, a corresponding bi-objective network flow model is presented in a static manner for an oversaturated network, and a Genetic Algorithm-based solution method is used to solve the evacuation problem. The numerical results from optimizing a city-scale evacuation network for a super typhoon justify the validity and usefulness of the network aggregation and optimization control methods.     

Integrated planning of static and dynamic charging infrastructure for electric vehicles

This paper investigates the optimal deployment of static and dynamic charging infrastructure considering the interdependency between transportation and power networks. Static infrastructure means plug-in charging stations, while the dynamic counterpart refers to electrified roads or charging lanes enabled by charging-while-driving technology. A network equilibrium model is first developed to capture the interactions among battery electric vehicles’ (BEVs) route choices, charging plans, and the prices of electricity. A mixed-integer bi-level program is then formulated to determine the deployment plan of charging infrastructure to minimize the total social cost of the coupled networks. Numerical examples are provided to demonstrate travel and charging plans of BEV drivers and the competitiveness of static and dynamic charging infrastructure. The numerical results on three networks suggest that (1) for individual BEV drivers, the choice between using charging lanes and charging stations is more sensitive to parameters including value of travel time, service fee markup, and battery size, but less sensitive to the charging rates and travel demand; (2) deploying more charging lanes is favorable for transportation networks with sparser topology while more charging stations can be more preferable for those denser networks.     

Impact of transition between signal timing plans in social cost based in delay,fuel consumption and air emissions

Significant effects of traffic congestion include the cost associated with extra travel time, fuel consumption, and gas emissions. This paper develops a mathematical function to quantify the monetary impact of transition designs between signal timing plans on users and the environment. This function offers an approach to reduce problems such as excessive travel time, pollution emissions and fuel consumption. The proposed social cost function is evaluated for various transition plans to assess the impact of the number of steps required to adjust signal timing. The relationships between delay, fuel consumption and gas emissions and the number of steps needed to achieve the transition are also analysed.     

A bi-level programming for bus lane network design

This paper proposes a bi-level programming model to solve the design problem for bus lane distribution in multi-modal transport networks. The upper level model aims at minimizing the average travel time of travelers, as well as minimizing the difference of passengers’ comfort among all the bus lines by optimizing bus frequencies. The lower level model is a multi-modal transport network equilibrium model for the joint modal split/traffic assignment problem. The column generation algorithm, the branch-and-bound algorithm and the method of successive averages are comprehensively applied in this paper for the solution of the bi-level model. A simple numerical test and an empirical test based on Dalian economic zone are employed to validate the proposed model. The results show that the bi-level model performs well with regard to the objective of reducing travel time costs for all travelers and balancing transit service level among all bus lines.     

Policy analysis of third party electronic coupons for public transit fares

Mobile technologies are generating new business models for urban transport systems, as is evident from recent startups cropping up from the private sector. Public transport systems can make more use of mobile technologies than just for measuring system performance, improving boarding times, or for analyzing travel patterns. A new transaction model is proposed for public transport systems where travelers are allowed to pre-book their fares and trade that demand information to private firms. In this public-private partnership model, fare revenue management is outsourced to third party private firms such as big box retail or large planned events (such as sports stadiums and theme parks), who can issue electronic coupons to travelers to subsidize their fares. This e-coupon pricing model is analyzed using marginal cost theory for the transit service and shown to be quite effective for monopolistic coupon rights, particularly for demand responsive transit systems that feature high cost fares, non-commute travel purposes, and a closed access system with existing pre-booking requirements. However, oligopolistic scenarios analyzed using game theory and network economics suggest that public transport agencies need to take extreme care in planning and implementing such a policy. Otherwise, they risk pushing an equivalent tax on private firms or disrupting the urban economy and real estate values while increasing ridership.     

Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium

Establishment of industry facilities often induces heavy vehicle traffic that exacerbates congestion and pavement deterioration in the neighboring highway network. While planning facility locations and land use developments, it is important to take into account the routing of freight vehicles, the impact on public traffic, as well as the planning of pavement rehabilitation. This paper presents an integrated facility location model that simultaneously considers traffic routing under congestion and pavement rehabilitation under deterioration. The objective is to minimize the total cost due to facility investment, transportation cost including traffic delay, and pavement life-cycle costs. Building upon analytical results on optimal pavement rehabilitation, the problem is formulated into a bi-level mixed-integer non-linear program (MINLP), with facility location, freight shipment routing and pavement rehabilitation decisions in the upper level and traffic equilibrium in the lower level. This problem is then reformulated into an equivalent single-level MINLP based on Karush–Kuhn–Tucker (KKT) conditions and approximation by piece-wise linear functions. Numerical experiments on hypothetical and empirical network examples are conducted to show performance of the proposed algorithm and to draw managerial insights.     

Bi-level GA and GIS for Multi-objective TSP Route Planning

Abstract

Route planning is usually carried out to achieve a single objective such as to minimize transport cost, distance traveled or travel time. This article explores an approach to multi-objective route planning using a genetic algorithm (GA) and geographical information system (GIS) approach. The method is applied to the case of a tourist sight-seeing itinerary, where a route is planned by a tour operator to cover a set of places of interest within a given area. The route planning takes into account four criteria including travel time, vehicle operating cost, safety and surrounding scenic view quality. The multi-objective route planning in this paper can be viewed as an extension of the traditional traveling salesman problem (TSP) since a tourist needs to pass through a number of sight points. The four criteria are quantified using the spatial analytic functions of GIS and a generalized cost for each link is calculated. As different criteria play different roles in the route selection process, and the best order of the multiple points needs to be determined, a bi-level GA has been devised. The upper level aims to determine the weights of each criterion, while the lower level attempts to determine the best order of the sights to be visited based on the new generalized cost that is derived from the weights at the upper level. Both levels collaborate during the iterations and the route with the minimal generalized cost is thus determined. The above sight-seeing route planning methodology has been examined in a region within the central area of Singapore covering 19 places of interest.