Bi-level Network Design Problem Research Articles

Regulating hazardous material transportation: a scenario-based network design approach with integrated risk-mitigation mechanisms

Integrating both proactive and reactive risk-mitigation mechanisms, this research constructs a bi-level network design problem for hazardous materials (hazmats) to regulate the carriers' use of roads, such that the environmental impact is minimized. In more detail, by embedding the emergency response time into the risk assessment, the locations of hazmat response teams are determined along with toll schemes, road closures, and new road constructions. The uncertainties of demand, including differences in the number of shipments, origin/destination changes, and amount variations, are also taken into account by applying a scenario-based approach. The proposed bi-level model is first solved optimally by a single-level reformulation, and then by a three-stage heuristic method for larger instances. Through numerical experiments on a real-world road network in Nanchang, a city in China, a set of management insights are derived to facilitate policy-making in regulating hazmat transportation.

Optimization strategies for the bilevel network design problem with affine cost functions

Optimization strategies for the bilevel network design problem with affine cost functions

Multi-period transportation network investment decision making and policy implications using econometric framework

Transportation infrastructure projects take numerous years of planning before they are scheduled for construction. Prioritization of such projects over a multi-period planning horizon (under a limited budget) is a difficult task, as it is usually formulated as a bilevel network design problem (NDP). Although multi-period network investment is studied in the literature, its application by public agencies is limited because of the complexities involved in network design problems and the computational time needed to analyze large scale networks (i.e., performing the traffic assignment at the lower level of the NDP). The contribution of this research is two-fold. First, it extends a previously published single year discrete network design formulation to a multi-period discrete network design problem (MPNDP) to capture both the spatial and temporal patterns of multi-period network investment decisions. Second, using the MPNDP investment results; and the network characteristics, this research develops and evaluates a new econometric model the Multi-Period Econometric Network Investment Model (MENIM). MENIM can be used by agencies in place of MPNDP to approximate network investments. The proposed model is calibrated and validated using medium to large scale networks and results show that it provides comparable results to MPNDP within acceptable computational times. Patterns of multi-period network investments from these numerical experiments are also extensively discussed along with policy recommendations for public agencies.

Optimizing Road Networks for Automated Vehicles with Dedicated Links, Dedicated Lanes, and Mixed-Traffic Subnetworks

This study focuses on network configurations to accommodate automated vehicles (AVs) on road networks during the transition period to full automation. The literature suggests that dedicated infrastructure for AVs and enhanced infrastructure for mixed traffic (i.e., AVs on the same lanes with conventional vehicles) are the main alternatives so far. We utilize both alternatives and propose a unified mathematical framework for optimizing road networks for AVs by simultaneous deployment of AV-ready subnetworks for mixed traffic, dedicated AV links, and dedicated AV lanes. We model the problem as a bilevel network design problem where the upper level represents road infrastructure adjustment decisions to deploy these concepts and the lower level includes a network equilibrium model representing the flows as a result of the travelers’ response to new network topologies. An efficient heuristic solution method is introduced to solve the formulated problem and find coherent network topologies. Applicability of the model on real road networks is demonstrated using a large-scale case study of the Amsterdam metropolitan region. Our results indicate that for low AV market penetration rates (MPRs), AV-ready subnetworks, which accommodate AVs in mixed traffic, are the most efficient configuration. However, after 30% MPR, dedicated AV lanes prove to be more beneficial. Additionally, road types can dictate the viable deployment plan for certain parts of road networks. These insights can be used to guide planners in developing their strategies regarding road network infrastructure during the transition period to full automation.

A multi-objective integrated model for selecting, scheduling, and budgeting road construction projects

In this paper, an integrated ‎model for selecting, scheduling, and budgeting urban road construction projects is introduced as a ‎multi-objective time-dependent ‎bi-level network design problem. Three criteria are considered as upper-level objective functions: total travel time, user satisfaction over time, and spatial ‎equity. Two new measures are developed to ‎assess network design scenarios from the perspectives of user satisfaction over time and spatial ‎equity. Given the great complexity of the intended problem, two multi-objective evolutionary approaches (an interactive and a-posteriori) are proposed to solve the model in a reasonable time. These two approaches are novel combinations of ‎different techniques, such as: Genetic Algorithm (GA), Non-dominated Sorting Genetic Algorithm (NSGA-II), Frank-Wolfe algorithm, ‎ordered logit model, and knees identification algorithm. Computational results for various test problems ‎show that proposed approaches have acceptable performance in terms of both‎ solution quality and ‎solution time.‎ ‎To show applicability of the proposed approach in large-sized networks, it is applied to a real case on Isfahan City in Iran.

Transportation Investment Decision Making for Medium to Large Transportation Networks

One of the challenges for transportation decision makers is to identify capacity expansion in the network under the constraint of budget such that various objectives of the decision maker [such as total system travel time is minimized, social welfare (consumer surplus) is maximized, or total system emission is minimized], while accounting for the route choice behavior of users. Such type of investment decision making in the context of network design problems can be solved using optimization techniques. This type of optimization problem is particularly difficult to solve since two hierarchical decision making entities are involved (decision makers and road users). These two players have different objectives. The road users select routes such that their individual travel costs are minimized while the decision makers’ optimally seek to select capacity expansion projects in the network in such a way that planning objectives are achieved. The objective of this paper is to propose numerical methods and application algorithms such that optimal investment decisions are made in moderate and large transportation networks. The problem is formulated as a bi-level network design problem in which upper level determines the optimal capacity expansions of links and the lower level consist of the traditional Wardrop’s user equilibrium. The upper level provides a trial capacity expansion vector with additional network capacities. The lower level considers new link capacities for user equilibrium. The output from the lower level is a vector of link flows which is transferred to the upper level. This process is iterated using kth best algorithm till convergence. The upper level problem is solved using PSWARM algorithm and the solution for the lower level is obtained using an efficient static traffic assignment algorithm. Adequacy of the model is examined by first conducting numerical experiments using small networks from the literature and then using moderate to large scale networks. Results of numerical experiments indicates that proposed methodology from this study can be efficiently used for real-world applications in practice for transportation infrastructure capacity expansion decision making.

A new one-level convex optimization approach for estimating origin–destination demand

Accurately estimating Origin–Destination (OD) trip tables based on traffic data has become crucial in many real-time traffic applications. The problem of OD estimation is traditionally modeled as a bilevel network design problem (NDP), which is challenging to solve in large-scale networks. In this paper, we propose a new one-level convex optimization formulation to reasonably approximate the bilevel structure, thus allowing the development of more efficient solution algorithms. This one-level approach is consistent with user equilibrium conditions, and improves previous one-level relaxed OD estimation formulations in the literature by ‘equilibrating’ path flows using external path cost parameters. Our new formulation can, in fact, be viewed as a special case of the user equilibrium assignment problem with elastic demand, and hence can be solved efficiently by standard path-based traffic assignment algorithms with an iterative parameter updating scheme. Numerical experiments indicate that this new one-level approach performs very well. Estimation results are robust to network topology, sensor coverage, and observation error, and can achieve further improvements when additional data sources are included.

Analytically Derived versus Numerically Derived Urban Transit Guidelines

Urban transit guidelines yield optimal network characteristics relating to factors such as stop density, network density, service frequency, and network hierarchy. These guidelines are typically derived from a simple analytical formulation of the bilevel network design problem. This optimization problem can be solved analytically only when simplifying assumptions are made regarding the demand distribution, local constraints, and travel behavior. The primary objective of this paper is to verify the validity of the assumptions underlying analytically derived guidelines. To this end, a new numerical optimization tool is developed and applied to the design of several detailed topological transit networks (including routes and line-specific properties) for the medium-sized Dutch city of Utrecht, Netherlands. Average network characteristics are derived, and a comparison is made between the existing analytically derived guidelines, the new numerically derived optimal characteristics, and the characteristics of the present network. Both analytically derived and numerically derived guidelines recommend lower stop densities, coarser networks, and higher frequencies than those found in real life. Furthermore, the introduction of zone lines would improve network quality, while express lines are beneficial only for large demand concentrations. Although existing (typically analytically derived) guidelines are found to be in line with numerically derived guidelines, the former are less suitable because local constraints are not accounted for, and only average network characteristics are computed. Therefore, the detailed network designs that are numerically derived in this study are easier to implement.

A Dantzig-Wolfe Decomposition Based Heuristic Scheme for Bi-level Dynamic Network Design Problem

We present a heuristic to solve the NP-hard bi-level network design problem (NDP). The heuristic is developed based on the Dantzig-Wolfe decomposition principle such that it iteratively solves a master problem and a pricing problem. The master problem is the budget allocation linear program solved by CPLEX to determine the budget allocation and construct a modified cell transmission network for the pricing problem. The pricing problem is the user-optimal dynamic traffic assignment (UODTA) solved by an existing combinatorial algorithm. To facilitate the decomposition principle, we propose a backward connectivity algorithm and complementary slackness procedures to efficiently approximate the required dual variables from the UODTA solution. The dual variables are then employed to augment a new column in the master program in each iteration. The iterative process repeats until a stopping criterion is met. Numerical experiments are conducted on two test networks. Encouraging results demonstrate the applicability of the heuristic scheme on solving large-scale NDP. Though a single destination problem is considered in this paper, the proposed scheme can be extended to solve multi-destination problems as well.

Investment Selection Model for Multicommodity Multimodal Transportation Networks

A Multicommodity Multimodal Network Design (MCMND) model is presented; the model is to be used as a planning tool for determining investment priorities for freight intercity networks. The MCMND model is designed to select the best set of investment options for a multimodal regional network, given a limited investment budget. The main component of the model comprises the solution of a nonlinear bilevel network design problem formulated to choose investments that minimize both the transportation costs incurred by users and the environmental impacts of less efficient modes of transportation. Investment options to be considered by the model involve the addition of new physical links to the network, the improvement of existing links, and the location of intermodal transfer facilities at specified nodes of the network. The representation of the multimodal network is at a level of detail appropriate for strategic planning for a large region. The demand for transportation services is fixed and exogenous to the mo...

Investment Selection Model for Multicommodity Multimodal Transportation Networks

A Multicommodity Multimodal Network Design (MCMND) model is presented; the model is to be used as a planning tool for determining investment priorities for freight intercity networks. The MCMND model is designed to select the best set of investment options for a multimodal regional network, given a limited investment budget. The main component of the model comprises the solution of a nonlinear bilevel network design problem formulated to choose investments that minimize both the transportation costs incurred by users and the environmental impacts of less efficient modes of transportation. Investment options to be considered by the model involve the addition of new physical links to the network, the improvement of existing links, and the location of intermodal transfer facilities at specified nodes of the network. The representation of the multimodal network is at a level of detail appropriate for strategic planning for a large region. The demand for transportation services is fixed and exogenous to the model. Mode choice in shipping freight is modeled in combination with flow assignment, assuming that goods are shipped at minimum total generalized costs. A new path-based stochastic user equilibrium assignment algorithm is proposed to distribute trips over the multimodal network according to a logit-type model. The Tietê-Paraná Valley in Brazil was selected for the development of a pilot application of the MCMND model to assess its efficiency when dealing with large networks. This application also served to emphasize the importance of an interface between the MCMND model and a geographic information system in solving real-life problems.