User Equilibrium Traffic Assignment Problem Research Articles

A hybrid deep-learning-metaheuristic framework for bi-level network design problems

This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture for road network design problems (NDPs). We train a graph neural network (GNN) to approximate the solution of the user equilibrium (UE) traffic assignment problem and use inferences made by the trained model to calculate fitness function evaluations of a genetic algorithm (GA) to approximate solutions for NDPs. Using three test networks, two NDP variants and an exact solver as benchmark, we show that on average, our proposed framework can provide solutions within 1.5 % gap of the best results in less than 0.5 % of the time used by the exact solution procedure. Our framework can be utilized within an expert system for infrastructure planning to determine the best infrastructure planning and management decisions under different scenarios. Given the flexibility of the framework, it can easily be adapted to many other decision problems that can be modeled as bi-level problems on graphs. Moreover, we foreseen interesting future research directions, thus we also put forward a brief research agenda for this topic. The key observation from our research that can shape future research is that the fitness function evaluation time using the inferences made by the GNN model was in the order of milliseconds, which points to an opportunity and a need for novel heuristics that 1) can cope well with noisy fitness function values provided by deep learning models, and 2) can use the significantly enlarged efficiency of the evaluation step to explore the search space effectively (rather than efficiently). This opens a new avenue for a modern class of metaheuristics that are crafted for use with AI-powered predictors.

An ADMM-based parallel algorithm for solving traffic assignment problem with elastic demand

Efficiently solving the user equilibrium traffic assignment problem with elastic demand (UE-TAPED) for transportation networks is a critical problem for transportation studies. Most existing UE-TAPED algorithms are designed using a sequential computing scheme, which cannot take advantage of advanced parallel computing power. Therefore, this study focuses on model decomposition and parallelization, proposing an origin-based formulation for UE-TAPED and proving an equivalent reformulation of the original problem. Furthermore, the alternative direction method of multipliers (ADMM) is employed to decompose the original problem into independent link-based subproblems, which can solve large-scale problems with small storage space. In addition, to enhance the efficiency of our algorithm, the parallel computing technology with optimal parallel computing schedule is implemented to solve the link-based subproblems. Numerical experiments are performed to validate the computation efficiency of the proposed parallel algorithm.

A network-based analysis of critical resource accessibility during floods

Numerous government and non-governmental agencies are increasing their efforts to better quantify the disproportionate effects of climate risk on vulnerable populations with the goal of creating more resilient communities. Sociodemographic based indices have been the primary source of vulnerability information the past few decades. However, using these indices fails to capture other facets of vulnerability, such as the ability to access critical resources (e.g., grocery stores, hospitals, pharmacies, etc.). Furthermore, methods to estimate resource accessibility as storms occur (i.e., in near-real time) are not readily available to local stakeholders. We address this gap by creating a model built on strictly open-source data to solve the user equilibrium traffic assignment problem to calculate how an individual's access to critical resources changes during and immediately after a flood event. Redundancy, reliability, and recoverability metrics at the household and network scales reveal the inequitable distribution of the flood's impact. In our case-study for Austin, Texas we found that the most vulnerable households are the least resilient to the impacts of floods and experience the most volatile shifts in metric values. Concurrently, the least vulnerable quarter of the population often carries the smallest burdens. We show that small and moderate inequalities become large inequities when accounting for more vulnerable communities' lower ability to cope with the loss of accessibility, with the most vulnerable quarter of the population carrying four times as much of the burden as the least vulnerable quarter. The near-real time and open-source model we developed can benefit emergency planning stakeholders by helping identify households that require specific resources during and immediately after hazard events.

A non-additive path-based reward credit scheme for traffic congestion management

This study investigates the potential of non-additive path-based pricing for congestion management in urban transportation networks. We propose a novel path-based reward credit scheme to provide commuter incentives with the goal of reducing traffic congestion. We consider that a known proportion of commuters subscribe to this reward credit scheme and may earn credits when traveling in the network. We introduce a bilevel optimization formulation to determine optimal non-additive, path-based reward credits under traffic equilibrium conditions. In this formulation, the follower problem is a parameterized user equilibrium traffic assignment problem with two classes of users and non-additive path costs. We develop a single-level reformulation based on its first-order optimality conditions and derive theoretical properties of the reward credit scheme. Customized branch-and-bound algorithms are designed to solve the problem. We also introduce a heuristic approach that repeatedly solves parameterized follower problems to enhance scalability. We report numerical results that demonstrate the computational efficiency of the proposed methods over a benchmarking approach. We conduct a comprehensive evaluation of this path-based reward credit scheme compared with a link-based subsidy pricing scheme. We find that, on average, under a limited budget and a user participation level of at least 40%, the proposed path-based incentive mechanism yields larger reductions in traffic congestion over link-based approaches.

Integrating alternating direction method of multipliers and bush for solving the traffic assignment problem

This paper introduces two novel parallel algorithmic frameworks to address the user equilibrium traffic assignment problem (UE-TAP). Most of the existing solution algorithms for the UE-TAP are executed in a sequential manner. This study endeavors to explore parallel computing methods based on model decomposition. Considering that the TAPs can be decomposed based on their origins, thus, following the spirit of the alternating direction method of multipliers (ADMM), a new parallel algorithm B-ADMM is proposed, which integrates the concept of the bush. Subsequently, the convergence of the proposed algorithm is rigorously proven. To enhance the algorithmic parallelism while maintaining the convergence efficiency of the B-ADMM algorithm, this paper further employs the parallel block coordinate descent (PBCD) method to improve the B-ADMM algorithm. We develop a bi-level parallel algorithm PBCD-ADMM, in which the independent origins/bushes are separated into several blocks, and the origin/bush-based restricted subproblems in each block can be solved in parallel. Furthermore, for the given bush belonging to a block, the bush links can also be grouped into several sub-blocks based on the original link-blocking scheme. Thus, these link-based subproblems in each sub-block can also be solved in parallel. A numerical experiment is conducted to validate the proposed algorithms, which indicates that the two new parallel algorithms perform better in terms of convergence speed compared with the original ADMM algorithm.

A novel flow update policy in solving traffic assignment problems: Successive over relaxation iteration method

This paper presents a novel flow update policy, namely the successive over relaxation (SOR) iteration method, which can be implemented in traffic assignment algorithms. Most existing solution algorithms for the user equilibrium traffic assignment problem (UE-TAP) mainly use two flow update policies: Jacobi and Gauss-Seidel iteration methods. The proposed flow update policy SOR can be a more efficient replacement. Following the path-based gradient projection (GP) algorithm, we developed a new method GP-SOR for the UE-TAP. This study first provides the complete procedure of applying the GP-SOR algorithm to solve the UE-TAP. Subsequently, a few properties of the proposed method are rigorously proven. However, empirical tests of the GP-SOR algorithm demonstrate serious oscillations and poor convergence. To cope with this problem, the Armijo Rule is employed to determine the relaxation factor, which substantially improves the convergence of GP-SOR algorithm. The preliminary numerical examples show that the GP-SOR algorithm has speedier convergence compared with the known alternatives, which is reflected by the evident reduction of the computing time and the number of iterations.

A Distributed Coordination Method for Coupled Traffic-Power Network Equilibrium Incorporating Behavioral Theory

The increasing penetration of electric vehicles (EVs) gradually evolves the urban transportation network (UTN) and power distribution network (PDN) from being independent to being coupled. To analyze the impact of drivers' behavior on the coupled network, and reveal the relationship between the two networks, a coupled traffic-distribution (CTD) model is proposed, in which the total traveling cost of UTN and the power service cost of PDN is minimized. In the CTD model, A stochastic user equilibrium traffic assignment problem (SUE-TAP) with elastic traffic demand and discrete path selection of drivers is formulated to capture the traffic flow distribution comprised of EVs and gasoline vehicles (GVs). An alternative current optimal power flow (ACOPF) model of PDN is utilized to provide the optimal charging price and scheduling plan. Besides, the SUE-TAP with nonlinear functions is difficult to solve, a novel piecewise linear approximation method is presented to deal with the nonlinear items of the SUE-TAP caused by drivers' traveling cost and traveling tendency incorporating perception. Incorporating the behavioral theory, a distributed coordination method derived from optimal condition decomposition is proposed for the coupled traffic-power network equilibrium. The proposed distributed scheme is examined using a coupled network, which consists of a 20-road UTN and a 33-bus PDN. Numerical results demonstrate the effectiveness and practicability of the proposed model and the distributed coordination method.

Traffic assignment problem for footpath networks with bidirectional links

The estimation of pedestrian traffic in urban areas is often performed with computationally intensive microscopic models that usually suffer from scalability issues in large-scale footpath networks. In this study, we present a new macroscopic user equilibrium traffic assignment problem (UE-pTAP) framework for pedestrian networks while taking into account fundamental microscopic properties such as self-organization in bidirectional streams and stochastic walking travel times. We propose four different types of pedestrian volume-delay functions (pVDFs), calibrate them with empirical data, and discuss their implications on the existence and uniqueness of the traffic assignment solution. We demonstrate the applicability of the developed UE-pTAP framework in a small network as well as a large scale network of Sydney footpaths.

Multi-Agent Deep Reinforcement Learning Method for EV Charging Station Game

The ongoing quest for transportation electrification with the massive proliferation of EV charging stations (EVCSs) will deepen the interaction and require the further coordination of coupled power and transportation networks (PTN). The individually-owned EVCSs located in an urban transportation network (UTN) will compete using price signals to maximize their respective payoffs. In this paper, a multi-agent deep reinforcement learning (MA-DRL) method is proposed to model the pricing game in UTN and determine the optimal charging prices for a single EVCS. The EVCS charging demand is first analyzed using a modified user equilibrium traffic assignment problem (UE-TAP) with elastic traveling demands and different charging prices. The price competition problem is then formulated as a game with incomplete information in which the market environment is complex due to nonlinear traffic assignments. Thus, the MA-DRL approach is proposed to learn the charging pricing strategies of multiple EVCSs and approximate the Nash Equilibrium (NE) of the pricing game using the incomplete information. The proposed solution will determine the optimal pricing strategies for an EVCS in UTN. The case studies on a 24-node Sioux-Falls network, and the real-world Xi'an and Hangzhou cities are conducted to verify the effectiveness and scalability of the proposed approach.

Development of a solution algorithm to solve the user equilibrium traffic assignment problem with soft link capacity constraints

Development of a solution algorithm to solve the user equilibrium traffic assignment problem with soft link capacity constraints

An improved parallel block coordinate descent method for the distributed computing of traffic assignment problem

An improved parallel block coordinate descent (iPBCD) algorithm for solving the user equilibrium traffic assignment problem is proposed. The iPBCD algorithm is developed based on the parallel block coordinate descent algorithm (PBCD). The hybrid flow update policy is investigated to enhance the robustness and performance of the PBCD algorithm. Two update order rules, namely a cyclic rule and a greedy rule are compared for block indices. Then, the block size is optimized using a sensitivity analysis test. Finally, five index-grouping rules are tested for comparative purposes. Numerical experiments indicate that index-grouping rules have a significant influence on convergence: the information-based drop-out rule performs better in terms of convergence and efficiency.

A parallel computing approach to solve traffic assignment using path-based gradient projection algorithm

This paper presents a Parallel Block-Coordinate Descent (PBCD) algorithm for solving the user equilibrium traffic assignment problem. Most of the existing algorithms for the user equilibrium-based traffic assignment problem are developed and implemented sequentially. This paper aims to study and investigate the parallel computing approach to utilize the widely available parallel computing resources. The PBCD algorithm is developed based on the state-of-the-art path-based algorithm, i.e., the improved path-based gradient projection algorithm (iGP). The computationally expensive components in the iGP are identified and parallelized. A parallel block-coordinate method is proposed to replace the widely used Gauss-Seidel method for the procedure of path flow adjustment. A new rule is proposed to group OD pairs into different blocks. The numerical examples show that the implemented PBCD algorithm can significantly reduce the computing time.

Estimation of the value of travel time and of travel time reliability for heterogeneous drivers in a road network

Travel time reliability has been recognized as an important factor in cost–benefit analysis in a transportation network. To estimate the benefit and cost of travel time reliability, several network models have been proposed to estimate the monetary values both of travel time and of travel time reliability based on the driver’s route choice behavior. In this study, we propose a network model that addresses monetary values that are specific to each origin–destination pair in a road network. The proposed model is formulated as a utility maximization problem with constraints in a manner similar to studies that address the value of travel time only. The proposed model has the same equilibrium conditions as a multiclass user equilibrium traffic assignment problem with elastic demand in which the risk-averse driver’s route choice behavior is explicitly considered. By accounting for data availability, we propose a parameter estimation method based on the maximum likelihood method with two alternative approaches; namely link flow-based and route flow-based approaches. However, the two proposed methods require link flow data only. Numerical experiments are carried out to demonstrate the performance of the two proposed methods together with some insightful findings.

Reduced gradient algorithm for user equilibrium traffic assignment problem

ABSTRACT A path-based algorithm is developed for the static traffic assignment problem (TAP). In each iteration, it decomposes the problem into origin-destination (OD) pairs and solves each subproblem separately using the Wolfe reduced gradient (RG) method. This method reduces the dimensions of each single-OD subproblem by selecting a basic path between the OD pair and reformulating the subproblem in terms of the nonbasic paths. A column generation technique is included to avoid path enumeration in large scale networks. Also, some speed-up techniques are designed to improve the computational efficiency. The algorithm shifts flows from costlier paths to cheaper paths; however, the amount of flow shifted from a costlier path is proportional to not only the travel time but also the flow on the path. It is applied to the Philadelphia and Chicago test problems, while different strategies for choosing the basic paths are examined. The RG algorithm shows an excellent convergence to relative gaps of the order of 1.0E-14 when compared against several reference TAP algorithms.

Network performance evaluation under disruptive events through a progressive traffic assignment model

The purpose of this paper is to present an assignment model as a basis for evaluating the performance of a traffic network, capable of describing its evolution immediately after the occurrence of a disruptive event. First of all, a User-Equilibrium traffic assignment problem is solved in order to obtain an estimation of the system state before the disruption. Starting from the critical event, a Progressive Assignment procedure is performed in order to obtain reasonable traffic assignments on the network, taking into account the users’ tolerance to increases in travel times as well as the inherent inertia of the system. Therefore a metric for the description of the network performance is proposed as well as implementation of the model on a test network.

A Greedy Path-Based Algorithm for Traffic Assignment

This paper presents a new path-based algorithm for the static user equilibrium traffic assignment problem. Path-based algorithms are generally considered less efficient than bush-based counterparts, such as Algorithm B, traffic assignment by paired alternative segments (TAPAS), and iTAPAS, an improved version of TAPAS, because explicitly storing and manipulating paths appears wasteful. However, our numerical experiments indicate that the proposed path-based algorithm can outperform TAPAS or iTAPAS by a wide margin. The proposed algorithm, sharing the same Gauss-Seidel decomposition scheme with existing path-based algorithms, delivered a surprising performance, most likely due to its two main features. First, it adopts a greedy method to solve the restricted subproblem defined on each origin–destination (O-D) pair. Second, instead of sequentially visiting every O-D pair in each iteration, it introduces an intelligent scheme to determine which O-D pairs need more or less work. The proposed algorithm is also more straightforward to implement than bush-based algorithms.

An outer approximation method for the road network design problem

Best investment in the road infrastructure or the network design is perceived as a fundamental and benchmark problem in transportation. Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as a bilevel Discrete Network Design Problem (DNDP) of NP-hard computationally complexity. We engage with the complexity with a hybrid exact-heuristic methodology based on a two-stage relaxation as follows: (i) the bilevel feature is relaxed to a single-level problem by taking the network performance function of the upper level into the user equilibrium traffic assignment problem (UE-TAP) in the lower level as a constraint. It results in a mixed-integer nonlinear programming (MINLP) problem which is then solved using the Outer Approximation (OA) algorithm (ii) we further relax the multi-commodity UE-TAP to a single-commodity MILP problem, that is, the multiple OD pairs are aggregated to a single OD pair. This methodology has two main advantages: (i) the method is proven to be highly efficient to solve the DNDP for a large-sized network of Winnipeg, Canada. The results suggest that within a limited number of iterations (as termination criterion), global optimum solutions are quickly reached in most of the cases; otherwise, good solutions (close to global optimum solutions) are found in early iterations. Comparative analysis of the networks of Gao and Sioux-Falls shows that for such a non-exact method the global optimum solutions are found in fewer iterations than those found in some analytically exact algorithms in the literature. (ii) Integration of the objective function among the constraints provides a commensurate capability to tackle the multi-objective (or multi-criteria) DNDP as well.

Congestion patterns of electric vehicles with limited battery capacity.

The path choice behavior of battery electric vehicle (BEV) drivers is influenced by the lack of public charging stations, limited battery capacity, range anxiety and long battery charging time. This paper investigates the congestion/flow pattern captured by stochastic user equilibrium (SUE) traffic assignment problem in transportation networks with BEVs, where the BEV paths are restricted by their battery capacities. The BEV energy consumption is assumed to be a linear function of path length and path travel time, which addresses both path distance limit problem and road congestion effect. A mathematical programming model is proposed for the path-based SUE traffic assignment where the path cost is the sum of the corresponding link costs and a path specific out-of-energy penalty. We then apply the convergent Lagrangian dual method to transform the original problem into a concave maximization problem and develop a customized gradient projection algorithm to solve it. A column generation procedure is incorporated to generate the path set. Finally, two numerical examples are presented to demonstrate the applicability of the proposed model and the solution algorithm.

A modified Physarum-inspired model for the user equilibrium traffic assignment problem

• A modified Physarum -inspired model for the user equilibrium problem is proposed. • Two-way traffic characteristics and multiple OD pairs are considered. • The proposed Physarum -inspired model is very efficient in terms of both the accuracy and the execution time. The user equilibrium traffic assignment principle is very important in the traffic assignment problem. Mathematical programming models are designed to solve the user equilibrium problem in traditional algorithms. Recently, the Physarum shows the ability to address the user equilibrium and system optimization traffic assignment problems. However, the Physarum model are not efficient in real traffic networks with two-way traffic characteristics and multiple origin–destination pairs. In this article, a modified Physarum -inspired model for the user equilibrium problem is proposed. By decomposing traffic flux based on origin nodes, the traffic flux from different origin–destination pairs can be distinguished in the proposed model. The Physarum can obtain the equilibrium traffic flux when no shorter path can be discovered between each origin–destination pair. Finally, numerical examples demonstrate the rationality and convergence properties of the proposed model.

Direct formulation and algorithms for the probit-based stochastic user equilibrium traffic assignment problem

ABSTRACTThis paper proposes simple and direct formulation and algorithms for the probit-based stochastic user equilibrium traffic assignment problem. It is only necessary to account for random variables independent of link flows by performing a simple transformation of the perceived link travel time with a normal distribution. At every iteration of a Monte-Carlo simulation procedure, the values of the random variables are sampled based on their probability distributions, and then a regular deterministic user equilibrium assignment is carried out to produce link flows. The link flows produced at each iteration of the Monte-Carlo simulation are averaged to yield the final flow pattern. Two test networks demonstrate that the proposed algorithms and the traditional algorithm (the Method of Successive Averages) produce similar results and that the proposed algorithms can be extended to the computation of the case in which the random error term depends on measured travel time.