A computational study of traffic assignment algorithms (original) (raw)
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Computational Study of Traffic Assignment Algorithms
2013
Traffic congestion is an issue in most cities worldwide. One way to model and analyse the effect of congestion and other factors on route choice behaviour and to predict the impact of traffic management projects and transport policies is traffic assignment (TA). The most commonly used TA model is known as user equilibrium (UE), which is based on the assumption that all drivers want to minimise their travel time or generalised cost. As a result, an equilibrium is achieved when no one has an incentive to switch to another route. Although the conventional mathematical model of TA belongs to the convex optimisation domain and, hence, is relatively easy to solve, efficient algorithms are required in order to be able to solve TA in a reasonable amount of time for realistic transport networks. This motivates researchers to propose numerous methods and algorithms to solve this problem in the literature. However, there is no comprehensive empirical study that compares the performance of different approaches on benchmark instances. In this study, our objective is to fill this gap. We provide a literature review of the most promising methods. We classify algorithms according to the way the solution is represented, namely, link-based (solution is represented by link flows), path-based (solution is represented by path flows) and origin-based (solution is represented by link flows corresponding to each origin), and implement the most representative algorithms in each group. We perform numerical tests on benchmark instances of various sizes, compare the algorithms and analyse the impact of their main components on their running time. We also study the convergence behaviour of the methods with respect to different levels of solution accuracy.
Procedia - Social and Behavioral Sciences, 2012
Many algorithms have been investigated extensively for decades to solve the user equilibrium (UE) assignment problem, and new algorithms are actively proposed even in this new century. The first objective of this study is to compare the performance of the proposed algorithms on several practical networks and demonstrate their characteristics empirically. At earlier stages of iteration, every algorithm shows a fairly similar performance of convergence with regard to the calculation time, but at later stages of iteration, advanced algorithms exhibit faster performance. The use of some of these fast algorithms results in the convergence error reaching the maximum limit of arithmetic precision of the computer, which means that a virtually exact solution can be achieved. The second objective of this study is to investigate the convergence error and seek an appropriate convergence criterion for the UE assignment in practice. We found that the difference between the temporal and exact solutions for the link flow (i.e., convergence error of the link flow) is nearly proportional to the duality gap of the mathematical optimization problem equivalent to the UE traffic assignment problem. This means that the convergence error of a link flow can possibly be estimated from the duality gap.
Cost driven traffic assignment in transportation networks
International Journal of Modelling in Operations Management, 2013
A cost driven traffic assignment model is proposed to maximise the global benefit of transportation network users. A decentralised primal-dual time synchronised approach is used to solve for the optimal traffic rates subjecting the objective function to the bounds of the network tolerable costs. For a successful operation of the transportation network, the affordable upper bounds on the costs have to be set carefully. A breakeven analysis was presented to estimate the network charges. It came across that the longer the route, the higher its charge. The breakeven surcharges represent the minimum quantities a network may charge from its commuters for a profitable operation. The presented scheme demonstrates a great control on the queue sizes and motivates resource allocation in heterogeneous transportation networks. The experimental results reveal an attractive convergence, performance and sensible resource assignment between the network users while achieving comprehensive optimality in a distributed approach.
Reduced gradient algorithm for user equilibrium traffic assignment problem
Transportmetrica A: Transport Science, 2020
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.
Link- and Path-Based Traffic Assignment Algorithms: Computational and Statistical Study
Transportation Research Record: Journal of the Transportation Research Board, 2002
The computational performance of five algorithms for the traffic assignment problem (TAP) is compared with that of mid- to large-scale randomly generated grid networks. The applied procedures include the Frank-Wolfe, PARTAN, gradient projection, restricted simplicial decomposition, and disaggregate simplicial decomposition algorithms. A statistical analysis is performed to determine the relative importance of various properties (network size, congestion level, solution accuracy, zone-node ratio) of the traffic assignment problem for the five selected algorithms. Regression models, which measure central processing unit time and number of iterations consumed by each algorithm using various factors and their combinations, are derived to provide a quantitative evaluation. Ultimately, the findings of this research will be useful in guiding transportation professionals to choose suitable solution algorithms and to predict the resulting algorithm performance in TAPs.
A Framework for the Evaluation of Methods for Road Traffic Assignment
Research in traffic assignment relies largely on experimentation. The outcomes of experiments using different traffic assignment methods on different road network scenarios may vary greatly. It is difficult for the reader to assess the quality of the results without prior knowledge about the difficulty of the road network. In the current work, we propose an approximate metric to characterise the difficulty of network scenarios which takes travellers’ origins and destinations as well as link capacities into account rather than relying on the size of the network. As this metric considers number of overlapping routes between the origins and destinations of the travelles, a higher number in the metric would indicate a higher possibility of congestion in the road network scenario.
Path-Constrained Traffic Assignment: Model and Algorithm
Transportation Research Record, 2012
This paper presents a mathematical programming model and solution method for the path-constrained traffic assignment problem, in which route choices simultaneously follow the Wardropian equilibrium principle and yield the distance constraint imposed on the path. This problem is motivated by the need for modeling distance-restrained electric vehicles in congested networks, but the resulting modeling and solution method can be applied to various conditions with similar path-based constraints. The equilibrium conditions of the problem reveal that any path cost in the network is the sum of corresponding link costs and a path-specific out-of-range penalty term. The suggested method, based on the classic Frank-Wolfe algorithm, incorporates an efficient constrained shortest path algorithm as its subroutine. This algorithm fully exploits the underlying network structure of the problem and is relatively easy to implement. Numerical results from the provided example problems clearly show how the equilibrium conditions are reshaped by the path constraint and how the traffic flow patterns are impacted by different constraint tightness levels.
User equilibrium traffic assignment: k paths subtracting-adding algorithm
ArXiv, 2021
The traffic assignment problem is one of the most important transportation planning problems. The task faced by transportation planners, traffic engineers, and computer scientists is to generate high quality, approximate solutions of users equilibrium, that enable traffic scenario comparisons in a reasonable CPU time. We introduce the k Paths Subtracting-Adding (k-PSA) algorithm to approximate the user equilibrium of the traffic assignment problem. The k-PSA algorithm consists of two alternating phases: (1) enlargement of the set of attractive paths; (2) subtracting-adding trips between generated attractive paths for each origin-destination pair of nodes. The proposed algorithm performs the two phases iteratively until the number of paths for each origin-destination pair is k. We tested the proposed algorithm on four benchmark transportation networks from the literature. The performed numerical tests show that the proposed approach generates, in short, computation times, solutions t...
Computer-Aided Civil and Infrastructure Engineering
This paper presents a decomposition scheme to find near-optimal solutions to a cell transmission model-based system optimal dynamic traffic assignment problem with multiple origin-destination pairs. A linear and convex formulation is used to define the problem characteristics. The decomposition is designed based on the Dantzig-Wolfe technique that splits the set of decision variables into subsets through the construction of a master problem and subproblems. Each subproblem includes only a single origin-destination pair with significantly less computational burden compared to the original problem. The master problem represents the coordination between subproblems through the design of interactive flows between the pairs. The proposed methodology is implemented in two case study networks of 20 and 40 intersections with up to 25 origin-destination pairs. The numerical results show that the decomposition scheme converges to the optimal solution, within 2.0% gap, in substantially less time compared to a benchmark solution, which confirms the computational efficiency of the proposed algorithm. Various network performance measures have been assessed based on different traffic state scenarios to draw managerial insights. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.