Origin-based Network Assignment

This paper addresses a general stochastic user equilibrium (SUE) traffic assignment problem with link capacity constraints. It first proposes a novel linearly constrained minimization model in terms of path flows and then shows that any of its local minimums satisfies the generalized SUE conditions. As the objective function of the proposed model involves path‐specific delay functions without explicit mathematical expressions, its Lagrangian dual formulation is analyzed. On the basis of the Lagrangian dual model, a convergent Lagrangian dual method with a predetermined step size sequence is developed. This solution method merely invokes a subroutine at each iteration to perform a conventional SUE traffic assignment excluding link capacity constraints. Finally, two numerical examples are used to illustrate the proposed model and solution method.

Strategies to Enhance the Performance of Path‐Based Static Traffic Assignment Algorithms

As the last process of traditional four processes management method, traffic assignment plays an important role both in theory and practice. User Equilibrium (UE) traffic assignment is a basic problem in the field of urban traffic equilibrium assignment and many studies focus on it. Ant colony algorithm is a new simulating evolution algorithm which has solved many typical combinatorial optimization problems. This paper tries to solve UE traffic assignment problem with ant colony algorithm and improve the goal function value and the formula of transition probability according to the character of UE traffic assignment. The algorithm may get brush-fire optimum result and stop earlier in large scale problems. To solve this problem, this paper optimizes the formula of trail pheromone increment and use max-min ant system to limit the concentration of path pheromone into a scope. Finally, a numerical example is given to prove the feasibility and validity of this algorithm; the result is also compared with the one gotten by traditional algorithm.

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.

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.

A new approach to solving dynamic user equilibrium traffic assignment problem

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.

Dynamic user optimal traffic assignment on congested multidestination networks

Algorithms for Solving the Probit Path-Based Stochastic User Equilibrium Traffic Assignment Problem with One or More User Classes

Stochastic traffic assignment, Lagrangian dual, and unconstrained convex optimization

This chapter presents the fundamentals of the theory and techniques of traffic assignment problem. It first presents the steady-state traffic assignment problem formulation which is also called static assignment, followed by Dynamic Traffic Assignment (DTA), where the traffic demand on the network is time varying. The static assignment problem is shown in a mathematical programming setting for two different objectives to be satisfied. The first one where all users experience same travel times in alternate used routes is called user-equilibrium and another setting called system optimum in which the assignment attempts to minimize the total travel time. The alternate formulation uses variational inequality method which is also presented. Dynamic travel routing problem is also reviewed in the variational inequality setting. DTA problem is shown in discrete and continuous time in terms of lumped parameters as well as in a macroscopic setting, where partial differential equations are used for the link traffic dynamics. A Hamilton–Jacobi- based travel time dynamics model is also presented for the links and routes, which is integrated with the macroscopic traffic dynamics. Simulation-based DTA method is also very briefly reviewed. This chapter is taken from the following Springer publication and is reproduced here, with permission and with minor changes: Pushkin Kachroo, and Neveen Shlayan, “Dynamic traffic assignment: A survey of mathematical models and technique,” Advances in Dynamic Network Modeling in Complex Transportation Systems (Editor: Satish V. Ukkusuri and Kaan Ozbay) Springer New York, 2013. 1-25.

Recent methods in the literature to parallelize the traffic assignment problem consider partitioning a network into subnetworks to reduce the computation time. In this article, a partitioning method is sought that generates subnetworks minimizing the computation time of a decomposition approach for solving the traffic assignment (DSTAP). The aim is to minimize the number of boundary nodes, the interflow between subnetworks, and the computation time when the traffic assignment problem is solved in parallel on the subnetworks. Two different methods for partitioning are tested. The first is an agglomerative clustering heuristic that reduces the subnetwork boundary nodes. The second is a flow weighted spectral partitioning algorithm that uses the normalized graph Laplacian to partition the network. The performance of both algorithms is assessed on different test networks. The results indicate that the agglomerative heuristic generates subnetworks with a lower number of boundary nodes, which reduces the per iteration computation time of DSTAP. However, the partitions generated may be heavily imbalanced leading to a higher computation time when the subnetworks are solved in parallel separately at a particular DSTAP iteration. For the Austin network partitioned into four subnetworks, the agglomerative heuristic requires 3.5 times more computation time to solve the subnetworks in parallel. The results also show that the spectral partitioning method is superior for minimizing the interflow between subnetworks. This leads to a faster convergence rate of the DSTAP algorithm.

The standard traffic assignment problem (TAP) is often augmented with additional constraints to address non-standard applications. These models are called TAP with side constraints (TAPSC). Despite the rising significance of TAPSC models, the ability to efficiently solve them to satisfactory precision remains limited in real-world applications. The purpose of this paper is to fill this gap by integrating a recently developed high performance TAP solver, known as the path-based Greedy algorithm, with the augmented Lagrangian multiplier (ALM) method. This paper examines how precisely the subproblems in the ALM method should be solved to optimize the overall convergence performance. It is found that insufficiently converged subproblem solutions sometimes lead to catastrophic failures, although pursuing extremely high precision could also be counterproductive. Accordingly, it is proposed to adjust the precision required to solve the subproblems based on an approximate gap measured by the augmented Lagrangian. Results of numerical experiments show that adaptively adjusting the subproblem precision limit produces a 25% speed-up compared with the algorithm with a fixed limit.

Having recognized the mutual interaction that exists between traffic signal control and route choice behavior, this paper considers the traffic assignment problem for a traffic signal controlled network. The interaction is characterized by (1) the effects of delay, due to traffic signals, on route choice, and (2) the influence of the resulting traffic assignment, due to the changes in route selection, on the timing of traffic signals. In this paper Webster’s method for calculating green splits and the HCM delay model are used to develop a link performance function that implicitly produces optimal signal settings for the arriving traffic volumes. This link-performance function is then used in an assignment procedure to develop a combined traffic signal control/traffic assignment model. The model provides simultaneous solution of the traffic signal control problem and the traffic assignment problem. The result is a set of signal settings that optimally matches the assigned traffic flows. The combined model results in a non-convex problem which produces multiple equilibria. A modification of Wardrop’s two principles is proposed to produce an assignment which converges to a single solution.KeywordsTraffic SignalRoute ChoiceDelay FunctionTraffic AssignmentArrival Flow RateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

User-equilibrium (UE) traffic assignment is widely used in travel forecasting models. Analyses of assignment results often require detailed information about route flows. For a given UE model, total link flows are uniquely determined, but there can be many route flow solutions. Our goal is to evaluate the potential disagreement between different route flow solutions for the same UE model. We considered a case study of a UE model for the Chicago region. We examined 1,000 different UE route flow solutions. Out of 127,248 routes used by UE solutions, 53,134 have alternatives. For 51,748 routes (97%) the flow is completely undetermined, meaning that it is zero in one UE solution and equal to the total origin-destination (O-D) flow in another UE solution. Significant differences were also found in the distribution of users of a given link among O-D pairs (“select link analysis”). We conclude that in analyses that require route flows, it is important to make a proper choice of a specific route flow solution, such as the maximum entropy user equilibrium route flow solution.