Cross‐comparison of convergence algorithms to solve trip‐based dynamic traffic assignment problems

Abstract

Solving a dynamic traffic assignment problem in a transportation network is a computational challenge. This study first reviews the different algorithms in the literature used to numerically calculate the user equilibrium (UE) related to dynamic network loading. Most of them are based on iterative methods to solve a fixed-point problem.Two elements must be computed: the path set and the optimal path flow distribution between all origin-destination pairs. In a generic framework, these two steps are referred to as the outer and the inner loops, respectively. The goal of this study is to assess the computational performance of the inner loop methods that calculate the path flow distribution for different network settings (mainly network size and demand levels). Several improvements are also proposed to speed up convergence: four new swapping algorithms and two new methods for the step size initialization used in each descent iteration. All these extensions significantly reduce the number of iterations to obtain a good convergence rate and drastically speed up the overall simulations. The results show that the performance of different components of the solution algorithm is sensitive to the network size and saturation. Finally, the best algorithms and settings are identified for all network sizes with particular attention being given to the largest scale.

Simulation‐based dynamic traffic assignment: Meta‐heuristic solution methods with parallel computing

“…The MSA algorithm is chosen as a reference algorithm. MSAR and gap-based are chosen as the best algorithms for large-scale networks based on several studies in the literature such as Sbayti et al (2007), Lu et al (2009), Levin, Pool et al (2014), Verbas, Mahmassani, and Hyland (2016), and our comprehensive benchmark on simulation-based DTA solution methods (Ameli et al, 2020). All the experiments are first initiated by the first outer loop with the all-or-nothing assignment algorithm (see Step 1 in Figure 1).…”

“…The main advantage of this framework is that it attempts to find the UE path flow distribution with a minimum number of running a time-dependent shortest path algorithm. The authors performed a comprehensive study on F I G U R E 1 Solution algorithm for trip-based dynamic network equilibrium this framework and proposed an extension to improve the two loops framework (Ameli et al, 2020). Figure 1 presents the optimization framework of this study.…”

“…The green box in Figure 1 presents the classical inner loop structure. For the details of outer loop steps (Steps 1 to 4), readers can refer to Ameli et al (2020).…”

“…The perfect UE means Violation= 0 with = ′ = 0. In this study, the values of and ′ are fixed at 10% based on the study of Ameli, Lebacque, and Leclercq (2020) to evaluate the quality of the solution from a perspective different from . Please note that the Violation indicator is not used in the convergence test.…”

Computational Methods for Calculating Multimodal Multiclass Traffic Network Equilibrium: Simulation Benchmark on a Large-Scale Test Case

“…Based on this indication, several heuristic approaches are proposed to improve the determination of the step size (e.g., [14][15][16]). Ameli et al [17] did a benchmark on most of the heuristic methods in the literature. Here, in addition to heuristic algorithms, we also considered metaheuristic approaches (proposed by [18]) in order to compare different methods to solve the DTA problem.…”