Simulation-based user equilibrium: improving the fixed point solution methods
Résumé
Calculating dynamic network equilibrium is a challenging problem. This study first analyzes the different frameworks for the simulation-based User Equilibrium (UE) in the literature. Most of them are based on solving a fixed-point problem by iterative methods. Two elements have to be determined: the path set between all origin-destination pairs and the optimal path flow distribution. The most advanced solution methods expressed the problem with two-layers, the outer and the inner loop, that tackle each element respectively. The goal of this study is to improve the inner loop, i.e. the path flow calculation. The first improvement is keeping the best assignment pattern during the inner loop iterations and send it to the outer loop. It improves the solution quality in trip-based traffic assignment because flows are then discretized into units of user, which makes the point-fix calculation much harder. This study proposes three new swapping methods and two new methods for the step size initialization that is used in each descent iteration. Moreover, this study proposes two alternative methods to initialize the path flow distribution at the beginning of the outer loop. Two quality indicators are considered to examine the quality of UE solution and then the methods are applied to three networks with different sizes (small, medium and large). The results show that the performance of different components of the solution algorithm is sensitive to the network size. Finally, the best configurations of the solution algorithms are recommended for all network sizes with a particular focus on the large-scale.