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.

Multi‐objective optimization of cordon sanitaire with vehicle waiting time constraint

“…An initial trip distribution matrix can be produced by a multinomial logit model with initialized origin‐destination (OD) pair travel times. The trips are then assigned the road network by the state‐of‐the‐art Reduced Gradient (RG) algorithm [36] which is demonstrated to be more efficient than the conventional Frank–Wolfe algorithm. The link travel flows and link travel times can be generated.…”

Peak-easing strategies for urban subway operations in the context of COVID-19 epidemic

“…The traditional equilibrium assignment model, such as the Wardrop equilibrium method, is an integral model ( Zhang et al, 2011 ) that requires a large number of partial derivatives calculations. This makes it difficult to generate multiple points assignments and long-term assignments ( Babazadeh et al, 2020 ). Our model has the advantages in solution scale and speed.…”

Fast Traffic Assignment by Focusing on Changing Edge Flows (Extended Abstract)

“…The critical OD pairs can be identified by tracking edge changes and storing the OD pairs associated with each edge. The convergence of the proposed algorithm is directly compared to the conventional ODBFW, as well as RG (Babazadeh et al 2020) algorithm.…”