A multi-modal network equilibrium model with captive mode choice and path size logit route choice

A Two-Phase Gradient Projection Algorithm for Solving the Combined Modal Split and Traffic Assignment Problem with Nested Logit Function

“…For a detailed description of the GP algorithm, readers should refer to [26,35]. e modifications for solving the CMSTA model with NL modal split function and the improvement strategies for solving large-scale multimodal transportation networks are described as follows.…”

“…See [60] for more detailed results. Based on the literatures (see, e.g., [26,35,61,62]), a unit stepsize (i.e., α � 1.0) is adopted for all iteration n since the second derivative information for an automatic scaling and the one O-D at-a-time flow update strategy is used in the equilibration procedure. is scheme has been found to be helpful in reducing computational efforts.…”

“…Computational results conducted by LeBlanc and Farhangian [20] revealed Evan's partial linearization method performed better than Frank-Wolfe's complete linearization method, while Ryu et al [21] recently demonstrated the superiority of the gradient projection (GP) algorithm over Evan's algorithm. Note that very few studies have focused on developing solution algorithms for solving large-scale problems with multiple modes in a multimodal transportation network [24][25][26].…”

“…On the other hand, the path-based algorithm does not exhibit the zigzagging effect for the same initial solution. In the transportation literature [26,27], the computational performance of link-and pathbased algorithms for the traffic assignment problem is compared in medium-to large-scale randomly generated grid networks and real-size networks. Based on the conclusion, a path-based algorithm is consistently faster in approaching the neighborhood of the optimal solution.…”

Impacts of COVID-19 pandemic on foreign trade intermodal transport accessibility: Evidence from the Yangtze River Delta region of mainland China

“…As discussed by Oyama and Hato, 2017 , Duncan et al, 2020 , and Wang et al (2020) , the choice of the transportation paths of shippers is usually based on the utilities of the paths. The higher utility of a path can correspond to a higher possibility that the path will be chosen.…”