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Title: A two-phase gradient projection algorithm for solving the combined modal split and traffic assignment problem with nested logit function
Authors: Ryu, S
Chen, A 
Kitthamkesorn, S
Issue Date: 2021
Source: Journal of advanced transportation, 2021, v. 2021, 1986851
Abstract: This study provides a gradient projection (GP) algorithm to solve the combined modal split and traffic assignment (CMSTA) problem. The nested logit (NL) model is used to consider the mode correlation under the user equilibrium (UE) route choice condition. Specifically, a two-phase GP algorithm is developed to handle the hierarchical structure of the NL model in the CMSTA problem. The Seoul transportation network in Korea is adopted to demonstrate an applicability in a large-scale multimodal transportation network. The results show that the proposed GP solution algorithm outperforms the method of the successive averages (MSA) algorithm and the classical Evan's algorithm.
Publisher: John Wiley & Sons
Journal: Journal of advanced transportation 
ISSN: 0197-6729
EISSN: 2042-3195
DOI: 10.1155/2021/1986851
Rights: © 2021 Seungkyu Ryu et al.
This is an open access article distributed under the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The following publication Seungkyu Ryu, Anthony Chen, Songyot Kitthamkesorn, "A Two-Phase Gradient Projection Algorithm for Solving the Combined Modal Split and Traffic Assignment Problem with Nested Logit Function", Journal of Advanced Transportation, vol. 2021, Article ID 1986851, 18 pages, 2021 is available at
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