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

Anthony Chen,Seungkyu Ryu,Ludovic Leclercq,Songyot Kitthamkesorn

doi:10.1155/2021/1986851

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.

Highlights

Combined travel demand models have been used as a network equilibrium approach to resolve the inconsistency problem in the traditional four-step travel demand model
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
Our goal is to demonstrate that the improved GP algorithm can solve large-scale multiclass or multimodal traffic assignment problems in combined modal split and traffic assignment (CMSTA) with nested logit (NL) function

Summary

Introduction

Combined travel demand models (or combined models) have been used as a network equilibrium approach to resolve the inconsistency problem (i.e., flow) in the traditional four-step travel demand model (see, e.g., [1]). Please refer to [6, 12, 16, 17] for a review of the different formulation approaches for modeling CDA, CMSTA, and combined travel demand models. Ese combined models have been adopted to represent different emerging technological applications, such as mixed gasoline and electric vehicles with destination, route, and parking choices [16], electric vehicle charging stations using the CDA model [17], and ridesharing as a new mode choice option using the CMSTA model [18]. Most of the above studies adopted either the complete linearization method of the Frank–Wolfe algorithm [19] or the partial linearization method of Evan’s algorithm [2] for solving these emerging technological applications. 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]

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