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

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.

A P-Hub Location Problem for Determining Park-and-Ride Facility Locations with the Weibit-Based Choice Model

“…Similarly, we have the MNW travel choice model in Equations ( 12) and ( 13). Hence, the MILP in Equations ( 14)-( 17) and (19), and Equations ( 23)- (26) gives the optimum number of the P&R facility users under the MNW choice behavior. This completes the proof.…”

“…These two drawbacks stem from the independently and identically distributed (IID) assumption embedded in the random error term of the MNL model [23]. In the hypernetwork, the MNL model cannot account for route similarity (route correlation or route overlapping) [20,[24][25][26] and the heterogeneous perception variance from different trip lengths [22,27]. It has been shown that heterogeneity is an important factor of the P&R facility location selection [28].…”

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

“…However, as aforementioned, some travelers are captive to one travel mode for most daily trips due to social, economic, and physical issues. Few studies consider mode captivity in the combined travel choice problems, only one paper (to the best of our knowledge) focuses on algorithm development for solving an MMNE problem with considering captive mode traveler and route overlapping (Ryu et al, 2018). In this paper, we consider the captive mode travelers in the MMNE problem by adopting the dogit model (Gaudry and Dagenais, 1979) to consider the captive mode choice behavior, and the path-size logit (PSL, Ben-Akiva and Bierlaire, 1999) The paper contributes to the literature in two aspects:…”