Route choice models are one of the most important foundations for transportation research. Traditionally, theory-based models have been utilized for their great interpretability, such as logit models and Recursive logit models. More recently, machine learning approaches have gained attentions for their better prediction accuracy. In this study, we propose novel hybrid models that integrate the Recursive logit model with Graph Neural Networks (GNNs) to enhance both predictive performance and model interpretability. To the authors' knowldedge, GNNs have not been utilized for route choice modeling, despite their proven effectiveness in capturing road network features and their widespread use in other transportation research areas. We mathematically show that our use of GNN is not only beneficial for enhancing the prediction performance, but also relaxing the Independence of Irrelevant Alternatives property without relying on strong assumptions. This is due to the fact that a specific type of GNN can efficiently capture multiple cross-effect patterns on networks from data. By applying the proposed models to one-day travel trajectory data in Tokyo, we confirmed their higher prediction accuracy compared to the existing models.
Figures & tables
Figure 1: Conceptual framework of the literature review: research gaps and study positioning. This framework highlights existing research gaps, indicated by dotted lines, and emphasizes the focus of this study, represented by red lines and blocks.
Figure 2: Framework of ResLogit.
Figure 3: Illustrative road network for Recursive Logit model
Figure 4: Framework of ResDGCN-RL. F(⋅) represents the modified DGCN propagation rule.
Figure 5: llustration of neighbor, ingoing and outgoing link pair.
Figure 6: Illustration of four cross-effect patterns. For each pattern, the colored arrows denote links, and the diagrams on the right illustrate the action pairs whose cross-effects can be captured.
Figure 7: A simple network for illustrative example.
Link
Travel time
0→1
0
1→2
1
2→3
2
2→4
1
4→3
1
3→5
1
Table 1: Link features for illustrative example.
Before
After
Path 1
19
25
Path 2
14
24
Path 3
19
–
Path 4
48
51
Table 2: Number of observations choosing each path before and after removing link 4→5
Parameter
RL
Res-RL
ResDGCN-RL
βt
−1.000
−0.608
−0.863
α
–
–
0.994
β
–
–
0.997
γ
–
–
0.996
log-likelihood
−248.491
−229.416
−229.112
Table 3: Estimation result for illustrative example.
Paths
Observed choice probability
Predicted choice probability
RL
Res-RL
ResDGCN-RL
Before
After
Before
After
Before
After
Before
After
Path 1
19.00%
25.00% (+31.57%)
25.00%
33.33% (+33.33%)
21.18%
23.85% (+12.61%)
19.00%
25.00% (+31.57%)
Path 2
14.00%
24.00% (+71.43%)
25.00%
33.33% (+33.33%)
14.05%
24.60% (+75.09%)
14.00%
24.00% (+71.43%)
Path 4
48.00%
51.00% (+6.25%)
25.00%
33.33% (+33.33%)
45.77%
51.55% (+12.61%)
48.00%
51.00% (+6.25%)
Table 4: Choice probabilities before and after removing link 4→5 , where the values in parentheses indicate the relative increase. Notice that the change rates of Paths 1 and 4 in Res-RL are identical. This is due to the missing cross-effect capability. On the other hand, ResDGCN-RL accurately predicts all cases.
Figure 9: Distribution of nonzero elements in Normalized First-order and Second-order proximity.
Figure 10: Visualization of time-varying travel time of link 884.
Parameter
RL
RL-LS
NRL
Res-RL (M=2,λ=0)
ResDGCN- RL (M=2,λ=0)
βTT
-0.737 (0.002)
-0.788 (0.002)
-0.762 (0.005)
-0.603 (0.006)
-0.600 (0.005)
βSpd
0.087 (0.007)
0.221 (0.005)
0.396 (0.007)
-0.007 ∗ ( 0.023)
-0.023 ∗ (0.011)
βRT
-1.610 (0.003)
-1.733 (0.004)
-1.655 (0.010)
-1.605 (0.008)
-1.581 (0.006)
βLC
-0.139 (0.005)
-0.152 (0.004)
-0.318 (0.006)
-0.136 (0.016)
-0.102 (0.008)
βLS
–
-0.172 (0.002)
–
–
–
γTT
–
–
0.118 (0.001)
–
–
Table 5: Parameter estimates (standard errors in parentheses) and model performance comparison across models.
Figure 11: Visualization of the eight links selected for cross-effect analysis. The highlighted red segments represent the target links with their IDs labeled. Note that, in order to enable effective analysis, intersections that are too close to each others are properly aggregated to one node considering their usage patterns in the data using the method of Zhong et al. (2023).
Figure 12: Visualization of θr,0 and θd,0 submatrices (rows 15–23, columns 15–23).
Parameter
Res - RL (M=2,λ=0)
Res - RL (M=2,λ=0.4)
Res - RL (M=2,λ=0.8)
Res - RL (M=2,λ=1.2)
Res - RL (M=2,λ=1.6)
Res - RL (M=2,λ=2)
βTT
-0.603 (0.006)
-0.674 (0.003)
-0.693 (0.011)
-0.710 (0.008)
-0.724 (0.002)
-0.736 (0.006)
βSpd
-0.007 ∗ (0.023)
-0.045 (0.007)
-0.035 (0.002)
-0.015 (0.003)
0.018 (0.004)
0.060 (0.006)
βRT
-1.605 (0.008)
-1.700 (0.008)
-0.167 (0.024)
-0.188 (0.013)
-1.614 (0.003)
-1.619 (0.003)
βLC
-0.136 (0.016)
-0.240 (0.008)
-0.215 (0.011)
-0.187 (0.009)
-0.160 (0.007)
-0.138 (0.005)
Log-likelihood
-64133.562
-71502.867
-88718.571
-103081.914
-116116.002
-119725.300
Penalty
3.885
0.763
0.408
0.234
0.124
0.041
Table 6: Systematic component parameter estimates (standard errors in parentheses) and performance comparison across Res-RL models with different penalty coefficients.
Parameter
ResDGCN - RL (M=2,λ=0)
ResDGCN - RL (M=2,λ=0.4)
ResDGCN - RL (M=2,λ=0.8)
ResDGCN - RL (M=2,λ=1.2)
ResDGCN - RL (M=2,λ=1.6)
ResDGCN - RL (M=2,λ=2)
βTT
-0.600 (0.005)
-0.699 (0.002)
-0.719 (0.001)
-0.731 (0.002)
-0.737 (0.002)
-0.740 (0.002)
βSpd
-0.023 ∗ (0.011)
-0.035 (0.007)
-0.019 ∗ (0.022)
0.004 ∗ (0.004)
0.013 ∗ (0.006)
0.032 (0.006)
βRT
-1.581 (0.006)
-1.708 (0.004)
-1.667 (0.004)
-1.626 (0.003)
-1.596 (0.003)
-1.595 (0.005)
βLC
-0.102 (0.008)
-0.244 (0.015)
-0.222 (0.018)
-0.205 (0.003)
-0.186 (0.004)
-0.165 (0.005)
Log-likelihood
-62726.610
-68936.664
-81324.587
-93140.191
-103654.232
-113392.875
Penalty
8.874
0.663
0.407
0.263
0.172
0.108
Table 7: Systematic component parameter estimates (standard errors in parentheses) and performance comparison across ResDGCN-RL models with different penalty coefficients.
Figure 13: Sensitivity analysis on model depth.
Figure 14: Expected link flow distributions under different models from node 0 to 52 using the link features at 6 p.m. on August 17. The colorbar shows log(1+10000×F) , where F denotes the expected link flow.
Figure 15: The most frequent trajectory from node 0 to 52 and the route with the highest choice probability predicted by different models.
Route
Component
RL
Res-RL (M=2,λ=0)
ResDGCN-RL (M=2,λ=0)
Route predicted by RL
Systematic utility
-21.131
-18.577
-17.727
Total instantaneous utility
-21.131
-22.562
-22.812
Most frequent trajectory
Systematic utility
-29.464
-26.006
-24.836
Total instantaneous utility
-29.464
-18.010
-17.606
Table 8: Systematic and total utility for two routes.
Figure 16: Model performance of temporal holdout (TH) and destination holdout (DH).
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Symbol
Definition
G=⟨A,V⟩
Road network graph; A is the set of nodes and V is the set of links.
A
Adjacency matrix of links.
Aka
Entry of A ; Aka=1 if link a is reachable from link k .
δ(a∣k)
Feasibility indicator; equals 1 if Aka=1 , otherwise 0 .
O(k)
Set of outgoing links from link k .
uRL(a∣k;β)
Instantaneous utility of choosing a from k in RL.
Appendix
Table 9: Notations for the RL model and its variants.
Symbol
Definition
ur(a∣k)
Instantaneous utility of choosing link a from link k in Res-RL.
vr(a∣k)
Systematic component of ur(a∣k) in Res-RL; specified as a linear function of action features.
gr(a∣k)
Residual component of ur(a∣k) in Res-RL.
M
Number of residual layers.
hr,m
m -th hidden layer of Res-RL.
hkar,0
The input layer of Res-RL, which is defined as hkar,0=vr(a∣k) .
Appendix
Table 10: Notations for Res-RL.
Symbol
Definition
ud(a∣k)
Instantaneous utility of choosing link a from link k in ResDGCN-RL (destination-specific).
vd(a∣k)
Systematic component of ud(a∣k) in ResDGCN-RL.
gd(a∣k)
Residual component of ud(a∣k) in ResDGCN-RL learned by the modified DGCN.
Gd
Residual component matrix with entries Gd(k,a)=gd(a∣k) .
hd,m
m -th hidden layer of ResDGCN-RL.
hk,ad,0
The input layer of ResDGCN-RL, which is defined as hk,ad,0=vd(a∣k) . .
Appendix
Table 11: Notations for the ResDGCN-RL model.
Figure 17: A very simple 3-path network for Appendix B.
Parameter
RL
RL-LS
NRL
Res-RL (M=2,λ=0)
ResDGCN- RL (M=2,λ=0)
βTT
-0.745 (0.003)
-0.788 (0.002)
-0.762 (0.005)
-0.603 (0.006)
-0.635 (0.005)
βSpd
0.124 (0.010)
0.221 (0.005)
0.396 (0.007)
-0.007 ∗ ( 0.023)
0.026 (0.008)
βRT
-1.647 (0.004)
-1.733 (0.004)
-1.655 (0.010)
-1.605 (0.008)
-1.606 (0.008)
βLC
-0.181 (0.007)
-0.152 (0.004)
-0.318 (0.006)
-0.136 (0.016)
-0.136 (0.004)
βLS
–
-0.170 (0.004)
–
–
–
γTT
–
–
0.121 (0.005)
–
–
Appendix
Table 12: Parameter estimates (standard errors in parentheses) and model performance comparison across models of temporal holdout .
Parameter
RL
RL-LS
NRL
Res-RL (M=2,λ=0)
ResDGCN- RL (M=2,λ=0)
βTT
-0.740 (0.002)
-0.801 (0.004)
-0.777 (0.005)
-0.582 (0.002)
-0.578 (0.003)
βSpd
0.162 (0.008)
0.161 (0.006)
0.120 (0.004)
-0.014 ( 0.003)
0.010 ∗ (0.011)
βRT
-1.545 (0.003)
-1.733 (0.004)
-1.347 (0.011)
-1.617 (0.006)
-1.585 (0.006)
βLC
-0.171 (0.006)
-0.152 (0.004)
-0.328 (0.009)
-0.141 (0.004)
-0.106 (0.009)
βLS
–
-0.152 (0.003)
–
–
–
γTT
–
–
0.128 (0.014)
–
–
Appendix
Table 13: Parameter estimates of destination holdout(standard errors in parentheses) and model performance comparison across models.
Generalized extreme value models capture dependence among choice alternatives in discrete choice modeling, but require this dependence to be predefined, symmetric, and shared uniformly across individuals. Recent efforts to synergize discrete choice models with deep neural networks have improved predictive performance but still cannot explicitly represent alternative dependence within neural architectures. To address these gaps, we introduce the alternative graph -- a graph in which nodes represent choice alternatives and edges encode their dependence -- and propose Alternative Graph Neural Networks (Alt-GNNs), a family of GNN-based discrete choice models that embed alternative dependence within a unified framework. Theoretically, Alt-GNNs incorporate multinomial logit, nested logit, and ASU-DNN as special cases and enable innovative model designs, including Nested Alt-GNN, Complete Alt-GNN, and Attention Alt-GNN. Alt-GNNs are consistent with random utility maximization theory, enforce behavioral constraints through alternative graphs, and offer a novel graph-based interpretation of utility functions. Empirically, on two travel mode choice datasets from London and Chicago, Alt-GNNs significantly improve predictive performance over all benchmark models in mode choice modeling because of their flexible alternative graph design and vast hyperparameter space. Even the simplest Alt-GNN variant -- Nested Alt-GNN -- generalizes the nested logit model while preserving its unique two-layer substitution properties, enabling graph-based behavioral constraints over otherwise unconstrained behavioral patterns from deep neural networks.
Yuqi Zhou, Zhanhong Cheng, Dingyi Zhuang +3
aDepartment of Urban and Regional Planning, University of Florida · dDepartment of Civil and Environmental Engineering, Massachusetts Institute of Technology · bCollege of Architecture, Texas A&M University +1
Previous methods that predict system-wide travel time, predominantly grounded in graph neural networks, remain limited to typical and recurring demand patterns. While they successfully predict future congestion following daily commute, they inherently approximate a single demand realisation and fail to capture varying route choices. In this work, we propose a Generalised Travel Time Predictor (GenTTP) that successfully differentiates route choices and offers accurate flow and travel time predictions. Our framework learns to uncover complex spatiotemporal traffic patterns and microscopic relationships between route choices and the resulting travel times. This addresses a critical gap: the lack of travel time prediction models that generalise across varying route assignments, where the same demand can produce substantially different network-wide outcomes depending on how travellers are distributed over available paths.
Łukasz Gorczyca, Kacper Drozd, Michał Bujak +1
Jagiellonian University Doctoral School of Exact and Natural Sciences · Jagiellonian University
Autonomous driving systems rely on precise trajectory prediction to plan safe and efficient movement. Graph Neural Networks (GNNs) have become a promising approach for modelling spatiotemporal interactions among road agents. However, designing GNN architectures for trajectory prediction remains non-standardized, with little guidance on which graph layers effectively capture spatial interactions and temporal dynamics. This paper offers a detailed comparative study of 19 graph layer types, focusing on their spatial and temporal processing capabilities to discover the most effective architectures for trajectory prediction. Within the explored hyperparameter setting, we highlight five standout layer combinations, with ARMA, Chebyshev, and topology-aware layers consistently performing better than others. Beyond performance metrics, our findings yield practical design principles: sum-based aggregation is more effective than mean-based methods, multi-head attention mechanisms enable richer interactions, and assigning different weights to different hop distances significantly improves prediction accuracy. These findings offer useful guidance for designing more interpretable and effective trajectory prediction models.