Incorporating graph neural network into route choice model

Yuxun Ma; Toru Seo

cs.LGMar 4, 2025

Incorporating graph neural network into route choice model

Authors: Yuxun Ma, Toru Seo

Organizations: Department of Civil and Environmental Engineering, Institute of Science Tokyo, 2-12-1-M6-10, Meguro, Ookayama, 152-8552, Tokyo, Japan

Abstract

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 3: Illustrative road network for Recursive Logit model

Figure 4: Framework of ResDGCN-RL. $F(\cdot)$ 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
$0\rightarrow 1$	0
$1\rightarrow 2$	1
$2\rightarrow 3$	2
$2\rightarrow 4$	1
$4\rightarrow 3$	1
$3\rightarrow 5$	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\rightarrow 5

Parameter	RL	Res-RL	ResDGCN-RL
$\beta_{t}$	$-1.000$	$-0.608$	$-0.863$
$\alpha$	–	–	$0.994$
$\beta$	–	–	$0.997$
$\gamma$	–	–	$0.996$
log-likelihood	$-248.491$	$-229.416$	$-229.112$

Table 3: Estimation result for illustrative example.

Paths	Observed choice probability		Predicted choice probability
	Observed 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\rightarrow 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 8: An aggregate road network. Source: © OpenStreetMap contributors, available under the Open Database License (ODbL).

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 $(M=2,\lambda=0)$	ResDGCN- RL $(M=2,\lambda=0)$
$\beta_{\mathrm{TT}}$	-0.737 (0.002)	-0.788 (0.002)	-0.762 (0.005)	-0.603 (0.006)	-0.600 (0.005)
$\beta_{\mathrm{Spd}}$	0.087 (0.007)	0.221 (0.005)	0.396 (0.007)	-0.007 ∗ ( 0.023)	-0.023 ∗ (0.011)
$\beta_{\mathrm{RT}}$	-1.610 (0.003)	-1.733 (0.004)	-1.655 (0.010)	-1.605 (0.008)	-1.581 (0.006)
$\beta_{\mathrm{LC}}$	-0.139 (0.005)	-0.152 (0.004)	-0.318 (0.006)	-0.136 (0.016)	-0.102 (0.008)
$\beta_{\mathrm{LS}}$	–	-0.172 (0.002)	–	–	–
$\gamma_{\mathrm{TT}}$	–	–	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 $\theta^{r,0}$ and $\theta^{d,0}$ submatrices (rows 15–23, columns 15–23).

Parameter	Res - RL $(M=2,\lambda=0)$	Res - RL $(M=2,\lambda=0.4)$	Res - RL $(M=2,\lambda=0.8)$	Res - RL $(M=2,\lambda=1.2)$	Res - RL $(M=2,\lambda=1.6)$	Res - RL $(M=2,\lambda=2)$
$\beta_{\mathrm{TT}}$	-0.603 (0.006)	-0.674 (0.003)	-0.693 (0.011)	-0.710 (0.008)	-0.724 (0.002)	-0.736 (0.006)
$\beta_{\mathrm{Spd}}$	-0.007 ∗ (0.023)	-0.045 (0.007)	-0.035 (0.002)	-0.015 (0.003)	0.018 (0.004)	0.060 (0.006)
$\beta_{\mathrm{RT}}$	-1.605 (0.008)	-1.700 (0.008)	-0.167 (0.024)	-0.188 (0.013)	-1.614 (0.003)	-1.619 (0.003)
$\beta_{\mathrm{LC}}$	-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 $(M=2,\lambda=0)$	ResDGCN - RL $(M=2,\lambda=0.4)$	ResDGCN - RL $(M=2,\lambda=0.8)$	ResDGCN - RL $(M=2,\lambda=1.2)$	ResDGCN - RL $(M=2,\lambda=1.6)$	ResDGCN - RL $(M=2,\lambda=2)$
$\beta_{\mathrm{TT}}$	-0.600 (0.005)	-0.699 (0.002)	-0.719 (0.001)	-0.731 (0.002)	-0.737 (0.002)	-0.740 (0.002)
$\beta_{\mathrm{Spd}}$	-0.023 ∗ (0.011)	-0.035 (0.007)	-0.019 ∗ (0.022)	0.004 ∗ (0.004)	0.013 ∗ (0.006)	0.032 (0.006)
$\beta_{\mathrm{RT}}$	-1.581 (0.006)	-1.708 (0.004)	-1.667 (0.004)	-1.626 (0.003)	-1.596 (0.003)	-1.595 (0.005)
$\beta_{\mathrm{LC}}$	-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.

Panel of Figure 14 — 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 $\log(1+10000\times F)$ , 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 $(M=2,\lambda=0)$	ResDGCN-RL $(M=2,\lambda=0)$
Route predicted by RL	Systematic utility	-21.131	-18.577	-17.727
Route predicted by RL	Total instantaneous utility	-21.131	-22.562	-22.812
Most frequent trajectory	Systematic utility	-29.464	-26.006	-24.836
Most frequent trajectory	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
$G=\langle\mathcal{A},\mathcal{V}\rangle$	Road network graph; $\mathcal{A}$ is the set of nodes and $\mathcal{V}$ is the set of links.
$A$	Adjacency matrix of links.
$A_{ka}$	Entry of $A$ ; $A_{ka}=1$ if link $a$ is reachable from link $k$ .
$\delta(a\mid k)$	Feasibility indicator; equals $1$ if $A_{ka}=1$ , otherwise $0$ .
$O(k)$	Set of outgoing links from link $k$ .
$u^{\mathrm{RL}}(a\mid k;\beta)$	Instantaneous utility of choosing $a$ from $k$ in RL.

Appendix

Table 9: Notations for the RL model and its variants.

Symbol	Definition
$u^{r}(a\mid k)$	Instantaneous utility of choosing link $a$ from link $k$ in Res-RL.
$v^{r}(a\mid k)$	Systematic component of $u^{r}(a\mid k)$ in Res-RL; specified as a linear function of action features.
$g^{r}(a\mid k)$	Residual component of $u^{r}(a\mid k)$ in Res-RL.
$M$	Number of residual layers.
$h^{r,m}$	$m$ -th hidden layer of Res-RL.
$h^{r,0}_{ka}$	The input layer of Res-RL, which is defined as $h^{r,0}_{ka}=v^{r}(a\mid k)$ .

Appendix

Table 10: Notations for Res-RL.

Symbol	Definition
$u^{d}(a\mid k)$	Instantaneous utility of choosing link $a$ from link $k$ in ResDGCN-RL (destination-specific).
$v^{d}(a\mid k)$	Systematic component of $u^{d}(a\mid k)$ in ResDGCN-RL.
$g^{d}(a\mid k)$	Residual component of $u^{d}(a\mid k)$ in ResDGCN-RL learned by the modified DGCN.
$G^{d}$	Residual component matrix with entries $G^{d}(k,a)=g^{d}(a\mid k)$ .
$h^{d,m}$	$m$ -th hidden layer of ResDGCN-RL.
$h^{d,0}_{k,a}$	The input layer of ResDGCN-RL, which is defined as $h^{d,0}_{k,a}=v^{d}(a\mid k)$ . .

Appendix

Table 11: Notations for the ResDGCN-RL model.

Parameter	RL	RL-LS	NRL	Res-RL $(M=2,\lambda=0)$	ResDGCN- RL $(M=2,\lambda=0)$
$\beta_{\mathrm{TT}}$	-0.745 (0.003)	-0.788 (0.002)	-0.762 (0.005)	-0.603 (0.006)	-0.635 (0.005)
$\beta_{\mathrm{Spd}}$	0.124 (0.010)	0.221 (0.005)	0.396 (0.007)	-0.007 ∗ ( 0.023)	0.026 (0.008)
$\beta_{\mathrm{RT}}$	-1.647 (0.004)	-1.733 (0.004)	-1.655 (0.010)	-1.605 (0.008)	-1.606 (0.008)
$\beta_{\mathrm{LC}}$	-0.181 (0.007)	-0.152 (0.004)	-0.318 (0.006)	-0.136 (0.016)	-0.136 (0.004)
$\beta_{\mathrm{LS}}$	–	-0.170 (0.004)	–	–	–
$\gamma_{\mathrm{TT}}$	–	–	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 $(M=2,\lambda=0)$	ResDGCN- RL $(M=2,\lambda=0)$
$\beta_{\mathrm{TT}}$	-0.740 (0.002)	-0.801 (0.004)	-0.777 (0.005)	-0.582 (0.002)	-0.578 (0.003)
$\beta_{\mathrm{Spd}}$	0.162 (0.008)	0.161 (0.006)	0.120 (0.004)	-0.014 ( 0.003)	0.010 ∗ (0.011)
$\beta_{\mathrm{RT}}$	-1.545 (0.003)	-1.733 (0.004)	-1.347 (0.011)	-1.617 (0.006)	-1.585 (0.006)
$\beta_{\mathrm{LC}}$	-0.171 (0.006)	-0.152 (0.004)	-0.328 (0.009)	-0.141 (0.004)	-0.106 (0.009)
$\beta_{\mathrm{LS}}$	–	-0.152 (0.003)	–	–	–
$\gamma_{\mathrm{TT}}$	–	–	0.128 (0.014)	–	–

Appendix

Table 13: Parameter estimates of destination holdout(standard errors in parentheses) and model performance comparison across models.

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Abstract

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