# A Hybrid Control Path Planning Architecture Based on Traffic Equilibrium Assignment for Emergency
## 4 The Proposed Hybrid Control Architecture for Path Planning
### Spatial Feature Extraction Based on Hierarchy Graph Convolution  
To extract spatial features of OD and background load, we uniformly adopted a hierarchy graph convolution. The real-time OD data are then counted for each network node by time slices to form the OD evacuation volume. With the time dimension, the OD evacuation volume carries real-time spatial trend information. The graph convolutional networks have been widely applied to extract spatial features in status snapshots of traffic network [38; 40]. The topology of the traffic graph can be well portrayed by the Laplace matrix. The first-order Chebyshev graph convolution [45] simplified as \(\Theta*x\approx\theta(\hat{D}^{-\frac{1}{2}}\hat{A}\hat{D}^{-\frac{1}{2}})x\), where \(\theta(\hat{D}^{-\frac{1}{2}}\hat{A}\hat{D}^{-\frac{1}{2}})\) is the approximating convolution filter, \(x\) is the input feature. Thus, the traffic status of one node in the road network can be treated as an aggregation of surrounding traffic. The perception field of the graph convolution can be expanded by stacking multiple GCNs embedded in the network. The feature transfer between the GCN layers is as in Equation (7):  
\[H^{(l+1)}=\Gamma^{(GCN)}(\hat{D}^{-\frac{1}{2}}\hat{A}\hat{D}^{-\frac{1}{2}} \cdot H^{(l)}\cdot\Theta^{(l)}). \tag{7}\]  
\(H^{(l)}\) denotes the output vector of the \(l\)-th layer, and \(\Gamma^{(GCN)}\) is the ReLU activation function for performing the first-order spectral convolution. The GCN layer finally converts the input traffic background flow or OD evacuation volume \(X^{t}{=}(x_{1}^{t},\cdots,x_{i-1}^{t},x_{i}^{t})\) into a code \(H^{t}{=}(h_{1}^{t},\cdots,h_{i-1}^{t},h_{i}^{t})\). In a real road network, due to the complex connectivity of geographic space, it is not enough to explore the intrinsic relationships and regularities from the individual features of the nodes [46]. The network nodes form the OD volume matrix have extremely high dimensionality. It records all node-to-node traffic volumes. Since some intersections are low-level and often have no vehicles passing through them, the OD data are extraordinarily sparse, which usually makes it difficult to capture the effective trend characteristics carried by real-time OD. Moreover, it is impractical to use such a fine-grained road network to analyze and calculate traffic features. The spatial features can be further aggregated by semantic information and described in a coarse-grained manner. The grid partition is a commonly used method for coarse-grained road network analysis, but the equidistant grid scales tend to disrupt the semantic relationships of the roads. The contraction hierarchy [47] generates a hierarchy structure by iteratively merging the lower ranked nodes in the road network. The contraction process is continuously adding the shortcuts to the edge set, and finally obtaining an overlay graph \(G_{\uparrow}:=(N_{\uparrow},R_{\uparrow})\) that preserves the shortest path feature of the original graph. After the coarse-grained contraction of the road sections, the traffic graph structural complexity and connection sparsity were improved. Furthermore, we encoded the coarse-grained spatial features based on the overlay graph \(G_{\uparrow}\) through the hierarchy graph convolution and skip graph  
Figure 1: The hybrid control architecture for path planning based on equilibrium traffic assignment. convolution, as shown in Figure 2. The neurons represent links in \(G_{\uparrow}\) and their activation statuses correspond to their traffic. The weight on the link can be interpreted as the probability of traffic assignment. The hierarchy features of nodes in \(G_{\uparrow}\) are encoded using graph convolution for the node that can be contracted.