# Airport Field Path Optimization Method Based on Conflict Hotspot Avoidance Mechanism
## 2 Modelling  
### Identification of Key Conflict Hotspot Areas  
Currently, most hotspot identification in airport fields relies on static hotspots derived from historical data, which do not take into account the temporal and spatial variations in traffic flow. To address this limitation, this section utilizes findings from another study by the authors. It employs the Gated Recurrent Unit (GRU) model, along with a self-attention mechanism to develop a dynamic risk indicator prediction model for airport surfaces. This model aims to identify critical conflict hotspot areas more effectively.  
The field dynamic risk indicator prediction model includes an input layer, a GRU layer, a self-attention mechanism layer, a fully connected layer, and an output layer. To prevent overfitting, the dropout layer is set after each GRU layer. Among them, the forward propagation formula [31] for the GRU layer is as follows:  
\[r_{t}=\sigma(W_{r}[h_{t-1},x_{t}]_{r}) \tag{1}\]  
\[z_{t}=\sigma(W_{z}[h_{t-1},x_{t}]) \tag{2}\]  
\[h^{\prime}_{t}=\tanh(W_{h^{\prime}}[r_{t}\times h_{t-1},x_{t}]) \tag{3}\]  
\[h_{t}=(1-z_{t})\times h_{t-1}+z_{t}\times h^{\prime}_{t} \tag{4}\]  
where \(x_{t}\) is the input at the current moment \(t\); \(z_{t}\) is the update gate; \(r_{t}\) is the reset gate; \(h^{\prime}_{t}\) is the memory storage state; \(h_{t}\) is the output at the current moment \(t\); \(h_{t-1}\) is the output at the previous moment; \(W_{r},W_{z},W_{h^{\prime}}\) are the matrices of the weight coefficients to be learned; \(\sigma\) is the sigmoid activation function; and \(\tanh\) is the activation function.  
The formula for the self-attention layer is as follows:  
\[q_{i} =W^{q}h_{i} \tag{5}\] \[k_{i} =W^{k}h_{i}\] (6) \[v_{i} =W^{v}h_{i}\] (7) \[a_{t,i} =\frac{q_{t}\bullet k_{t}^{T}}{\sqrt{d}}\] (8) \[a_{t,i}^{\prime} =softmax(a_{t,i})\] (9) \[\hat{h}_{t} =\sum\limits_{i}a_{t,i}^{\prime}v_{i} \tag{10}\]  
where \(h_{i}\) denotes the implicit state feature of the \(ith\) output time step of the output in the GRU layer; \(q,\ k,\ v\) denote \(Query,\ Key,\ Value\) in the attention mechanism, respectively; \(W^{q}\), \(W^{v}\) denote the matrices of the weight coefficients; \(d\) denotes the variance of the elements of the \(q\times k^{T}\) matrix for solving the gradient vanishing problem, where \(q=(q_{t-T+1},\cdots q_{t})^{T}\), \(k=(k_{t-T+1},\cdots k_{t})^{T}\); \(a_{t,i}^{\prime}\) denotes the attention score, i.e., the weight of the time step \(i\) on the time step \(t\); and \(\hat{h}_{t}\) denotes the value of the time step \(t\) weighted by the attention score. The \(soft\)max function is a normalized exponential mapping that takes any real vector scaled by \(\exp(\cdot)\) and normalizes it by the sum, outputting a set of probability weights between 0 and 1 and summing to 1, thus highlighting the relative advantage of high-scoring elements.  
For the above neural network model, the loss function is defined as follows:  
\[\textit{Los}=\frac{\sum\limits_{n=1}^{N}\sum\limits_{t=1}^{T}\left(y_{n,t}^{ \prime}-y_{n,t}\right)^{2}}{NT} \tag{11}\]  
where \(N\) is the number of potential conflict hotspot regions; \(T\) is the total number of predicted time steps; \(y_{n,t}^{\prime}\) is the predicted value of the \(n\ th\) potential conflict hotspot region at the \(t\ th\) time step; and \(y_{n,t}\) is the labeled value of the \(n\ th\) potential conflict hotspot region at the \(t\ th\) time step.