## 3 Materials and Methods  
Figure 1 presents the end-to-end architecture of the proposed SE-TFF framework, which integrates feature recalibration and reinforcement learning for robust multi-objective tourism forecasting under sparse data conditions. Table 1 summarizes the mathematical symbols and notations used throughout this section. On the left side of the figure is the SE module, responsible for adaptively re-weighting the input features. The model receives multi-source inputs--environmental, economic, and social features--encoded as a unified feature tensor. These inputs are first combined through an element-wise addition operation. The resulting aggregated feature is passed through a Squeeze block, where a global pooling operation extracts global statistical descriptors across the temporal dimension. These pooled representations are then fed into an excitation block, comprising a two-layer fully connected network with ReLU and sig \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Description** \\ \hline \(x_{l}(t)\) & The value of the \(i\)-th state variable at time \(t\) \\ \(F\) & Feature vector (input to the SE mechanism) \\ \(W_{1},W_{2}\) & Learnable parameter matrices (SE mechanism) \\ \(\sigma(\cdot)\) & Sigmoid activation function \\ \(s_{c}\) & Global descriptor for the \(c\)-th feature channel (computed via global average pooling) \\ \(H\times W\) & Spatial dimensions of the feature map \\ \(z,v,u\) & Intermediate variables in the SE mechanism (outputs of the fully connected layers) \\ \(w_{c}\) & Weight for the \(c\)-th feature channel (computed via the SE mechanism) \\ \(w_{j}\) & Weight coefficient for the \(j\)-th objective function \\ \(\lambda p(t)\) & Penalty term for constraint violation \\ \(r(t)\) & Reward function in reinforcement learning \\ \(\lambda_{1},\lambda_{2},\lambda_{3}\) & Reward coefficients for environmental, economic, and social indices \\ \(\chi_{\text{old}},\chi_{\text{new}}\) & Old and new solutions in the optimization problem \\ \(\delta\) & Step size in local search \\ \(N(\theta,1)\) & Normal distribution with mean \(\theta\) and variance 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbol table. Figure 1: The framework of our study. moid activations. This network generates channel-wise weights, which are applied in the Weighting stage to emphasize task-relevant feature channels dynamically. The recalibrated features serve as the high-quality representation for downstream forecasting. On the right side is the reinforcement learning (RL) module, which optimizes the forecasting strategy via dynamic multi-objective balancing. The recalibrated feature tensor is fed into the RL agent, which maintains a value function to evaluate each state. Using state transition dynamics and observed rewards (e.g., prediction error, constraint violation), the agent iteratively updates the Return signal. Based on this Return, the system derives a global optimal decision using the learned value policy. The decision is influenced by a degree of approximation, which reflects task complexity and data sparsity. The Final output layer produces three parallel forecasts: tourist arrivals, tourism revenue, and accommodation demand, enabling multi-task prediction. Together, the SE module ensures high-quality feature encoding tailored to contextual factors, while the RL module adaptively learns optimal trade-offs across competing forecasting goals. Figure 2 focuses specifically on the internal structure of the SE module. As a core component of the feature recalibration stage in SE-TFF, the SE module dynamically adjusts the importance of environmental, economic, and social inputs via a Squeeze-and-Excitation mechanism. The detailed flow shown in Figure 2 complements the high-level pipeline by providing an interpretable breakdown of how contextual attention weights are derived and applied to input features before they are passed to the reinforcement learning module.