## 3 Materials and Methods
### Proposed MOIBBO-CNN-LSTM  
The proposed MOIBBO-CNN-LSTM model, as illustrated in Figure 4, represents a hybrid DL framework optimized using a MOIBBO algorithm. The figure is divided into two main sections: the upper part depicts the optimization process carried out by MOIBBO, while the lower part shows the CNN-LSTM architecture used for processing input data. The optimization pipeline begins with parameter initialization, followed by the computation of a fitness function, after which nondominated sorting is applied to categorize solutions into different Pareto fronts. If the stopping condition is not met, migration and mutation operators refine the population, generating new candidate solutions in each iteration. Once convergence is reached, the optimal solutions are finalized. The CNN-LSTM component in the lower section of the figure consists of convolutional layers for feature extraction, LSTM layers for sequence modeling, and fully connected layers for final prediction. The MOIBBO optimizer enhances the overall framework by simultaneously optimizing three objective functions (Equations (42)-(44)): the root mean squared error (RMSE), which ensures that predictions are accurate; the total number of CNN layers, which controls the network complexity; and the number of neurons in hidden layers, which balances computational cost and expressiveness. The nondominated sorting approach in MOIBBO ensures that the optimization process explores multiple trade-offs between these objectives, enabling an adaptive and efficient search for the best model configuration. \[F_{1}(\mathbf{x})=\min\left(\frac{1}{N}\sum_{i=1}^{N}[P_{i}-O_{i}]^{2}\right)^ {\frac{1}{2}} \tag{41}\]  
\[F_{2}(\mathbf{x})=\min L \tag{42}\]  
\[F_{3}(\mathbf{x})=\min\sum_{l=1}^{L}Q_{l} \tag{43}\]  
where \(N\) is the number of observations; \(P_{i}\) is the calculated parameter; \(O_{i}\) is the observed parameter; \(L\) represents the total number of hidden layers in the CNN; and \(Q_{l}\) is a binary indicator for the presence of a neuron in layer \(l\). In the CNN-LSTM framework, input data undergo a hierarchical transformation, where CNN first extracts spatial dependencies. The convolutional layers apply filters to detect localized patterns, while the pooling layers reduce dimensionality and retain the most important features. After multiple layers of convolution and pooling, the extracted feature maps are flattened and passed into the LSTM component, where long-term dependencies in the data are learned. Unlike CNN, which only captures spatial features, LSTM processes sequential information by maintaining memory over past observations. This allows the model to handle time-dependent variations, making it particularly effective for applications where historical dependencies play a critical role, such as predictive modeling in IoT  
Figure 4: The flowchart of the proposed MOIBBO-CNN–LSTM model. networks. The integration of MOIBBO with CNN-LSTM offers multiple advantages. Instead of relying on conventional backpropagation-based training, which often leads to overfitting or suboptimal convergence, MOIBBO optimizes the hyperparameters in a global search manner, ensuring that the CNN-LSTM model is not only accurate but also computationally efficient. The migration and mutation mechanisms in MOIBBO actively refine the network architecture, allowing it to self-adjust according to the complexity of the problem. This optimization process ensures that the resulting model does not suffer from unnecessary complexity while still maintaining high predictive accuracy. For our SEE optimization in CF-mMIMO-based IoT networks, the proposed model is particularly well-suited. IoT networks require a balance between EE and security, which is often challenging due to power constraints and dynamic communication environments. The CNN-LSTM framework provides a data-driven approach to optimize SEE, where CNN identifies spatial characteristics of network signals, and LSTM captures temporal variations, making the model highly effective in understanding and predicting network behavior.