## 3 Proposal
### Energy Consumption Prediction  
After refining the acquired data, the EECP is accomplished using the metaheuristics-based LSTM network. The LSTM network is an extension of a Recurrent Neural Network (RNN). The RNN has numerous problems, such as short-term memory and vanishing gradient issues, when it processes large data sequences [38]. In addition, the RNN is inappropriate for larger data sequences because it removes the important information from the input data. In the RNN model, the gradient updates the weights during back propagation, where sometimes it reduced highly and the initial layers get low gradient and stops further learning. To tackle these issues, the LSTM network was developed by [PERSON] [39]. The LSTM network overcomes the issues of RNNs by replacing hidden layers with memory cells for modelling long-term dependencies. The LSTM network includes dissimilar gates, such as a forget gate, input gate, and output gate, along with activation functions for learning time-based relations. The LSTM network and the individual LSTM unit are graphically depicted in Figures 4 and 5. Figure 3: Refined data samples of (**a**) the AEP dataset and (**b**) the IHEPC dataset. The mathematical expressions of the input gate \(in_{t}\), forget gate \(f_{t}\), cell \(c_{t}\), and output gate \(ou_{t}\) are defined in Equations (3)-(6):  
\[in_{t}=\sigma(W_{inh}h_{t-1}+W_{ina}a_{t}+b_{in}) \tag{3}\]  
\[f_{t}=\sigma(W_{fh}h_{t-1}+W_{fa}a_{t}+b_{f}) \tag{4}\]  
\[c_{t}=f_{t}\odot c_{t-1}+in_{t}\odot\tanh(W_{ch}h_{t-1}+W_{ca}a_{t}+b_{c}) \tag{5}\]  
\[ou_{t}=\sigma(W_{outh}h_{t-1}+W_{oua}a_{t}+b_{ou}) \tag{6}\]  
where \(t\) represents different time steps, \(a_{t}=A[t,\,.\,]\in\mathbb{R}^{F}\) represents temporal quasi-periodic feature vectors, \(tanh\) (.) denotes a hyperbolic tangent function, \(\sigma(. )\) states a sigmoid function, and \(W\) and \(b\) work coefficients. The output of the LSTM unit \(h_{t-1}\) is mathematically specified in Equation (7), and it is graphically presented in Figure 5:  
\[h_{t}=ou_{t}\odot\tanh(c_{t}) \tag{7}\]  
The cell state \(\{c_{t}|t=1,2...T\}\) learns the necessary information from \(a_{t}\) on the basis of the dependency relationship during the training and testing mechanism. Finally, the extracted feature vectors are specified by the last LSTM unit output \(h_{T}\). The hyperparametric values selected using BOA for the LSTM network are listed as follows: the number of sequences are 2 and 3, the sequence length is from 7 to 12, the minimum batch size is 20, the learning rate is 0.001, the number of the LSTM unit is 55, the maximum epoch is 120, and the gradient threshold value is 1. The BOA is a popular metaheuristic algorithm, which mimics the butterfly's behavior in foraging and mating. Biological  
Figure 4: Graphical presentation of the LSTM network. Figure 5: Graphical presentation of the LSTM unit. adapted for foraging, possessing sense receptors that allow them to detect the presence of food. The sense receptors are known as chemoreceptors and are dispersed over several of the butterfly's body parts, such as the antennae, palps, legs, etc. In the BOA, the butterfly is assumed as a search agent to perform optimization and the sensing process depends on three parameters such as sensory modality, power exponent and stimulus intensity. If the butterfly is incapable of sensing the fragrance, then it moves randomly in the local search space [40]. Whereas, the sensory modality is in the form of light, sound, temperature, pressure, smell, etc. and it is processed by the stimulus. In the BOA, the magnitude of the physical stimulus is denoted as \(M\) and it is associated with the fitness of butterfly with greater fragrance value in the local search space. In the BOA, the searching phenomenon depends on two important issues: formulation of fragrance \(q\) and variations of physical stimulus \(M\). For simplicity purpose, the stimulus intensity \(M\) is related with encoded-objective-function. Hence, \(q\) is relative and is sensed by other butterflies in the local search space.