## 4 Results and Discussion  
All computational works within the context of this study were carried out via a personal computer possessing a Macintosh operating system (version 15.1.1), an 8-core 3.6 GHz CPU (Intel Core i9, Intel, Santa Clara, CA, USA), and 100 GB RAM. For all computing tasks, RStudio Desktop (version 2024.09.1+394) was utilized as an integrated development environment due to having a well-suited rich ecosystem for machine learning applications and providing elegant visualization for academic writing [59].  
The data set was normalized between 0 and 1 according to minimum-maximum normalization due to the fact that scaling operation triggers eliminating the units of diversified variables, reduces computational time, reserves a smaller space on system memory, and benchmarks a myriad of features in a similar manner.  
In the solution of the electricity demand forecasting problem via DNN and GEP methods during the COVID-19 pandemic, coefficient of determination (R\({}^{2}\)), normalized mean absolute error (nMAE), and normalized root mean squared error (nRMSE) were  
Figure 5: Visualization of a basic expression tree.  
Figure 6: The flowchart of GEP algorithm [43].  
used for performance evaluation along with computational time. The formulae of the aforementioned evaluation metrics are stated as follows:  
\[R^{2}(\%)=(1-\frac{\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}{\sum_{i=1}^{n}(y_{i}- \hat{y})^{2}})\times 100,\]  
\[nMAE(\%)=\frac{1}{n}\frac{\sum_{i=1}^{n}|y_{i}-\hat{y}_{i}|}{\hat{y}}\times 1 00,\]  
\[nRMSE(\%)=\frac{\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}}{\hat {y}}\times 100,\]  
where \(y_{i}\) and \(\hat{y}_{i}\) are actual and predicted instances of the data, \(\hat{y}\) illustrates the mean of the actual data and \(n\) indicates the number of observations [60; 61].  
In this work, the quadratic reference function with two variables demonstrated in Equation (1) is preferred for the DNN method. Model building parameters for the DNN method are thoroughly stated in the following:  
* The network parameters: 1. The maximum number of network layers: 20 2. The maximum number of polynomial order: 16 3. The tolerance for the convergence: \(10^{-4}\)
* The number of neurons per layer: 20
* Network layer connections: Only the previous layer
* Overfitting protection control: Hold-out sample (20%)  
Moreover, the GEP method utilizes several functions, including summation (+), subtraction (-), multiplication (\(*\)), division (/), and square root (\(Q\)) for all simulations. Model building parameters for the GEP method are canonically represented as follows:  
* The magnitude of initial population: 50
* The count of utmost attempts for primary population: 10,000
* The number of genes per chromosome: 4
* The head length of gene: 8
* The number of utmost creations: 2000
* The number of creations without enhancement: 1000
* The termination value of the top chromosome's fitness score: 1
* The fitness function: Relative selection range
* The rates of evolution parameter: 1. Mutation: 44%
* Gene, inversion, and transposition: 10%
* One-point and two-point recombination: 30%
* The linking function for all genes: Summation (+)
* Features of random constants: 1. Type of constants: Real (Floating point)
* Random real constants per gene: 10
* Least constant value: -10
* Uttmost constant value: 10
* Mutation rate: 1%  
In addition to those, simple random sampling is used to validate both DNN and GEP methods in such a way that the in-sample covers 80% of the data set for training, while the out-of-sample is the rest 20% for testing, respectively.