## 3 Methodology
### Evaluation Metrics  
Evaluating the accuracy of the forecasting model is crucial for assessing the effectiveness of the proposed methods. This section discusses the key performance criteria used in this study. The mean absolute error (MAE) and mean absolute percentage error (MAPE) are the most important static metrics used by researchers [56]. In the simulation, MAPE is utilized as an objective function of LSSVM-IBFOA (fitness function value). It is a widely adopted performance measure in the electric power industry due to its simplicity and ease of interpretation [57]. The MAPE value was classified into four forecasting capabilities, as provided in Table 6 for business and industrial data as reviewed in [58]. This table was also referred in [59; 60] for annual power load forecasting at regional and national levels considering LTLF.  
\begin{table}
\begin{tabular}{c c} \hline
**Number of Steps** & **Description** \\ \hline
**Step 4** & Generate the initial population of bacteria with random positions \\ \hline
**Step 5** & Create an initial population of bacteria with random positions where each bacterium’s positions encode the LSSVM parameters \\ \hline
**Step 6** & Set the fitness function \\ \hline
**Step 7** & For each bacterium, train an LSSVM model with the corresponding parameters on historical load data. Evaluate the fitness of each bacterium \\  & based on the mean absolute percentage error (MAPE) value: \\
**Step 7** & Fitness = MAPE = \(\frac{1}{p}\sum_{i=1}^{p}\left|\frac{w_{i}-w}{w_{i}}\right|\) (23) \\  & where p is the total number of forecasting data, \(w_{i}\) is the actual value and \(\bar{w}_{i}\) is the forecasted value \\ \hline
**Step 8** & Elimination-dispersal: \(e\) = \(e+1\) \\ \hline
**Step 9** & Reproduction loop: \(r\) = \(r\) + \(1\) \\ \hline
**Step 10** & Chemotaxis loop: \(t\) = \(t\) + \(1\) \\ \hline
**Step 11** & Update the positions of bacteria based on BFOA’s chemotaxis mechanism (Equation (20)) \\ \hline
**Step 12** & Go to step 8 if \(t\) \(<\) Nc \\ \hline
**Step 13** & Perform reproduction \\ \hline
**Step 14** & Select bacteria for reproduction based on their fitness value \\ \hline
**Step 15** & Go to step 7 if \(r\) \(<\) Nre \\ \hline
**Step 16** & Perform elimination-dispersal \\ \hline
**Step 17** & Eliminate and disperse each bacterium with probability of Ped. Go to step 6 if \(e\) \(<\) Ned \\ \hline
**Step 18** & Evaluate fitness and selection \\ \hline
**Step 19** & Train LSSVM models using the updated positions of bacteria. Evaluate \\  & the fitness of the updated bacteria by using Equation (23) \\ \hline
**Step 20** & Use the LSSVM-IBFOA to forecast the test data and select MAPE as the objective function for forecasting \\  & \(\text{Fobj}=\text{MAPE}=\frac{1}{p}\sum_{i=1}^{p}\left|\frac{w_{i}-w}{w_{i}}\right|\) (24) \\ \hline
**Step 21** & Inverse normalize the forecasting results \\ \hline
**Step 22** & Output the accuracy measures for evaluation \\ \hline \end{tabular}
\end{table}
Table 5: _Cont._A thorough assessment of the model's performance requires employing a diverse set of accuracy measures. This section details the metrics used in this study along with their interpretations. These accuracy measures include MAE, MSE, RMSE, R2, NRMSE, and NMSE, which are obtained by equations in Table 7, where p is the total number of forecasting data, \(w_{i}\) is the actual value, \(\hat{w}_{i}\) is the forecasted value and \(\overline{x}\) is the average value of forecasted value [61]. The best state to evaluate the accuracy of forecasting results using such measures is the maximum value for R2 and the minimum value for forecasting error measures [62]. The simulation of LSSVM models is done using MATLAB language version R2022b and the DNN model using Python language. All development and experimental works were carried out on a personal computer with processor Intel(R) Core(TM) i7-4790 @ 3.60 Ghz with 16 GB of RAM.