## 3 Results and Discussion  
### Sensitivity Analysis for Optimization Algorithms  
To apply the optimization algorithms to the ANFIS and MFNN models, accurate adjustment of random parameters must be obtained a priori. As in the evolutionary algorithms, the BA and WA are fully sensitive to initialize random parameters. In fact, the random parameters change the accuracy of optimization algorithms. Thus, it is necessary to find the optimal value of random parameters so that the objective function values (RMSE in this study) converges to the lowest value.  
Hence, to obtain better efficiency of the BA and WA, it is necessary to set the random parameters. As the WA and BA parameters were various, to create confidence that a suitable adjustment of random parameters was used, different experiments were used for generating the sensitivity analysis. The value of desired parameters was gradually changed, and the analysis was accomplished. The default values of other random parameters were constant when the user varied one parameter. The algorithm variations were examined based on the mean of the objective function value (i.e., RMSE). One sample of implanted sensitivity analysis to obtain proper adjustment of parameters systematically as the consecutive levels of needed analysis is shown in Table 2. In fact, Table 2 is a sample to show how to obtain the optimal value of random parameters. First, a population size, MaxF, MinF, MaxA, and MinA (1) were selected, and an objective function was computed for this combination. Then, MaxF, MinF, and MaxA with next value of MinA (3) were applied to compute the objective function value for the next combination. When all of the available MaxF, MinF, and MaxA with different values of MinF were generated, and the objective function value for each combination was generated, Max f was changed to the next value (0.5). Then, the available combination was generated for the previous population size (10), MaxF (0.5), the previous MinF (0.1), and the previous MaxA (3) with MinA (1). Then, all available combinations for SP:10, MaxF (0.5), MinF (0.1), MaxA (3), and Min A from 1 to 4 were generated, and the objective function value was computed. This process was similarly repeated for the other population sizes and parameter values. Each combination had the lowest value for the objective function, and the best value of random parameters can be seen in Table 3. In fact, the parameters in Table 3 are the optimal values of random parameters that generated the lowest value of the objective function.  
It should be mentioned that the best value of the parameters occurred at the lowest objective function value. RMSE or objective function had small error index values and were suitable for the simulations. Finally, Table 3 reports the best values of BA and WA parameters based on the above process.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**SP: Size of** & **Maximum Frequency** & **Minimum** & **Maximum** & **Minimum** \\
**Population** & **(MaxF)** & **Frequency (MinF)** & **Loudness (MaxA)** & **Loudness (MinA)** \\ \hline
10 & 0.3 & 0.10 & 3 & **1** \\
30 & 0.5 & 0.20 & 5 & **2** \\
50 & 0.7 & 0.30 & 7 & **3** \\
70 & 0.90 & 0.40 & 9 & **4** \\ \end{tabular}
\end{table}
Table 2: A sample of sensitivity analyses.