## 4 Result and Discussion
### Aspect of Transition of Weights  
There are two major components in metaheuristic algorithms: diversification and intensification [33]. These two components seem to be contradicting each other, but balancing their combination is crucial and important to the success of a metaheuristic algorithm. In the HS algorithm, diversification is controlled by the pitch adjustment and randomization, whereas intensification is represented by the harmony memory considering rate. Therefore, in this section, the results of training of neural networks for two different cases are compared and examined, _i.e._, the best combination and worst combination of HMCR and PAR. The case of the HS optimization with HMCR of 0.7 and PAR of 0.5 is chosen to be the best case (Case 1) since it has the largest average and smallest standard deviation of \(I_{a}\). The worst case (Case 2) is the case of HMCR of 0.1 and PAR of 0.5, which has the smallest average and largest standard deviation of \(I_{a}\). The optimization process of the HS algorithm regarding the weights of neural network is illustrated in Figures 7 and 8 for each case of parameter combination. Note that the results shown in these figures are those from one of the fifty runs described in the previous section. In the figures, each scatter plot indicates the relationship between calculated and observed stability numbers using (a) randomly selected initial weights; (b) optimal initial weights determined by HS algorithm; and (c) further trained weights after BP algorithm. The correlation coefficients and indices of agreement are also given. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Average**} \\ \hline  & HMCR\(\backslash\)PAR & 0.1 & 0.3 & 0.5 & 0.7 & 0.9 \\  & 0.1 & 0.885 & 0.926 & 0.872 & 0.843 & 0.905 \\ HS-ANN & 0.3 & 0.934 & 0.910 & 0.913 & 0.914 & 0.912 \\  & 0.5 & 0.913 & 0.929 & 0.929 & 0.934 & 0.929 \\  & 0.7 & 0.881 & 0.929 & 0.9481 & 0.9443 & 0.9404 \\  & 0.9 & 0.9482 & 0.935 & 0.913 & 0.9375 & 0.892 \\ \hline ANN & \multicolumn{6}{c}{0.804} \\ \hline  & \multicolumn{6}{c}{**Standard Deviation**} \\ \hline  & HMCR\(\backslash\)PAR & 0.1 & 0.3 & 0.5 & 0.7 & 0.9 \\  & 0.1 & 0.205 & 0.120 & 0.245 & 0.277 & 0.158 \\ HS-ANN & 0.3 & 0.137 & 0.175 & 0.155 & 0.183 & 0.189 \\  & 0.5 & 0.178 & 0.101 & 0.104 & 0.073 & 0.138 \\  & 0.7 & 0.224 & 0.130 & 0.0211 & 0.0313 & 0.0425 \\  & 0.9 & 0.0232 & 0.110 & 0.168 & 0.0314 & 0.200 \\ \hline ANN & \multicolumn{6}{c}{0.317} \\ \hline  & \multicolumn{6}{c}{**Minimum Value**} \\ \hline  & HMCR\(\backslash\)PAR & 0.1 & 0.3 & 0.5 & 0.7 & 0.9 \\  & 0.1 & 0.001 & 0.216 & 0.001 & 0.001 & 0.002 \\ HS-ANN & 0.3 & 0.002 & 0.001 & 0.029 & 0.004 & 0.002 \\  & 0.5 & 0.003 & 0.319 & 0.254 & 0.468 & 0.003 \\  & 0.7 & 0.001 & 0.051 & 0.8891 & 0.8523 & 0.7105 \\  & 0.9 & 0.8852 & 0.196 & 0.013 & 0.8014 & 0.005 \\ \hline ANN & \multicolumn{6}{c}{0.001} \\ \hline  & \multicolumn{6}{c}{**Maximum Value**} \\ \hline  & HMCR\(\backslash\)PAR & 0.1 & 0.3 & 0.5 & 0.7 & 0.9 \\  & 0.1 & 0.978 & 0.985 & 0.980 & 0.9871 & 0.981 \\ HS-ANN & 0.3 & 0.979 & 0.983 & 0.985 & 0.986 & 0.979 \\  & 0.5 & 0.980 & 0.977 & 0.980 & 0.978 & 0.984 \\  & 0.7 & 0.984 & 0.9862 & 0.979 & 0.983 & 0.985 \\  & 0.9 & 0.985 & 0.985 & 0.986 & 0.985 & 0.980 \\ \hline ANN & \multicolumn{6}{c}{0.985} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical parameters for index of agreement. Figure 7: Scatter plots of calculated _versus_ observed stability numbers for Case 1 (HMCR = 0.7; PAR = 0.5): (**a**) randomly selected initial weights; (**b**) optimal initial weights determined by HS algorithm; (**c**) further trained weights after BP algorithm. The first graphs in Figures 7 and 8 show that the stability numbers calculated by using the randomly selected initial weights are distributed in a wide range from large negative values to large positive values and have very weak and negative correlation with the observed stability numbers.