## 4 Model Development
### Iwo-Ann  
In this section, the new IWO-ANN model is implemented. According to our literature review, there is no research yet that has combined these two algorithms. However, the implementation steps of this new model are similar to previous models. The IWO algorithm described above is known as a new optimization algorithm that is used for optimization in various issues. Various parameters are involved in this algorithm; some of its most important ones, include the number of iterations, the initial population of seeds, and so on. Some of these parameters have less impact on the results and can be obtained by trial and error methods. Therefore, these parameters are initially determined. The minimum and maximum number of seeds (\(S_{\text{min}}\) and \(S_{\text{max}}\)) were investigated from zero to 30. In this case, the \(S_{\text{min}}\) value is zero, and the best condition for the \(S_{\text{max}}\) is 20. The initial and final value of standard deviation parameter actually helps to knock off the selection, using the variance reduction exponent parameter. Values of 0.5, 0.001, and 4 were selected for these three parameters (the initial and final value of standard deviation and the variance reduction exponent parameters), respectively. Finally, the main parameters such as the number of iterations and the final number of plants were determined according to Figure 9. To compare the number of iterations, similar to those presented in the previous sections, 600 iterations were selected for all the models. As shown in Figure 9, the RMSE of the models changes up to 300 iterations, and after that, they reach a constant level. For this reason, 300 iterations is the optimum value for designing next models. Finally, different models of plant seeds were designed (5-40), the results of which are presented in Table 3. Using this table, the best model is selected. As can be obtained, model number 7 provides the best conditions for TS prediction.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Model** \\ **No.** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Bees** \\ **No.** \\ \end{tabular} } & \multicolumn{3}{c}{**Network Result**} & \multicolumn{3}{c}{**Ranking**} & \multirow{2}{*}{
\begin{tabular}{c} **Total** \\ **Rank** \\ \end{tabular} } \\ \cline{3-3} \cline{5-10}  & & \multicolumn{1}{c}{**R\({}^{2}\)**} & \multicolumn{1}{c}{**RMSE**} & \multicolumn{1}{c}{**RMSE**} & \multicolumn{1}{c}{**RMSE**} & \multicolumn{1}{c}{**R\({}^{2}\)**} & \multicolumn{1}{c}{**RMSE**} & \multicolumn{1}{c}{**RMSE**} \\ \hline
1 & 5 & 0.843 & 0.1295 & 0.854 & 0.1264 & 1 & 1 & 1 & 1 & 4 \\
2 & 10 & 0.857 & 0.1122 & 0.867 & 0.1091 & 2 & 2 & 2 & 2 & 8 \\
3 & 15 & 0.896 & 0.0987 & 0.899 & 0.0971 & 5 & 5 & 6 & 6 & 22 \\
4 & 20 & 0.895 & 0.0986 & 0.879 & 0.0995 & 4 & 4 & 3 & 3 & 14 \\
5 & 25 & 0.906 & 0.0959 & 0.902 & 0.0963 & 7 & 7 & 7 & 7 & 28 \\
6 & 30 & 0.901 & 0.097 & 0.894 & 0.0978 & 6 & 6 & 5 & 5 & 22 \\
7 & 35 & 0.875 & 0.1001 & 0.891 & 0.0988 & 3 & 3 & 4 & 4 & 14 \\
8 & 40 & 0.908 & 0.0946 & 0.904 & 0.0955 & 8 & 8 & 8 & 8 & 32 \\ \hline \hline \end{tabular}  
* TR: Training, TS: Testing.  
\end{table}
Table 2: Investigating effects of various bees in predicting BTS.  
Figure 9: Hybrid models of invasive weed optimization (IWO) with various seed numbers.