## 4 Results and Discussion
### Test Systems  
4.2.1. Test System 1  
Six unimodal functions are included in the test functions. PSO and GWO are contrasted with the suggested ALGWO algorithm's solution. The unimodal test functions are described in Table 2. Figure 5 displays the two-dimensional parameter space for these six unimodal functions to show them more easily.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function Name** & **Expression** & **Search Space** & **Dim** \\ \hline F1 & F1 = \(\sum\limits_{i=1}^{n}{x_{i}^{2}}\) & [\(-\)100,100] & 30 \\ F2 & F2 = \(\sum\limits_{i=1}^{n}{|x_{i}|-\prod\limits_{i=1}^{n}{|x_{i}|}}\) & [\(-\)10,10] & 30 \\ F3 & F3 = \(\sum\limits_{i=1}^{n}{(\sum\limits_{j=1}^{i}{x_{j}})}\) & [\(-\)100,100] & 30 \\ F4 & F4 = max \(i\) \(\{|x_{i}|,1\leq i\leq n\}\) & [\(-\)100,100] & 30 \\ F5 & F5 = \(\sum\limits_{i=1}^{n}{\left[{100(x_{i+1}-x_{i}^{2})^{2}+(x_{i}-1)^{2}}\right]}\) & [\(-\)30,30] & 30 \\ F6 & F6 = \(\sum\limits_{i=1}^{n}{(|x_{i}+0.5|)\,^{2}}\) & [\(-\)100,100] & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Details of the unimodal test function.  
Figure 5: _Cont._  
The average and standard deviations for ten independent runs used to assess the resilience and average accuracy of algorithms are shown in Table 3. For each function, the best results are displayed in bold. Figure 6 shows the convergence curves of the six test functions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Base Function**} & \multicolumn{1}{c}{**GWO**} & \multicolumn{1}{c}{**ALGWO**} & \multicolumn{1}{c}{**PSO**} \\ \hline \multirow{2}{*}{F1} & STD & \(6.69\times 10^{-70}\) & 0 & \(1.40\times 10^{-11}\) \\  & AVE & \(2.49\times 10^{-70}\) & 0 & \(5.48\times 10^{-12}\) \\ \multirow{2}{*}{F2} & STD & \(3.49\times 10^{-41}\) & 0 & \(1.01\times 10^{-5}\) \\  & AVE & \(3.89\times 10^{-41}\) & \(3.01\times 10^{-238}\) & \(7.24\times 10^{-6}\) \\ \multirow{2}{*}{F3} & STD & \(1.57\times 10^{-20}\) & 0 & \(3.47\times 10^{0}\) \\  & AVE & \(8.72\times 10^{-21}\) & 0 & \(7.16\times 10^{0}\) \\ \multirow{2}{*}{F4} & STD & \(2.04\times 10^{-17}\) & 0 & \(1.20\times 10^{-1}\) \\  & AVE & \(1.77\times 10^{-17}\) & \(2.70\times 10^{-206}\) & \(3.90\times 10^{-1}\) \\ \multirow{2}{*}{F5} & STD & \(8.78\times 10^{-1}\) & \(4.90\times 10^{-1}\) & \(3.46\times 10^{1}\) \\ \multirow{2}{*}{F5} & AVE & \(2.66\times 10^{1}\) & \(2.62\times 10^{1}\) & \(5.04\times 10^{1}\) \\  & STD & \(2.71\times 10^{-1}\) & \(1.09\times 10^{0}\) & \(1.59\times 10^{-11}\) \\ \multirow{2}{*}{F6} & AVE & \(3.00\times 10^{-1}\) & \(3.58\times 10^{-1}\) & \(8.16\times 10^{-12}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison results of three algorithms on six groups of benchmark functions.  
Figure 5: The results of parameter space. (**a**) The parameter space of F1 and (**b**) the parameter space of F2 and (**c**) the parameter space of F3 and (**d**) the parameter space of F4 and (**e**) the parameter space of F5 and (**f**) the parameter space of F6.  
As shown in Table 3, the ALGWO algorithm indications are usually noticeably better than those of other algorithms. Figure 6 illustrates that the ALGWO algorithm provides better solution outcomes and faster convergence. As a result, the ALGWO method performs the best overall when solving unimodal test functions when compared to other algorithms.  
Figure 6: The results of convergence curves. (**a**) The convergence curves of F1 and (**b**) the convergence curves of F2 and (**c**) the convergence curves of F3 and (**d**) the convergence curves of F4 and (**e**) the convergence curves of F5 and (**f**) the convergence curves of F6.