## 4 Results and Discussion
### Swarm Diameter  
Figures 17 and 18 as well as Table 9 show the diversity results as computed using the swarm diameter measures, i.e., standard SDM, modified SDM (mSDM) and the niche diversity (nSDM).  
For the SDM, the computation is geared towards the maximum distance between any two particles/candidate solutions. As such, the expectation is that standard SDM will obtain high diversity during both the exploration and the exploitation phases. The obtained results are therefore as expected.  
The mSDM is only computed per each niche and then an average is calculated. As such, it is expected that the diversity will be small and tending towards zero as convergence towards the location of optima is achieved. As such, results of the mSDM are as expected.  
The nSDM is computed in a similar manner to that of the SDM. The only difference is that the nSDM is computed using only unique solutions. As such, the nSDM is expected to show a high diversity both at the exploration and exploitation phases.  
In summary, whereas the SDM measure can truly reflect how far apart both the solutions and candidate solutions are, these solutions are likely to also contain outliers. The high diversity as shown may thus not be a measure of how truly diverse the obtained solutions are.  
Figure 17: Quantification of diversity using the Swarm Diameter.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Function** & **Mean** & **Stdev** & **Mean** & **Stdev** & **Mean** & **Stdev** \\  & **(SDM)** & **(SDM)** & **(mSDM)** & **(mSDM)** & **(nSDM)** & **(nSDM)** \\ \hline \(f_{1}\) & \(1.86\times 10^{1}\) & \(5.09\times 10^{-1}\) & \(4.82\times 10^{0}\) & \(1.97\times 10^{0}\) & \(1.59\times 10^{1}\) & \(3.25\times 10^{-2}\) \\ \hline \(f_{2}\) & \(1.28\times 10^{3}\) & \(4.07\times 10^{1}\) & \(2.63\times 10^{1}\) & \(3.00\times 10^{1}\) & \(1.25\times 10^{3}\) & \(2.79\times 10^{1}\) \\ \hline \(f_{3}\) & \(1.17\times 10^{0}\) & \(6.38\times 10^{-2}\) & \(1.65\times 10^{-1}\) & \(3.62\times 10^{-2}\) & \(1.13\times 10^{0}\) & \(2.36\times 10^{-2}\) \\ \hline \(f_{4}\) & \(9.54\times 10^{0}\) & \(9.28\times 10^{-1}\) & \(2.38\times 10^{0}\) & \(6.42\times 10^{-1}\) & \(8.59\times 10^{0}\) & \(1.04\times 10^{-2}\) \\ \hline \(f_{5}\) & \(8.45\times 10^{-1}\) & \(6.72\times 10^{-1}\) & \(0.00\times 10^{0}\) & \(0.00\times 10^{0}\) & \(8.45\times 10^{-1}\) & \(6.72\times 10^{-1}\) \\ \hline \(f_{6}\) & \(2.43\times 10^{0}\) & \(3.61\times 10^{-1}\) & \(2.27\times 10^{-2}\) & \(4.81\times 10^{-2}\) & \(2.38\times 10^{0}\) & \(2.76\times 10^{-1}\) \\ \hline \(f_{7}\) & \(1.28\times 10^{1}\) & \(9.33\times 10^{-1}\) & \(2.06\times 10^{0}\) & \(1.01\times 10^{0}\) & \(4.95\times 10^{0}\) & \(1.04\times 10^{0}\) \\ \hline \(f_{8}\) & \(1.22\times 10^{3}\) & \(6.35\times 10^{1}\) & \(3.30\times 10^{0}\) & \(3.64\times 10^{0}\) & \(1.22\times 10^{3}\) & \(6.37\times 10^{1}\) \\ \hline \(f_{9}\) & \(4.94\times 10^{0}\) & \(8.02\times 10^{-1}\) & \(7.74\times 10^{-1}\) & \(3.43\times 10^{-1}\) & \(3.73\times 10^{0}\) & \(9.46\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 9: Mean (\(\mu\)) and standard deviation (\(\sigma\)) for SDM measure and its variants at the last iteration.  
Figure 18: Quantification of diversity using the Swarm Diameter(_Cont._).