# A Novel Swarm Optimisation Algorithm Based on a Mixed-Distribution Model
## 3 Population Distribution Model Based on a Mixed Distribution
#### 4.4.1 Statistical Results  
* Optimal Results  
The optimal result is the best result of an algorithm that runs 50 times. In Table 7, SD represents the standard deviation, which measures the amount of variation around the mean. We can see from the above results in Tables 7 and 8 that NBOA-3 obtains relative optimal results for six functions (F1, F2, F3, F4, F5, and F6). NBOA6 obtains relative optimal results for four functions (F7, F8, F9, and F10). The performance of BOA-6 is, relatively speaking, not very good but compared with the algorithms PSO and BOA-3, there is evidence of improvement. \begin{table}
\begin{tabular}{c c c c c} \hline
**Experimental Functions** & **Algorithms** & **Optimal Solutions** & **Average Results** & **SD** \\ \hline \multirow{4}{*}{\(F_{1}\)} & BOA-6 & \(1.29\times 10^{-14}\) & \(1.21\times 10^{-4}\) & \(4.09\times 10^{-4}\) \\  & NBOA-3 & \(3.42\times 10^{-67}\) & \(1.04\times 10^{-14}\) & \(7.37\times 10^{-14}\) \\  & NBOA-6 & \(1.31\times 10^{-33}\) & \(3.84\times 10^{-8}\) & \(2.18\times 10^{-7}\) \\  & PSO & \(6.97\times 10^{-3}\) & \(3.09\times 10^{-2}\) & \(1.88\times 10^{-2}\) \\ \hline \multirow{4}{*}{\(F_{2}\)} & BOA-6 & \(2.42\times 10^{-12}\) & \(3.45\times 10^{-4}\) & \(2.01\times 10^{-3}\) \\  & NBOA-3 & \(5.21\times 10^{-68}\) & \(8.44\times 10^{-17}\) & \(5.97\times 10^{-16}\) \\  & NBOA-6 & \(8.28\times 10^{-21}\) & \(1.81\times 10^{-7}\) & \(9.12\times 10^{-7}\) \\  & PSO & \(5.99\times 10^{-1}\) & \(1.99\) & \(1.04\) \\ \hline \multirow{4}{*}{\(F_{3}\)} & BOA-6 & \(2.39\times 10^{-12}\) & \(2.10\times 10^{-3}\) & \(4.01\times 10^{-3}\) \\  & NBOA-3 & \(3.89\times 10^{-48}\) & \(3.49\times 10^{-5}\) & \(2.47\times 10^{-4}\) \\  & NBOA-6 & \(1.13\times 10^{-17}\) & \(1.24\times 10^{-4}\) & \(6.2\times 10^{-4}\) \\  & PSO & \(9.34\times 10^{-1}\) & \(3.67\) & \(1.74\) \\ \hline \multirow{4}{*}{\(F_{4}\)} & BOA-6 & \(4.28\times 10^{-9}\) & \(2.16\times 10^{-3}\) & \(3.55\times 10^{-3}\) \\  & NBOA-3 & \(2.25\times 10^{-36}\) & \(1.88\times 10^{-17}\) & \(1.33\times 10^{-16}\) \\  & NBOA-6 & \(1.64\times 10^{-12}\) & \(1.71\times 10^{-7}\) & \(4.25\times 10^{-7}\) \\  & PSO & \(3.39\times 10^{-1}\) & \(8.77\times 10^{-1}\) & \(4.81\times 10^{-1}\) \\ \hline \multirow{4}{*}{\(F_{5}\)} & BOA-6 & \(2.88\times 10\) & \(2.89\times 10\) & \(8.89\times 10^{-2}\) \\  & NBOA-3 & \(2.86\times 10\) & \(2.89\times 10\) & \(1.31\times 10^{-1}\) \\  & NBOA-6 & \(2.86\times 10\) & \(2.92\times 10\) & \(6.79\times 10^{-1}\) \\  & PSO & \(2.28\times 10\) & \(3.92\times 10\) & \(2.93\times 10\) \\ \hline \multirow{4}{*}{\(F_{6}\)} & BOA-6 & \(4.79\times 10^{-5}\) & \(9.89\times 10^{-4}\) & \(6.63\times 10^{-4}\) \\  & NBOA-3 & \(1.19\times 10^{-5}\) & \(7.15\times 10^{-4}\) & \(6.22\times 10^{-4}\) \\ \cline{1-1}  & NBOA-6 & \(5.62\times 10^{-5}\) & \(6.90\times 10^{-4}\) & \(6.28\times 10^{-4}\) \\ \cline{1-1}  & PSO & \(2.64\times 10^{-2}\) & \(6.82\times 10^{-2}\) & \(3.38\times 10^{-2}\) \\ \hline \end{tabular}
\end{table} 
Table 7: Experimental results of unimodal function optimization.