# A Novel Swarm Optimisation Algorithm Based on a Mixed-Distribution Model
## 3 Population Distribution Model Based on a Mixed Distribution
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Experimental Functions** & **Distance Threshold** \\ \hline \hline \(F_{1}\) & D\({}_{\text{11}}\in\) (0, 12]; D\({}_{\text{2}}\in\) (0, 15]; D\({}_{\text{k3}}\in\) (0, 15]; D\({}_{\text{m4}}\in\) (0, 15]; D\({}_{\text{56}}\in\) (0, 15]; \(F_{2}\) & D\({}_{\text{11}}\in\) (0, 5]; D\({}_{\text{2}}\in\) (0, 5]; D\({}_{\text{k3}}\in\) (0, 6]; D\({}_{\text{m4}}\in\) (0,6]; D\({}_{\text{56}}\in\) (0, 6]; \(F_{3}\) & D\({}_{\text{11}}\in\) (0, 10]; D\({}_{\text{2}}\in\) (0, 10]; D\({}_{\text{k3}}\in\) (0, 12]; D\({}_{\text{m4}}\in\) (0, 12]; D\({}_{\text{56}}\in\) (0, 12]; \(F_{4}\) & D\({}_{\text{11}}\in\) (0, 10]; D\({}_{\text{2}}\in\) (0, 10]; D\({}_{\text{k3}}\in\) (0, 12]; D\({}_{\text{m4}}\in\) (0, 12]; D\({}_{\text{56}}\in\) (0, 12]; \(F_{5}\) & D\({}_{\text{11}}\in\) (0, 6]; D\({}_{\text{2}}\in\) (0, 6]; D\({}_{\text{k3}}\in\) (0, 9]; D\({}_{\text{m4}}\in\) (0, 9]; D\({}_{\text{56}}\in\) (0, 9]; \(F_{6}\) & D\({}_{\text{11}}\in\) (0, 4]; D\({}_{\text{2}}\in\) (0, 4]; D\({}_{\text{k3}}\in\) (0, 5]; D\({}_{\text{m4}}\in\) (0, 5]; D\({}_{\text{56}}\in\) (0, 5]; \(F_{7}\) & D\({}_{\text{11}}\in\) (0, 30]; D\({}_{\text{2}}\in\) (0, 30]; D\({}_{\text{k3}}\in\) (0, 35]; D\({}_{\text{m4}}\in\) (0, 35]; D\({}_{\text{56}}\in\) (0, 35]; \(F_{8}\) & D\({}_{\text{11}}\in\) (0, 3]; D\({}_{\text{2}}\in\) (0, 3]; D\({}_{\text{k3}}\in\) (0, 5]; D\({}_{\text{m4}}\in\) (0, 5]; D\({}_{\text{56}}\in\) (0, 5]; \(F_{9}\) & D\({}_{\text{11}}\in\) (0, 12]; D\({}_{\text{2}}\in\) (0, 12]; D\({}_{\text{k3}}\in\) (0, 15]; D\({}_{\text{m4}}\in\) (0, 15]; D\({}_{\text{56}}\in\) (0, 15]; \(F_{10}\) & D\({}_{\text{11}}\in\) (0, 60]; D\({}_{\text{2}}\in\) (0, 60]; D\({}_{\text{k3}}\in\) (0, 80]; D\({}_{\text{m4}}\in\) (0, 80]; D\({}_{\text{56}}\in\) (0, 80];  
\end{table} 
Table 4: Parameter settings of BOA-6/NBOA6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function** & **No.** & **Mathematical Representation _(f_(X))_** & **Initial Range** & **Best Objective** \\  & **Name** & **Function Value** \\ \hline \hline Sphere & \(F_{1}\) & \(F_{1}(x)=\sum\limits_{i=1}^{n}{x_{i}}^{2}\) & \([-100,100]^{n}\) & 0 \\ \hline Schwefel 2.22 & \(F_{2}\) & \(F_{2}(x)=\sum\limits_{i=1}^{n}{|x_{i}|}+\prod\limits_{i=1}^{n}{|x_{i}|}\) & \([-10,10]^{n}\) & 0 \\ \hline Schwefel 1.2 & \(F_{3}\) & \(F_{3}(x)=\sum\limits_{i=1}^{n}{(\sum\limits_{j=1}^{i}{x_{j}})}^{2}\) & \([-100,100]^{n}\) & 0 \\ \hline Schwefel 2.21 & \(F_{4}\) & \(F_{4}(x)=\max_{i}\{|x_{i}|,1\leq i\leq n\}\) & \([-100,100]^{n}\) & 0 \\ \hline Rosenbrock & \(F_{5}\) & \(F_{5}(x)=\sum\limits_{i=1}^{n-1}{\left(100{\left({x_{i+1}-x_{i}^{2}}\right)}^{2} +{\left({x_{i}-1}\right)}\right)}^{2}\) & \([-30,30]^{n}\) & 0 \\ \hline Quartic & \(F_{6}\) & \(F_{6}(x)=\sum\limits_{i=1}^{n}{\sum\limits_{i=1}^{n}{x_{i}^{4}}+random[0,1)}\) & \([-1.28,1.28]^{n}\) & 0 \\ \hline Schwefel 2.26 & \(F_{7}\) & \(F_{7}(x)=-\sum\limits_{i=1}^{n}{(x_{i}\sin(\sqrt{|x_{i}|}))}\) & \([-500,500]^{n}\) & \(-12,569.483\) \\ \hline Rastrigin & \(F_{8}\) & \(F_{8}(x)=\sum\limits_{i=1}^{n}{(x_{i}^{2}-10\cos(2\pi x_{i})+10)^{2}}\) & \([-5.12,5.12]^{n}\) & 0 \\ \[PERSON] & \(F_{9}\) & \(F_{9}(x)=-20\exp(-0.2\sqrt{\frac{1}{\hbar}\sum\limits_{i=1}^{n}{x_{i}^{2}}})- \exp(\frac{1}{\hbar}\sum\limits_{i=1}^{n}{\cos 2\pi x_{i}})+20+e\) & \([-32,32]^{n}\) & 0 \\ \[PERSON] & \(F_{10}\) & \(F_{10}(x)=\frac{1}{4000}\sum\limits_{i=1}^{n}{(x_{i})^{2}}-\prod\limits_{i=1}^{n} {\cos(\frac{x_{i}}{\sqrt{i}})}+1\) & \([-600,600]^{n}\) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test functions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Experimental Algorithms** & **Population Size** & **Generations** \\ \hline NBOA-3 & & \\ NBOA-6 & & \\ PSO & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental parameter settings.