# Effects of Random Values for Particle Swarm Optimization Algorithm
## 4 Experiments and Analysis
### Experimental Results and Comparisons
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \(r_{b}\)\(r_{2}\) & \(U(9,1)\) & **0.5** & \(U(-1.1)\) & \(G(0,1)\) \\ \cline{2-5}  & **Dimension** & **10/30/100** & **10/30/100** & **10/30/100** & **10/30/100** \\ \hline \multirow{4}{*}{Sphere1} & Average solution & 0/19.90/4203.68 & 0.74/1390.12/34/09.52 & 0/0/0 & 0/0/0/0 \\  & Standard deviation & 0/12.37/4400.60 & 1.62/575.44/10,343.18 & 0/0/0 & 0/0/0/0 \\  & The worst solution & 0/48.87/13/08.62 & 7.90/270.29/532.46.46 & 0/0/0 & 0/0/0 \\  & The best solution & 0/4.13/53/03.05 & 0/443.08/175.799.86 & 0/0/0 & 0/0/0/0 \\ \hline \multirow{4}{*}{Sphere2} & Average solution & 0/1726.67/9386.74 & 130.34/5076.33/56.870.86 & 0/0/183.33 & 0/0/220 \\  & Standard deviation & 0/466.04/6716.49 & 180.29/1111.775/98.84 & 0/159.92 & 0/0/174.99 \\  & The worst solution & 0/2600/447.00 & 0/600/380/320/323.87 & 0/0/0 & 0/0/0/0 \\  & The best solution & 0/900.00/6400.80 & 0.01/2319.72/9236.02 & 0/0/0 & 0/0/0 \\ \hline \multirow{4}{*}{Rastrigin} & Average solution & 10/523.83/357.43 & 1.01/116.61/810.69 & 0/0/0 & 0/0/0 \\  & Standard deviation & 10/61.28/287.81 & 9.70/332.87/26.28 & 0/0 & 0/0/0 \\  & The worst solution & 497/100.77/499.92 & 4.28/215.88/932.59 & 0/0/0 & 0/0/0 \\  & The best solution & 0/36.2/186.01 & 4.98/62.62/670.46 & 0/0/0 & 0/0/0 \\ \hline \multirow{4}{*}{Rosenbrock} & Average solution & 0/46.38/3089.92 & 250.63/612.31/36.654.70.29 & 1.93/28.86/98.92 & 0.98/280.98/98.94 \\  & Standard deviation & 1.22/292.83/182.46.39 & 63.65/59.89/636.37/579.27 & 2.86/0.08/0.05 & 2.43/0.07/0.03 \\  & The worst solution & 3.99/138.17/847.45/21.31 & 35.43/280.83/25.77/250.85 & 8.93/28.96/98.85 & 8.75/287.99/98.86 \\  & The best solution & 0.1658.48/409.44 & 5.86/1641.69/559.181.045 & 0.00/28.86/98.77 & 1.63/ \(\times\) 1428.69/98.86 \\ \hline \multirow{4}{*}{[PERSON]} & Average solution & 0.19/1.13/17.27 & 0.22/128.28/290.00 & 0/0/0 & 0/0/0 \\  & Standard deviation & 0.15/05/15.90 & 0.12/54.68/47.00 & 0/0/ & 0/0/0 \\  & The worst solution & 0.51/151.39/9.44 & 0.92/26.48/519.52 & 0/0/0 & 0/0/0 \\  & The best solution & 0/0.09/3.45 & 0.08/334/123.68 & 0/0/0 & 0/0/0 \\ \hline \multirow{4}{*}{Ackley} & Average solution & 1.46/67/11.12 & 1.64/90/15.63 & 0/0/0 & 0/0/0 \\  & Standard deviation & 1.22/150.2/26 & 1.01/2.15/1.10 & 0/0/0 & 0/0/0/0 \\  & The worst solution & 3.22/89.90/15.17 & 3.58/126.06/17.46 & 0/0/0 & 0/0/0 \\  & The best solution & 0/2.73/344 & 0.02/69/13.34 & 0/0/0 & 0/0/0 \\ \hline \multirow{4}{*}{Levy and Montalkov 2} & Average solution & 0.14/12.83 & 0.01/13.32/0.28 & 0.02/38.63 & 0.13/44.878 \\  & Standard deviation & 0/0.17/231 & 0.01/054.45/4.57 & 0/0.46/0.48 & 0/0.64/0.44 \\ \cline{1-1}  & The worst solution & 0/0.01/17.84 & 0.02/28.73/43.74 & 0/1.60/0.42 & 0/2.49/9.57 \\ \cline{1-1}  & The best solution & 0/0.01/9.09 & 0.00/28.142.8 & 0/0/0.73.88 & 0/0/0.7/8.99 \\ \hline \multirow{4}{*}{Sinusidal} & Average solution & -3.43/ -1.02/-0.11 & -3.43/ -0.41/0 & -3.50/-1.59/-0.09 & -3.18/ -1/0 \\ \cline{1-1}  & Standard deviation & 0.29/14.14/0.31 & 0.04/04.60 & 0.1/5.03/0.32 & 0.74/11.8/0 \\ \cline{1-1}  & The worst solution & -2.12/-0.01/0 & -2.93/-0.01/0 & -3.50/-0.01/0 & -0.86/ -1.00/1.01 \\ \cline{1-1}  & The best solution & -3.50/ -3.45/ -1.66 & -3.50/ -1.47/0 & -3.50/-3.50/-1.75 & -3.50/-3.50/ \\ \hline \multirow{4}{*}{Rotated Expanded Saffer} & Average solution & 1.27/67/26.10 & 2.58/10.92/43.13 & 0/0/0 & 0/0/0 \\ \cline{1-1}  & Standard deviation & 0.74/1.96/5.54 & 0.47/1.18/15.99 & 0/0/0 & 0/0/0 \\ \cline{1-1}  & The worst solution & 2.60/92.4/34.49 & 3.56/13.11/45.81 & 0/0/0 & 0/0/0 \\ \cline{1-1} \cline{2-1}  & The best solution & 0/1.92/13.45 & 1.73/8.63/99.45 & 0/0/0 & 0/0/0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of standard particle swarm optimization (PSO) algorithm with different types of random values for benchmark functions.