# Particle Swarm Optimization Based on a Novel Evaluation of Diversity
## 4 Experiments and Comparisons
### Comparison with Other PSO Variants
As shown in Table 8, in the Non-parametric Wilcoxon signed-rank test of PSO-ED and  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **GPSO** & **LPSO** & **SPSO** & **CLPSO** & **FIPS** & **DMSPSO** & **MPSO** & **PSO-ED** \\ \hline \multirow{3}{*}{F1} & Mean & \(5.05\times 10^{6}\) & \(1.17\times 10^{5}\) & \(2.78\times 10^{4}\) & \(5.53\times 10^{5}\) & \(2.51\times 10^{5}\) & \(9.64\times 10^{4}\) & \(2.63\times 10^{4}\) & \(\mathbf{2.03\times 10^{4}}\) \\  & Std & \(2.31\times 10^{7}\) & \(7.30\times 10^{4}\) & \(1.01\times 10^{4}\) & \(7.42\times 10^{4}\) & \(3.50\times 10^{4}\) & \(2.46\times 10^{5}\) & \(\mathbf{6.61\times 10^{3}}\) & \(1.65\times 10^{4}\) \\  & Mean & \(6.02\times 10^{8}\) & \(2.94\times 10^{7}\) & \(6.15\times 10^{3}\) & \(4.73\times 10^{4}\) & \(6.49\times 10^{3}\) & \(1.38\times 10^{4}\) & \(6.36\times 10^{3}\) & \(\mathbf{5.80\times 10^{2}}\) \\ F2 & Std & \(1.05\times 10^{9}\) & \(7.79\times 10^{7}\) & \(2.83\times 10^{4}\) & \(8.12\times 10^{4}\) & \(3.86\times 10^{2}\) & \(5.47\times 10^{3}\) & \(\mathbf{2.12\times 10^{2}}\) & \(9.94\times 10^{2}\) \\ F3 & Mean & \(2.03\times 10^{1}\) & \(2.02\times 10^{1}\) & \(2.02\times 10^{1}\) & \(2.02\times 10^{1}\) & \(2.03\times 10^{1}\) & \(2.01\times 10^{1}\) & \(\mathbf{1.87\times 10^{1}}\) & \(2\times 10^{1}\) \\  & Std & \(1.12\times 10^{1}\) & \(4.07\times 10^{2}\) & \(2.99\times 10^{2}\) & \(2.41\) & \(1.51\times 10^{1}\) & \(1.64\times 10^{1}\) & \(1.18\times 10^{-2}\) & \(\mathbf{4.34\times 10^{-3}}\) \\ F4 & Mean & \(1.48\times 10^{1}\) & \(1.35\times 10^{1}\) & \(4.87\times 10^{2}\) & \(1.02\times 10^{1}\) & \(6.75\) & \(9.19\) & \(\mathbf{3.23}\) & \(1.58\times 10^{1}\) \\  & Std & \(1.12\times 10^{1}\) & \(9.61\) & \(4.98\) & \(3.73\times 10^{1}\) & \(1.72\) & \(6.16\) & \(\mathbf{1.76\times 10^{-2}}\) & \(\mathbf{5.94}\) \\ F5 & Mean & \(5.76\times 10^{2}\) & \(2.91\times 10^{2}\) & \(4.14\times 10^{2}\) & \(6.11\times 10^{2}\) & \(5.14\times 10^{2}\) & \(3.34\times 10^{2}\) & \(\mathbf{1.89\times 10^{2}}\) & \(\mathbf{5.48\times 10^{2}}\) \\  & Std & \(9.36\times 10^{1}\) & \(8.95\times 10^{2}\) & \(6.49\times 10^{2}\) & \(1.46\times 10^{2}\) & \(4.58\times 10^{2}\) & \(1.76\times 10^{2}\) & \(\mathbf{8.85\times 10^{1}}\) & \(1.75\times 10^{2}\) \\  & Mean & \(4.69\times 10^{3}\) & \(5.83\times 10^{3}\) & \(1.13\times 10^{3}\) & \(1.72\times 10^{3}\) & \(7.11\times 10^{2}\) & \(1.78\times 10^{3}\) & \(5.20\times 10^{2}\) & \(\mathbf{4.11\times 10^{2}}\) \\  & Std & \(6.41\times 10^{3}\) & \(1.04\times 10^{4}\) & \(5.75\times 10^{3}\) & \(3.96\times 10^{2}\) & \(7.15\times 10^{2}\) & \(1.38\times 10^{4}\) & \(3.17\times 10^{2}\) & \(\mathbf{2.36\times 10^{2}}\) \\ F7 & Mean & \(5.56\times 3.60\) & \(1.34\) & \(1.53\) & \(8.87\times 10^{-1}\) & \(1.96\) & \(8.99\times 10^{1}\) & \(2.04\) \\  & Std & \(2.12\) & \(4.30\times 10^{1}\) & \(1.99\times 10^{1}\) & \(4.24\times 10^{1}\) & \(2.39\times 10^{1}\) & \(4.07\times 10^{1}\) & \(\mathbf{1.23\times 10^{-1}}\) & \(6.38\times 10^{-1}\) \\  & Mean & \(6.53\times 10^{3}\) & \(1.81\times 10^{3}\) & \(1.27\times 10^{3}\) & \(4.87\times 10^{2}\) & \(6.89\times 10^{2}\) & \(\mathbf{1.79\times 10^{2}}\) & \(4.46\times 10^{2}\) & \(3.09\times 10^{2}\) \\  & Std & \(4.98\times 10^{4}\) & \(3.51\times 10^{3}\) & \(2.54\times 10^{3}\) & \(2.88\times 10^{2}\) & \(1.67\times 10^{3}\) & \(\mathbf{6.33\times 10^{1}}\) & \(1.28\times 10^{2}\) & \(2.23\times 10^{2}\) \\ F9 & Mean & \(1.07\times 10^{2}\) & \(1.01\times 10^{2}\) & \(\mathbf{1\times 10^{2}}\) & \(\mathbf{1\times 10^{2}}\) & \(\mathbf{1\times 10^{2}}\) & \(\mathbf{1\times 10^{2}}\) & \(\mathbf{1\times 10^{2}}\) & \(\mathbf{1\times 10^{2}}\) & \(\mathbf{1\times 10^{2}}\) \\ F10 & Mean & \(3.14\times 10^{2}\) & \(2.59\times 10^{2}\) & \(2.15\times 10^{2}\) & \(\mathbf{1.62\times 10^{4}}\) & \(4.64\times 10^{1}\) & \(1.31\times 10^{2}\) & \(1.90\times 10^{2}\) & \(7.91\times 10^{2}\) \\  & Std & \(2.22\times 10^{1}\) & \(1.11\times 10^{2}\) & \(5.62\times 10^{2}\) & \(\mathbf{5.15}\) & \(1.13\times 10^{2}\) & \(4.49\times 10^{2}\) & \(2.66\times 10^{1}\) & \(8.97\times 10^{2}\) \\ F11 & Mean & \(6.25\times 10^{3}\) & \(5.47\times 1 other algorithms, PSO-ED have achieved obvious advantages on 10-\(D\) and 30-\(D\) except that MPOS and PSO-ED achieved the same optimal result on 10-\(D\).