## 5 Experimental Results and Analysis
### Comparison with DE, PSO, and Three State-of-the-Art DE Variants

Table 4: _Cont._  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Function** & **Metrics** & **HE-DEPSO** & **DEPSO** & **SHADE** & **CoDE** & **DE** & **PSO** \\ \hline \multirow{3}{*}{\(F_{1}\)} & Mean & **1.6045 \(\times\)10\({}^{-14}\)** & 2.0034 \(\times\)10\({}^{-4}\) & 2.3598\(\times\)10\({}^{3}\) & 1.2860\(\times\)10\({}^{8}\) & 2.0817 \(\times\)10\({}^{9}\) & 6.3600 \(\times\)10\({}^{10}\) \\  & Std & **6.0758 \(\times\)10\({}^{-15}\)** & 4.9086 \(\times\)10\({}^{-4}\) & 1.2985 \(\times\)10\({}^{3}\) & 3.5599 \(\times\)10\({}^{7}\) & 7.3074 \(\times\)10\({}^{8}\) & 5.8100 \(\times\)10\({}^{10}\) \\  & Rank & **1** & 2 & 3 & 4 & 5 & 6 \\  & Significance & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline \multirow{3}{*}{\(F_{3}\)} & Mean & **1.4486 \(\times\)10\({}^{-13}\)** & 1.3343 \(\times\)10\({}^{2}\) & 6.1189 \(\times\)10\({}^{4}\) & 7.0539 \(\times\)10\({}^{4}\) & 4.1473 \(\times\)10\({}^{5}\) & 2.1200 \(\times\)10\({}^{4}\) \\  & Std & **4.1092 \(\times\)10\({}^{-14}\)** & 8.8712 \(\times\)10\({}^{1}\) & 2.2749 \(\times\)10\({}^{4}\) & 2.6622 \(\times\)10\({}^{4}\) & 1.3053 \(\times\)10\({}^{5}\) & 2.9800 \(\times\)10\({}^{4}\) \\  & Rank & **1** & 2 & 4 & 5 & 6 & 3 \\  & Significance & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline \multirow{3}{*}{\(F_{4}\)} & Mean & **2.8405\(\times\)10\({}^{0}\)** & 1.2605 \(\times\)10\({}^{1}\) & 7.7040 \(\times\)10\({}^{1}\) & 9.6061 \(\times\)10\({}^{1}\) & 3.5736 \(\times\)10\({}^{1}\) & 1.7300 \(\times\)10\({}^{3}\) \\  & Std & **2.1842 \(\times\)10\({}^{0}\)** & 8.6176 \(\times\)10\({}^{0}\) & 3.8595 \(\times\)10\({}^{0}\) & 2.0503 \(\times\)10\({}^{1}\) & 3.2288 \(\times\)10\({}^{0}\) & 1.3000 \(\times\)10\({}^{3}\) \\  & Rank & **1** & 2 & 4 & 5 & 3 & 6 \\  & Significance & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline \multirow{3}{*}{\(F_{5}\)} & Mean & **2.3850 \(\times\)10\({}^{1}\)** & 1.8175 \(\times\)10\({}^{2}\) & 9.3463 \(\times\)10\({}^{1}\) & 1.8418 \(\times\)10\({}^{2}\) & 2.4169 \(\times\)10\({}^{2}\) & 1.8500 \(\times\)10\({}^{2}\) \\  & Std & **5.0701 \(\times\)10\({}^{0}\)** & 1.2845 \(\times\)10\({}^{1}\) & 1.0871 \(\times\)10\({}^{1}\) & 1.2630 \(\times\)10\({}^{1}\) & 1.2302 \(\times\)10\({}^{1}\) & 4.4900 \(\times\)10\({}^{1}\) \\  & Rank & **1** & 3 & 2 & 4 & 6 & 5 \\  & Significance & & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline \multirow{3}{*}{\(F_{6}\)} & Mean & 4.6793 \(\times\)10\({}^{-1}\) & **5.7971 \(\times\)10\({}^{-3}\)** & 3.7760 \(\times\)10\({}^{1}\) & 5.8751 \(\times\)10\({}^{1}\) & 2.4651 \(\times\)10\({}^{1}\) & 5.3800 \(\times\)10\({}^{1}\) \\  & Std & 3.5101 \(\times\)10\({}^{-1}\) & **2.9636 \(\  
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Function** & **Metrics** & **HE-DEPSO** & **DEPSO** & **SHADE** & **CoDE** & **DE** & **PSO** \\ \hline  & Significance & & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline  & Mean & **3.2932 \(\times\)10\({}^{1}\)** & 7.9240 \(\times\)10\({}^{1}\) & 7.3961 \(\times\)10\({}^{1}\) & 2.7578 \(\times\)10\({}^{2}\) & 2.1665 \(\times\)10\({}^{2}\) & 9.3600 \(\times\)10\({}^{2}\) \\ \(F_{11}\) & Std & 1.7540 \(\times\)10\({}^{1}\) & **9.4859\(\times\)10\({}^{0}\)** & 1.6453 \(\times\)10\({}^{1}\) & 6.0425 \(\times\)10\({}^{1}\) & 4.1872 \(\times\)10\({}^{1}\) & 1.7000\(\times\)10\({}^{3}\) \\  & Rank & **1** & 3 & 2 & 5 & 4 & 6 \\  & Significance & & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline  & Mean & **6.0704 \(\times\)10\({}^{3}\)** & 7.4374\(\times\)10\({}^{4}\) & 1.7001 \(\times\)10\({}^{6}\) & 5.9649 \(\times\)10\({}^{8}\) & 2.5500 \(\times\)10\({}^{9}\) & 1.1600 \(\times\)10\({}^{10}\) \\ \(F_{12}\) & Std & **5.2411 \(\times\)10\({}^{3}\)** & 7.3297 \(\times\)10\({}^{4}\) & 5.7892 \(\times\)10\({}^{5}\) & 1.8156 \(\times\)10\({}^{8}\) & 8.9672 \(\times\)10\({}^{8}\) & 1.5200 \(\times\)10\({}^{10}\) \\  & Rank & **1** & 2 & 3 & 4 & 5 & 6 \\  & Significance & & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline  & Mean & **5.3737 \(\times\)10\({}^{1}\)** & 2.3200 \(\times\)10\({}^{3}\) & 7.2862 \(\times\)10\({}^{3}\) & 3.3010 \(\times\)10\({}^{8}\) & 1.0201 \(\times\)10\({}^{8}\) & 1.0300 \(\times\)10\({}^{10}\) \\ \(F_{13}\) & Std & **4.9535 \(\times\)10\({}^{1}\)** & 5.3868 \(\times\)10\({}^{3}\) & 2.4057 \(\times\)10\({}^{4}\) & 8.7976 \(\times\)10\({}^{7}\) & 3.9539 \(\times\)10\({}^{7}\) & 1.5000 \(\times\)10\({}^{10}\) \\  & Rank & **1** & 2 & 3 & 5 & 4 & 6 \\  & Significance & & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline  & Mean & **5.1892 \(\times\)10\({}^{1}\)** & 9.7833 \(\times\)10\({}^{1}\) & 7.5446 \(\times\)10\({}^{1}\) & 1.5942 \(\times\)10\({}^{4}\) & 4.0951 \(\times\)10\({}^{3}\) & 2.2100 \(\times\)10\({}^{8}\) \\ \(F_{14}\) & Std & 1.3639 \(\times\)10\({}^{1}\) & 2.2150 \(\times\)10\({}^{1}\) & **1.0230 \(\times\)10\({}^{1}\)** & 4.5198 \(\times\)10\({}^{3}\) & 8.1599 \(\times\)10\({}^{2}\) & 4.9000 \(\times\)10\({}^{5}\) \\  & Rank & **1** & 3 & 2 & 5 & 4 & 6 \\  & Significance & & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline  & Mean & **6.7166 \(\times\)10\({}^{1}\)** & 7.9018 \(\times\)10\({}^{1}\) & 1.0487 \(\times\)10\({}^{2}\) & 3.0409 \(\times\)10\({}^{7}\) & 3.1028 \(\times\)10\({}^{6}\) & 2.9100 \(\times\)10\({}^{8}\) \\ \(F_{15}\) & Std & 4.6957 \(\times\)10\({}^{1}\) & 3.4973 \(\times\)10\({}^{1}\) & **2.4704 \(\times\)10\({}^{1}\)** & 9.9730 \(\times\)10\({}^{6}\) & 1.2198 \(\times\)10\({}^{6}\) & 1.6200 \(\times\)10\({}^{9}\) \\  & Rank & **1** & 2 & 3 & 5 & 4 & 6 \\  & Significance & & \(\approx\) & \(\approx\) & \(+\) & \(+\) & \(+\) \\ \hline  & Mean & **2.7544 \(\times\)10\({}^{2}\)** & 1.4323 \(\times\)10\({}^{3}\) & 8.5936 \(\times\)10\({}^{2}\) & 1.6794 \(\times\)10\({}^{3}\) & 2.3141 \(\times\)10\({}^{3}\) & 1.7100 \(\times\)10\({}^{3}\) \\ \(F_{16}\) & Std & 1.4178 \(\times\)10\({}^{2}\) & 1.6353 \(\times\)10\({}^{2}\) & **1.1941 \(\times\)10\({}^{2}\)** & 1.7833 \(\times\)10\({}^{2}\) & 1.8579 \(\times\)10\({}^{2}\) & 6.0700 \(\times\)10\({}^{2}\) \\  & Rank & **1** & 3 & 2 & 4 & 6 & 5 \\  & Significance & & \(+\) & \(+\) & \(+\) & \(+\) & \(+\) \\ \hline  & Mean & **6.6918 \(\times\)10\({}^{1}\)** & 3.8170 \(\times\)10\({}^{1}\) & 1.9226 \(\times\)10\({}^{2}\) & 6.8169 \(\times\)10\({}^{2}\) & 1.1646 \(\times\)10\({}^{3}\) & 8.4800 \(\times\)10\({}^{2}\) \\ \(F_{17}\) & Std & **1.3274 \(\times\)10\({}^{1}\)** & 1.0402 \(\times\)10\({}^{2}\) & 6.2540 \(\times\)10\({}^{1}\) & 9.4653 \(\times\)10\({}^{1}\) & 1.4710 \(\times\)10\({}^{2}\) & 3.2100 \(\times\)10\({}^{2}\) \\  & Rank & **1** & 3 & 2 & 4 & 6 & 5 \\  & Significance & & \(+\) & \