## 4 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **DPSO** & **PSO** & **GA** & **DE** \\ \hline \(f_{0}\) Norm & 1.000 & **4.286\(\times\)10\({}^{-27}\)** & _0.000_ & _2.788\(\times\)10\({}^{-8}\)_ \\ \hline \(f_{1}\) Norm & **4.198\(\times\)10\({}^{-6}\)** & 1.000 & _3.444\(\times\)10\({}^{-4}\)_ & _0.000_ \\ \hline \(f_{2}\) Norm & **2.965\(\times\)10\({}^{-5}\)** & 1.000 & _4.319\(\times\)10\({}^{-5}\)_ & _0.000_ \\ \hline \(f_{3}\) Norm & _0.000_ & **4.829\(\times\)10\({}^{-13}\)** & _2.276\(\times\)10\({}^{-12}\)_ & 1.000 \\ \hline \(f_{4}\) Norm & 1.000 & _1.317\(\times\)10\({}^{-1}\)_ & **8.409\(\times\)10\({}^{-2}\)** & _0.000_ \\ \hline \(f_{5}\) Norm & _0.000_ & _5.785\(\times\)10\({}^{-1}\)_ & **1.915\(\times\)10\({}^{-1}\)** & 1.000 \\ \hline \(f_{6}\) Norm & **2.713\(\times\)10\({}^{-1}\)** & 1.000 & _0.000_ & _5.643\(\times\)10\({}^{-1}\)_ \\ \hline \(f_{7}\) Norm & _5.350\(\times\)10\({}^{-1}\)_ & 1.000 & _4.485\(\times\)10\({}^{-1}\)_ & _0.000_ \\ \hline \(f_{8}\) Norm & _2.126\(\times\)10\({}^{-1}\)_ & 1.000 & _0.000_ & **9.816\(\times\)10\({}^{-2}\)** \\ \hline \(f_{9}\) Norm & _0.000_ & 1.000 & _2.284\(\times\)10\({}^{-1}\)_ & **4.773\(\times\)10\({}^{-3}\)** \\ \hline \(f_{10}\) Norm & _0.000_ & 1.000 & _2.065\(\times\)10\({}^{-1}\)_ & **1.180\(\times\)10\({}^{-1}\)** \\ \hline \(f_{11}\) Norm & _0.000_ & 1.000 & _9.790\(\times\)10\({}^{-2}\)_ & **3.169\(\times\)10\({}^{-2}\)** \\ \hline \(f_{12}\) Norm & **4.899\(\times\)10\({}^{-2}\)** & 1.000 & _0.000_ & _5.153\(\times\)10\({}^{-1}\)_ \\ \hline \(f_{13}\) Norm & _0.000_ & _8.458\(\times\)10\({}^{-1}\)_ & **2.568\(\times\)10\({}^{-1}\)** & 1.000 \\ \hline \(f_{14}\) Norm & **4.650\(\times\)10\({}^{-2}\)** & 1.000 & _3.996\(\times\)10\({}^{-1}\)_ & _0.000_ \\ \hline \(f_{15}\) Norm & _0.000_ & 1.000 & _8.147\(\times\)10\({}^{-1}\)_ & **8.099\(\times\)10\({}^{-1}\)** \\ \hline \(f_{16}\) Norm & **1.924\(\times\)10\({}^{-1}\)** & 1.000 & _0.000_ & _4.153\(\times\)10\({}^{-1}\)_ \\ \hline \(f_{17}\) Norm & _0.000_ & 1.000 & **7.439\(\times\)10\({}^{-1}\)** & _8.794\(\times\)10\({}^{-1}\)_ \\ \hline \(f_{18}\) Norm & _6.275\(\times\)10\({}^{-1}\)_ & **2.121\(\times\)10\({}^{-1}\)** & 1.000 & _0.000_ \\ \hline \(f_{19}\) Norm & **3.254\(\times\)10\({}^{-1}\)** & 9.631\(\times\)10\({}^{-1}\)** & 1.000 & _0.000_ \\ \hline \(f_{20}\) Norm & _0.000_ & 1.000 & _6.042\(\times\)10\({}^{-1}\)_ & **3.920\(\times\)10\({}^{-1}\)** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Normalized fitness w.r.t. each function problem with 7 dimensions and the resulting ranking: _rank 1 (best)_, rank 2, _rank 3,_ and rank 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **DPSO** & **PSO** & **GA** & **DE** \\ \hline \(f_{21}\) Norm & 1.000 & **3.965\(\times\)10\({}^{-4}\)** & _2.108\(\times\)10\({}^{-1}\)_ & _0.000_ \\ \hline \(f_{22}\) Norm & **2.659\(\times\)10\({}^{-3}\)** & 1.000 & _7.282\(\times\)10\({}^{-2}\)_ & _0.000_ \\ \hline \(f_{23}\) Norm & _0.000_ & 1.000 & _1.036\(\times\)10\({}^{-1}\)_ & **8.478\(\times\)10\({}^{-3}\)** \\ \hline Rank Factor & 1.000 & 3.560 & 1.228 & 1.299 \\ \hline Rank Sum & 47 & 84 & 59 & 50 \\ \hline Overall Rank & 1 & 4 & 3 & 2 \\ \hline \hline \end{tabular}
\end{table}