## 3 Results
### Objective Function Values
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multicolumn{2}{c}{**Function**} & \multirow{2}{*}{**GA**} & \multirow{2}{*}{**PSO**} & \multirow{2}{*}{**DE**} & \multirow{2}{*}{**PRS**} & \multirow{2}{*}{**PROS**} \\  & & & & & & \\ \hline F01 & Sphere & 7.50E-07 & 4.03E-26 & **3.70E+02** & **3.58E+04** & 2.17E-02 \\ F02 & Ellipsoid & 2.25E-05 & 1.15E-24 & **2.80E+03** & **4.57E+05** & 2.92E-01 \\ F03 & Sum of Dif. & 1.50E-12 & 1.54E-52 & **3.50E+03** & **2.46E+15** & 5.35E-06 \\ F04 & Quintic & 1.80E-02 & 4.43E-14 & **2.73E+03** & **1.92E+06** & 5.40E-01 \\ F05 & Drop- & 7.29E-01 & 3.76E-01 & 8.71E-01 & 9.63E-01 & 9.10E-01 \\ F06 & Weierstrass & 3.63E-01 & 1.55E-01 & **2.06E+01** & **4.06E+01** & 4.25E-01 \\ F07 & Alpine 1 & 3.37E-04 & 7.42E-15 & **2.54E+01** & **3.86E+01** & 2.36E-03 \\ F08 & Ackley’s & 6.89E-04 & 4.37E-14 & **6.08E+00** & **1.94E+01** & 3.99E-02 \\ F09 & Griewank’s & 1.23E-03 & 6.39E-03 & **1.07E+00** & **1.01E+01** & 2.51E-02 \\ F10 & Rastrigin’s & 1.99E-01 & **4.56E+01** & **2.34E+02** & **3.14E+02** & 1.03E-02 \\ F11 & HappyCat & 9.79E-01 & 3.39E-01 & 9.38E-01 & **2.88E+01** & 5.63E-01 \\ F12 & HGBat & 9.55E-01 & 4.95E-01 & **7.12E+00** & **8.32E+02** & 6.51E-01 \\ \hline \hline \end{tabular}  
* Average value (in 10 runs) of the obj. function at the end of the optimization process, for each algorithm.  
\end{table} 
Table 7: Best results * for all 5 optimizers and all 12 objective functions, for 30 dimensions (\(D=30\), averages of 10 runs). The target (optimum) value is zero in all cases considered. Figure 4: Best results (final values of the objective functions) for the various optimizers for \(D\) = 5, 10, 30, and 50, for all 12 objective functions (averages of 10 runs)—lower is better. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ID** & **Function Name** & **GA** & **PSO** & **DE** & **PRS** & **PROS** \\ \hline F01 & Sphere & 1.03E-06 & 2.04E-34 & **1.03E+04** & **8.00E+04** & 9.25E-03 \\ F02 & Ellipsoid & 3.50E-05 & 1.19E-32 & **1.46E+05** & **1.77E+06** & 3.77E-01 \\ F03 & Sum of Dif. & 8.98E-13 & 3.65E-60 & **6.01E+14** & **1.50E+30** & 2.80E-06 \\ F04 & Quintic & 1.87E-02 & 3.42E-15 & **4.79E+05** & **5.92E+06** & 5.18E-01 \\ F05 & Drop-Wave & 8.36E-01 & 6.09E-01 & 9.68E-01 & 9.82E-01 & 9.74E-01 \\ F06 & Weierstrass & 4.66E-01 & **2.08E+00** & **5.39E+01** & **7.30E+01** & 5.36E-01 \\ F07 & Alpine 1 & 3.84E-04 & 1.99E-14 & **6.33E+01** & **7.97E+01** & 2.46E-03 \\ F08 & Ackley\({}^{\ast}\) & 5.50E-04 & 1.16E-01 & **1.53E+01** & **2.01E+01** & 1.87E-02 \\ F09 & Griewank’s & 4.44E-08 & 2.47E-03 & **3.59E+00** & **2.04E+01** & 1.13E-02 \\ F10 & Rastrigin’s & 1.25E-04 & **9.60E+01** & **5.02E+02** & **5.99E+02** & 5.74E-03 \\ F11 & HappyCat & **1.08E+00** & 5.01E-01 & **8.57E+00** & **3.89E+01** & 6.92E-01 \\ F12 & HGBat & **1.06E+00** & 6.04E-01 & **2.46E+02** & **1.75E+03** & 5.97E-01 \\ \hline \hline \end{tabular}  
* Average value (in 10 runs) of the obj: function at the end of the optimization process, for each algorithm.  
\end{table} 
Table 8: Best results * for all 5 optimizers and all 12 objective functions, for 50 dimensions (\(D\) = 50, averages of 10 runs). The target (optimum) value is zero in all cases considered.