# A New Chaotic-Based Approach for Multi-Objective Optimization
## 4 Computational Experiments
### Comparison with Some State-Of The-Art Evolutionary Algorithms
In fact, in this kind of metaheuristics, an update of the archive of non dominated points is carried out after each cycle of the algorithms. Therefore, if all the algorithms in comparison were adopting an \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Nsq2**} & \multicolumn{2}{c}{**Pes2**} & \multicolumn{2}{c}{**Moead**} & \multicolumn{2}{c}{**Xtornado-TM**} \\ \hline
**Fct** & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** \\ \hline ine \(F_{1}\) & \(6.69\times 10^{-3}\) & \(1.50\times 10^{-3}\) & \(5.87\times 10^{-2}\) & \(1.22\times 10^{-2}\) & \(2.74\times 10^{-2}\) & \(2.49\times 10^{-2}\) & \(\mathbf{2.38\times 10^{-3}}\) & \(\mathbf{7.10\times 10^{-7}}\) \\ \(F_{2}\) & \(6.56\times 10^{-3}\) & \(1.43\times 10^{-3}\) & \(8.62\times 10^{-2}\) & \(5.97\times 10^{-3}\) & \(2.48\times 10^{-1}\) & \(1.04\times 10^{-1}\) & \(\mathbf{6.61\times 10^{-4}}\) & \(\mathbf{4.42\times 10^{-4}}\) \\ \(F_{3}\) & \(1.15\times 10^{-2}\) & \(4.57\times 10^{-3}\) & \(4.20\times 10^{-2}\) & \(3.75\times 10^{-3}\) & \(3.27\times 10^{-2}\) & \(1.71\times 10^{-2}\) & \(\mathbf{2.45\times 10^{-3}}\) & \(\mathbf{1.68\times 10^{-4}}\) \\ \(F_{4}\) & \(8.63\times 10^{-2}\) & \(8.00\times 10^{-2}\) & \(1.07\times 10^{+1}\) & \(2.87\times 10^{-1}\) & \(8.49\times 10^{+0}\) & \(2.04\times 10^{+0}\) & \(\mathbf{1.72\times 10^{-3}}\) & \(\mathbf{3.61\times 10^{-4}}\) \\ \(F_{5}\) & \(1.54\times 10^{-2}\) & \(3.14\times 10^{-2}\) & \(4.37\times 10^{-1}\) & \(8.26\times 10^{-3}\) & \(6.62\times 10^{-1}\) & \(1.78\times 10^{-1}\) & \(\mathbf{3.88\times 10^{-3}}\) & \(\mathbf{1.97\times 10^{-3}}\) \\ \(F_{6}\) & \(\mathbf{9.73\times 10^{-4}}\) & \(\mathbf{4.76\times 10^{-5}}\) & \(8.83\times 10^{-2}\) & \(2.49\times 10^{-2}\) & \(1.57\times 10^{-3}\) & \(1.31\times 10^{-3}\) & \(1.39\times 10^{-3}\) & \(3.41\times 10^{-5}\) \\ \(F_{7}\) & \(\mathbf{6.96\times 10^{-5}}\) & \(\mathbf{6.44\times 10^{-6}}\) & \(9.26\times 10^{+1}\) & \(1.00\times 10^{+1}\) & \(5.66\times 10^{-4}\) & \(9.35\times 10^{-4}\) & \(2.38\times 10^{-3}\) & \(5.41\times 10^{-7}\) \\ \(F_{8}\) & \(\mathbf{1.74\times 10^{-3}}\) & \(\mathbf{2.52\times 10^{-5}}\) & \(6.45\times 10^{-2}\) & \(5.93\times 10^{-3}\) & \(1.30\times 10^{-3}\) & \(2.12\times 10^{-4}\) & \(2.38\times 10^{-3}\) & \(1.23\times 10^{-6}\) \\ \(F_{9}\) & \(4.08\times 10^{-2}\) & \(9.28\times 10^{-3}\) & \(3.75\times 10^{-2}\) & \(4.12\times 10^{-3}\) & \(1.88\times 10^{-2}\) & \(4.04\times 10^{-3}\) & \(\mathbf{2.16\times 10^{-3}}\) & \(\mathbf{4.11\times 10^{-4}}\) \\ \(F_{10}\) & \(7.38\times 10^{-4}\) & \(8.84\times 10^{-5}\) & \(1.78\times 10^{-1}\) & \(1.08\times 10^{-2}\) & \(1.13\times 10^{-2}\) & \(1.26\times 10^{-2}\) & \(\mathbf{6.41\times 10^{-4}}\) & \(\mathbf{5.50\times 10^{-6}}\) \\ \(F_{11}\) & \(4.51\times 10^{-3}\) & \(6.32\times 10^{-4}\) & \(1.82\times 10^{-9}\) & \(1.89\times 10^{+8}\) & \(4.59\times 10^{+0}\) & \(1.01\times 10^{+1}\) & \(\mathbf{2.38\times 10^{-3}}\) & \(\mathbf{4.30\times 10^{-10}}\) \\ \(F_{12}\) & \(1.05\times 10^{-3}\) & \(1.27\times 10^{-4}\) & \(3.23\times 10^{-2}\) & \(1.03\times 10^{-3}\) & \(1.27\times 10^{-3}\) & \(4.30\times 10^{-4}\) & \(\mathbf{8.42\times 10^{-4}}\) & \(\mathbf{1.43\times 10^{-6}}\) \\ \(F_{13}\) & \(8.29\times 10^{-4}\) & \(9.40\times 10^{-5}\) & \(6.28\times 10^{-3}\) & \(1.81\times 10^{-3}\) & \(2.04\times 10^{-3}\) & \(3.16\times 10^{-3}\) & \(\mathbf{7.80\times 10^{-4}}\) & \(\mathbf{7.50\times 10^{-13}}\) \\ \(F_{14}\) & \(6.05\times 10^{-4}\) & \(6.94\times 10^{-5}\) & \(2.98\times 10^{-4}\) & \(1.79\times 10^{-4}\) & \(3.66\times 10^{-4}\) & \(8.88\times 10^{-5}\) & \(\mathbf{5.66\times 10^{-4}}\) & \(\mathbf{1.02\times 10^{-11}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The Generational distance metric (\(GD\)) comparison result for the for algorithms on the 14 selected problems.