## 4 Experimental and Discussions
### Experimental Results
Figure 1: Plots of the final non-dominated solutions in the objective space of DEB, ZDT1–ZDT4, and ZDT6. Figure 2: Plots of the all 30 PFs for DEB, ZDT1\(\sim\)ZDT4, and ZDT6. \begin{table}
\begin{tabular}{c c c c c c} \hline Function & Min & Mean & Std & Max & Algorithms \\ \hline \multirow{4}{*}{UF1} & 0.004711 & 0.023042 & 0.053302 & 0.259563 & MOEA/D \\  & **0.004466** & 0.028572 & 0.023609 & 0.071182 & MOEA/D-DE+PSO \\  & 0.004594 & **0.005203** & **0.000248** & **0.006144** & MOEA/D-CDDE \\ \hline \multirow{4}{*}{UF2} & 0.009082 & 0.014285 & 0.007173 & 0.049397 & MOEA/D \\  & 0.010218 & **0.011737** & **0.000756** & **0.013261** & MOEA/D-DE+PSO \\  & **0.008998** & 0.011877 & 0.001714 & 0.015334 & MOEA/D-CDDE \\ \hline \multirow{4}{*}{UF3} & 0.016796 & 0.062967 & 0.028005 & 0.142894 & MOEA/D \\  & **0.003940** & **0.006039** & **0.001826** & **0.010494** & MOEA/D-DE+PSO \\  & 0.008435 & 0.044706 & 0.029862 & 0.114730 & MOEA/D-CDDE \\ \hline \end{tabular}
\end{table} 
Table 2: The IGD values statistics of the non-dominated solutions found by MOEA/D, MOEA/D-DE+PSO and MOEA/D-CPDE on UF1-UF10 in 30 independent runs. Figure 3: Average IGD values versus number of function evaluations over DEB, ZDT1\(\sim\)ZDT4, and ZDT6 \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{UF4} & 0.061278 & 0.069968 & 0.006585 & 0.089038 & MOEA/D \\ \cline{2-6}  & 0.047843 & 0.054604 & 0.004053 & 0.071241 & MOEA/D-DE+PSO \\ \cline{2-6}  & **0.043632** & **0.045344** & **0.001319** & **0.049677** & MOEA/D-CPDE \\ \hline \multirow{2}{*}{UF5} & 0.208215 & 0.422297 & 0.128282 & 0.729846 & MOEA/D \\  & 0.282111 & 0.490882 & 0.118561 & 0.708999 & MOEA/D-DE+PSO \\  & **0.115859** & **0.203445** & **0.045309** & **0.258254** & MOEA/D-CPDE \\ \hline \multirow{2}{*}{UF6} & 0.162838 & 0.495739 & 0.199592 & 0.824257 & MOEA/D \\  & 0.186140 & 0.243517 & 0.237355 & 0.674953 & MOEA/D-DE+PSO \\  & **0.073819** & **0.091573** & **0.030068** & **0.210588** & MOEA/D-CPDE \\ \hline \multirow{2}{*}{UF7} & **0.005013** & 0.147765 & 0.219858 & 0.598471 & MOEA/D \\  & 0.006726 & 0.243517 & 0.237355 & 0.674953 & MOEA/D-DE+PSO \\  & 0.005112 & **0.006067** & **0.000640** & **0.007461** & MOEA/D-CPDE \\ \hline \multirow{2}{*}{UF8} & 0.090851 & 0.145518 & 0.031061 & 0.229571 & MOEA/D \\  & **0.057600** & **0.078455** & 0.006532 & **0.101902** & MOEA/D-DE+PSO \\  & 0.112641 & 0.123347 & **0.006231** & 0.139016 & MOEA/D-CPDE \\ \hline \multirow{2}{*}{UF9} & 0.087260 & 0.166323 & 0.033758 & 0.194023 & MOEA/D \\  & **0.035499** & **0.071131** & 0.035008 & 0.149478 & MOEA/D-DE+PSO \\  & 0.074763 & 0.080028 & **0.002555** & **0.083058** & MOEA/D-CPDE \\ \hline \multirow{2}{*}{UF10} & 0.231245 & 0.431299 & 0.084250 & 0.637907 & MOEA/D \\  & **0.184050** & **0.187158** & **0.001552** & **0.190097** & MOEA/D-DE+PSO \\  & 0.369133 & 0.499921 & 0.078278 & 0.688156 & MOEA/D-CPDE \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 4: _Cont._  
Figure 4: Plots of the best PF in the objective space of the UF1-UF10 in 30 independent runs. Figure 5: _Cont._  
Figure 5: Plots of the all 30 PFs in the objective space of the UF1-UF10 in 30 independent runs  
Figure 6: _Cont._