## 4 Consequences and Discussion
### Experimental Results on UF and DTLZ Problems  
As can be observed in Table 4, CMODE performed the best on UF1, and CMGBO performed second on UF1. The performances on the DTLZ problems are also compared in this section. The consequences reveal that, although MOCLPSO displayed the best performance on DTLZ1, CMGBO ranked third. Moreover, CMPSO and CMGBO demonstrated the best and the second-best performances on DTLZ7, respectively. Moreover, CMGBO and CMPSO ranked first and second in UF and DTLZ on average. Being significantly better than the other three competitors, these two algorithms were also confirmed by the Wilcoxon rank sum test to occupy the first place in performance. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Test Function**} & \multicolumn{1}{c}{**MOEA/D-DE**} & \multicolumn{1}{c}{**CMODE**} & \multicolumn{1}{c}{**MOCLPSO**} & \multicolumn{1}{c}{**CMPSO**} & \multicolumn{1}{c}{**CMGBO**} \\ \hline \multirow{3}{*}{UF1} & Mean & \(6.95\times 10^{-2}\) & \(4.68\times 10^{-2}\) & \(8.52\times 10^{-2}\) & \(7.57\times 10^{-2}\) & \(4.79\times 10^{-2}\) \\  & Std & \(3.00\times 10^{-2}\) & \(8.48\times 10^{-3}\) & \(2.41\times 10^{-2}\) & \(2.01\times 10^{-2}\) & \(1.96\times 10^{-2}\) \\  & Rank & \(3-\) & \(1\approx\) & \(5-\) & \(4-\) & \(2\) \\ \hline \multirow{3}{*}{UF5} & Mean & \(4.60\times 10^{-1}\) & \(2.42\times 10^{-1}\) & \(3.80\times 10^{-1}\) & \(2.52\times 10^{-1}\) & \(2.08\times 10^{-1}\) \\  & Std & \(1.06\times 10^{-1}\) & \(9.58\times 10^{-2}\) & \(9.25\times 10^{-2}\) & \(4.04\times 10^{-2}\) & \(3.24\times 10^{-2}\) \\  & Rank & \(5-\) & \(2-\) & \(4-\) & \(3-\) & \(1\) \\ \hline \multirow{3}{*}{DTLZ1} & Mean & \(9.47\times 10^{-2}\) & \(5.67\times 10^{-2}\) & \(2.07\times 10^{-3}\) & \(2.75\times 10^{-3}\) & \(3.15\times 10^{-3}\) \\  & Std & \(3.25\times 10^{-2}\) & \(2.21\times 10^{-2}\) & \(3.49\times 10^{-4}\) & \(4.36\times 10^{-4}\) & \(5.27\times 10^{-4}\) \\  & Rank & \(5-\) & \(4-\) & \(1+\) & \(2+\) & \(3\) \\ \hline \multirow{3}{*}{DTLZ7} & Mean & \(4.79\times 10^{-2}\) & \(6.61\times 10^{-3}\) & \(4.36\times 10^{-2}\) & \(2.42\times 10^{-3}\) & \(3.73\times 10^{-3}\) \\  & Std & \(9.51\times 10^{-3}\) & \(8.92\times 10^{-3}\) & \(9.12\times 10^{-3}\) & \(6.05\times 10^{-3}\) & \(5.92\times 10^{-3}\) \\  & Rank & \(5-\) & \(3-\) & \(4-\) & \(1+\) & \(2\) \\ \hline \multirow{3}{*}{Final Rank} & Total & \(18\) & \(10\) & \(14\) & \(10\) & \(8\) \\ \cline{2-6}  & Final & \(5\) & \(2\) & \(4\) & \(2\) & \(1\) \\ \hline \multicolumn{2}{c}{Better-Worse} & \(-4\) & \(-3\) & \(-2\) & \(0\) & \\ \hline \multicolumn{2}{c}{**Algorithm**} & \multicolumn{1}{c}{MOEA/D-DE} & \multicolumn{1}{c}{CMODE} & \multicolumn{1}{c}{MOCLPSO} & \multicolumn{1}{c}{CMPSO} & \multicolumn{1}{c}{CMGBO} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Consequences on UF and DTLZ problems. Figure 3: Non-dominated solutions of ZDT problems. Figure 4 indicates the dominant solutions achieved by different methods in solving UF1 problems. CMODE and CMGBO displayed the best uniformity in UF1, and MOCLPSO showed the poorest. The solutions achieved by comparison methods in solving UF5 problems are indicated in Figure 5. In Figure 5e, it can be seen that the solution of CMGBO was closer to the Pareto front of UF5. Moreover, in Figure 5a, MOEA/D-DE demonstrated the poorest performance on UF5, and the approximation distance between the achieved solutions and the PF of UF5 was the largest. Figure 4: Non-dominated solutions of UF1: (**a**) MOEA/D-DE; (**b**) CMODE; (**c**) MOCLPSO; (**d**) CMPSO; (**e**) CMGBO. Figure 5: Non-dominated solutions of UF5: (**a**) MOEA/D-DE; (**b**) CMODE; (**c**) MOCLPSO; (**d**) CMPSO; (**e**) CMGBO. Figure 6 indicates that the approximation degree between the solutions achieved by MOCLPSO and the Pareto front was the best when solving the DTLZ1 problem. CMPSO and CMGBO were placed at the second and the third ranks, respectively. However, the IGD values of the three are not significantly different. MOEA/D-DE and CMODE showed poor performances.