## 4 Consequences and Discussion  
### Experiment Settings  
In order to examine the proposed algorithm, four algorithms, MOEA with decomposition and DE operators (MOEA/D-DE) [31], CMODE [24], multi-objective comprehensive learning PSO (MOCLPSO) [32], and CMPSO [23], were compared. As summarized in Table 1, the parameters of the mentioned algorithms were set. In addition, in order to score the performance of the method by using IGD and HV indicator metrics, ZDTs (two-objective test functions) [25], UFs (two-objective test functions) [33], DTLZs (tri-objective test functions) [34] and MaFs (multi-objective test functions) [35] were used as the benchmark test functions. In total, 15 test problems (5 ZDTs, 2 UFs, 2 DTLZs and 6 MaFs) were carried out, the characteristics of which are described in Table 2. M is the number of objectives. Finally, all of the algorithms were executed 30 times.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Test Function** & **Variables M** & **Variables D** & **Range** & **Optimum** & **Characteristics** \\ \hline ZDT1 & 2 & 30 & \(x_{i}\in[0,1]\), \(x_{i}=0\), & Convex \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Convex \\ ZDT2 & 2 & 30 & \(x_{i}\in[0,1]\), \(x_{i}\in[0,1]\), \(x_{i}=0\), & Convex \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Concave \\ ZDT3 & 2 & 10 & \(x_{i}\in[0,1]\), \(x_{i}=0\), & Convex, \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Disconnected \\ ZDT4 & 2 & 10 & \(x_{1}\in[0,1]\), \(x_{i}=0\), & Concave \\  & & \(2\leq i\leq D\) & & Convex \\ ZDT6 & 2 & 10 & \(x_{i}\in[0,1]\), \(x_{i}\in[0,1]\), \(x_{i}=0\), & Concave \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Convex, \\  & & \(x_{i}\in[-1,1]\), & \(x_{i}=\sin\left(6\pi x_{1}+\frac{i\tau}{D}\right)\), & Disconnected \\  & & \(2\leq i\leq D\) & \(2\leq i\leq D\) & \\ UF5 & 2 & 30 & \(x_{i}\in[-1,1]\), & \((F_{1},F_{2})=\left(\frac{i}{2N},1-\frac{i}{2N}\right)\), & Scatter, \\  & & \(2\leq i\leq D\) & \(0\leq i\leq 2N\), \(N=10\) & Disconnected \\ DTLZ1 & 3 & 12 & \(x_{i}\in[0,1]\), \(x_{i}\in[0,1]\), \(x_{i}=0.5\), & Linear \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Convex, \\ DTLZ7 & 3 & 12 & \(x_{i}\in[0,1]\), \(x_{i}\in[0,1]\), \(x_{i}=0.5\), & Concave, \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Disconnected \\ MaF1 & 10 & 19 & \(x_{i}\in[0,1]\), \(x_{i}=0.5\), & Linear \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & \\ MaF2 & 10 & 19 & \(x_{i}\in[0,1]\), \(x_{i}=0.5\), & Concave \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Convex, \\ MaF3 & 10 & 19 & \(x_{i}\in[0,1]\), \(x_{i}=0.5\), & Multimodal \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Badly Scaled \\  & & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Badly Scaled \\  & & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Badly Scaled \\  & & & & \\ MaF5 & 10 & 19 & \(x_{i}\in[0,1]\), \(x_{i}=0.5\), & \(x_{i}\in[0,1]\), \(x_{i}=0.5\), & Biased, \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Badly Scaled \\  & & & \(x_{i}\in[0,1]\), \(x_{i}=0.5\), & Concave, \\  & & \(1\leq i\leq D\) & \(2\leq i\leq D\) & Degenerate \\ \hline \end{tabular}
\end{table}
Table 2: Characteristics of multi-objective test functions.  
\begin{table}
\begin{tabular}{c c c} \hline
**Algorithm** & **Parameters** \\ \hline MOEA/D-DE & \(N=100\), \(CR=1.0\), \(F=0.5\), \(h=20\), \\  & \(p_{m}=\frac{1}{D}\), \(T=20\), \(\delta=0.9\), and \(n_{r}=2\) \\ CMODE & \(N=20\), \(|A|=100\), \(CR=1.0\), \(F=0.5\), \(h=20\), \\  & \(p_{m}=\frac{1}{D}\), \(T=20\), \(\delta=0.9\), and \(n_{r}=2\) \\ MOCLPSO & \(N=100\), \(p_{c}=0.1\), \(p_{m}=0.4\), \(\omega=0.9\to 0.2\), \\  & and \(c=2\) & \(N=20\), \(|A|=100\), \(\omega=0.9\to 0.2\), \\  & & and \(c_{1}=c_{2}=c_{3}=2.0\) \\ CMGBO & \(N_{init}=5\), \(N_{max}=20\), \(|A|=100\), \(N_{sec}=5\), \\  & & \(n=3\), \(F=2\), and \(P=2\) \\ \hline \end{tabular}
\end{table}
Table 1: Preferences settings.