## 2 Knowledge and Tools of Model Preparation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & \multirow{2}{*}{**Objective Function Expression**} & \multirow{2}{*}{**Constraint Scope**} & \multicolumn{2}{c}{**Characteristic**} \\
**Function** & & & **Continuity** & **Convexity** \\ \hline
**ZDT1** & \(f_{1}(x)=x_{1}\);\(f_{2}(x)=g\big{(}1-\sqrt{f_{1}/g}\big{)}\); & & & \\  & \(g(x)=1+9\sum\limits_{i=2}^{n}x_{i}/(n-1)\) & [0,1] & ✓ & ✓ \\ \hline
**ZDT2** & \(f_{1}(x)=x_{1}\);\(f_{2}(x)=g\big{(}1-\left(f_{1}/g\right)^{2}\big{)}\); & & & \\  & \(g(x)=1+9\sum\limits_{i=2}^{n}x_{i}/(n-1)\) & [0,1] & ✓ & ✗ \\ \hline
**ZDT3** & \(f_{1}(x)=x_{1}\); & & & \\  & \(f_{2}(x)=g\big{(}1-\sqrt{f_{1}/g}-\left(f_{1}/g\right)\sin(10\pi f_{1})\big{)}\); & [0,1] & ✗ & ✓ \\  & \(g(x)=1+9\sum\limits_{i=2}^{n}x_{i}/(n-1)\) & & & \\ \hline
**ZDT4** & \(f_{1}(x)=x_{1}\);\(f_{2}(x)=g(x)\big{(}1-\sqrt{f_{1}/g}\big{)}\); & \(x_{1}\in[0,1]\) & & \\  & \(g(x)=91+\sum\limits_{i=2}^{n}\big{(}x_{i}^{2}-10\cos(4\pi x_{i})\big{)}\) & \(x_{2},\cdots,x_{n}\in[-5,5]\) & ✓ & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Test functions details of multi-objective optimization algorithm. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multirow{2}{*}{**Population**} & \multicolumn{4}{c}{**MOEA/D**} & \multicolumn{4}{c}{**MOGWO**} & \multicolumn{4}{c}{**MODA**} \\ \cline{2-11}  & & **IGD** & **Spread** & **Time** & **IGD** & **Spread** & **Time** & **IGD** & **Spread** & **Time** \\ \hline \multirow{4}{*}{**ZDT1**} & 100 & 0.0013 & 0.5739 & 3.1097 & 0.0193 & 0.8866 & 116.0957 & 0.0250 & 1.0384 & 20.4854 \\  & 200 & 0.0012 & 0.4851 & 6.1752 & 0.0130 & 0.9015 & 245.1288 & 0.0019 & 1.5494 & 68.4797 \\  & 300 & 0.0009 & 0.7106 & 9.0026 & 0.0192 & 0.9386 & 401.7427 & 0.0059 & 1.4796 & 153.8985 \\  & 500 & 0.0006 & 0.5515 & 15.3153 & 0.0227 & 0.9087 & 815.3593 & 0.0017 & 1.6583 & 366.6784 \\  & 100 & 0.0014 & 0.8703 & 3.1883 & 0.0192 & 0.9375 & 116.4861 & 0.0115 & 1.3818 & 23.7629 \\
**ZDT2** & 200 & 0.0009 & 0.4600 & 6.0418 & 0.0921 & 240.5254 & 0.0046 & 1.4826 & 76.2966 \\  & 300 & 0.0008 & 0.6134 & 9.2865 & 0.0369 & 1.1613 & 410.1265 & 0.0036 & 1.2181 & 135.2485 \\  & 500 & 0.0006 & 0.5741 & 15.3978 & 0.0248 & 1.0642 & 848.2862 & 0.0018 & 1.6289 & 363.9597 \\  & 100 & 0.0013 & 0.5202 & 3.1662 & 0.0257 & 1.3397 & 814.449 & 0.0137 & 1.3363 & 18.3297 \\
**ZDT3** & 200 & 0.0008 & 0.5452 & 6.1386 & 0.0275 & 1.1883 & 143.5205 & 0.0142 & 1.5089 & 57.9230 \\  & 300 & 0.0010 & 0.6783 & 9.0859 & 0.0284 & 1.2127 & 206.6538 & 0.0144 & 1.4316 & 116.3454 \\  & 500 & 0.0005 & 0.7504 & 15.5836 & 0.0286 & 1.1296 & 351.9125 & 0.0141 & 1.3629 & 301.9244 \\  & 100 & 0.0015 & 0.5218 & 3.1690 & 0.0165 & 9.0105 & 118.7787 & 0.0107 & 1.1224 & 16.4013 \\
**ZDT4** & 200 & 0.0008 & 0.4419 & 6.0650 & 0.0267 & 0.9716 & 240.0666 & 0.0028 & 1.4110 & 66.0034 \\  & 300 & 0.0006 & 0.4475 & 9.1421 & 0.0327 & 1.0000 & 406.4541 & 0.0026 & 1.4141 & 335.4201 \\  & 500 & 0.0010 & 0.6344 & 15.3649 & 0.0237 & 1.0559 & 858.8985 & 0.0053 & 1.3491 & 344.9575 \\ \hline \hline \end{tabular}
\end{table} 
Table 12. Results of MOEA/D and compared algorithms Multi-objective Grey Wolf Optimization (MOGWO), Multi-objective Ant Lion Optimizer (MOALO) and Multi-objective Dragonfly Algorithm (MODA). Specially, the simple average method is to use the simple average formula under statistical sense to calculate the final predicted value. The method formula is briefly introduced as follows:

\[f=\frac{f_{1}+f_{2}+f_{3}+f_{4}}{4} \tag{23}\]

where \(f_{i}\) is the prediction results of the corresponding model. The linear combination of the models is the weighted combination of the results of the four single models, and a final prediction value is obtained. The weights are determined by the multi-objective optimization algorithm, which increases the intelligence of the method. The effects of each combination mechanism are compared based on five point forecasting error measurement rules and four interval error forecasting measurement rules.