## 6 Conclusions  
This paper presents a population knowledge mining approach combined with a hybrid machine learning algorithm to solve the MOJSSP with makespan and total tardiness criteria. The purpose \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**IP**} & \multicolumn{3}{c}{**IT100**} & \multicolumn{3}{c}{**IT300**} \\ \cline{3-7}  & & \multicolumn{2}{c}{**Cov**} & \multicolumn{2}{c}{**Spacing**} & \multicolumn{2}{c}{**Cov**} & \multicolumn{2}{c}{**Spacing**} \\ \hline \multirow{4}{*}{ADSM} & \multirow{2}{*}{25} & best & **1** & \multirow{2}{*}{**37**} & **1** & \multirow{2}{*}{**0.42**} & \multirow{2}{*}{**8.8**} \\  & & average & **0.54** & & & & \\ \cline{2-7}  & \multirow{2}{*}{50} & best & **1** & \multirow{2}{*}{**25**} & **1** & \multirow{2}{*}{**0.47**} & \multirow{2}{*}{39} \\  & & average & **0.59** & & & & \\ \cline{2-7}  & \multirow{2}{*}{100} & best & **1** & \multirow{2}{*}{**29**} & **1** & \multirow{2}{*}{**0.39**} & \multirow{2}{*}{**22**} \\  & & average & **0.55** & & & & \\ \hline \multirow{4}{*}{Nasiri’s} & \multirow{2}{*}{25} & best & 0.75 & \multirow{2}{*}{41} & \multirow{2}{*}{0.35} & \multirow{2}{*}{44} \\  & & average & 0.19 & & & & \\ \cline{2-7}  & \multirow{2}{*}{50} & best & 0.9 & \multirow{2}{*}{46} & \multirow{2}{*}{0.33} & \multirow{2}{*}{**29**} \\  & & average & 0.21 & & & \\ \cline{2-7}  & \multirow{2}{*}{100} & best & 0.8 & \multirow{2}{*}{71} & \multirow{2}{*}{0.37} & \multirow{2}{*}{64} \\  & & average & 0.16 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Comparison of Cov and Spacing of two rule-based populations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **IP** & **IT** & **F1** & **F2** & **RE** \\ \hline \multirow{4}{*}{ADSM} & \multirow{2}{*}{25} & best & **852** & \(\mathbf{-4693}\) & \(8.49\)[\(6.58\) \\  & & average & 924.3 & \(\mathbf{-4384.3}\) & / \\ \cline{3-5}  & & 300 & best & \(\mathbf{848}\) & \(\mathbf{-4731}\) & \(\mathbf{5.83\)[\(4.34\)] \\  & & average & \(\mathbf{897.4}\) & \(\mathbf{-4525.9}\) & / \\ \cline{2-7}  & \multirow{2}{*}{50} & best & \(\mathbf{852}\) & \(\mathbf{-4568}\) & \(\mathbf{5.94\)[\(3.27\) \\  & & average & \(\mathbf{902.6}\) & \(\mathbf{-4418.4}\) & / \\ \cline{3-5}  & & 300 & best & \(\mathbf{848}\) & \(\mathbf{-4835}\) & \(8.54\)[\(4.87\) \\  & & average & \(\mathbf{920.4}\) & \(\mathbf{-4599.3}\) & / \\ \hline \multirow{4}{*}{100} & \multirow{2}{*}{100} & best & \(\mathbf{848}\) & \(\mathbf{-4696}\) & \(7.5\)[\(4\) \\  & & average & \(\mathbf{912}\) & \(\mathbf{-4500}\) & / \\ \cline{3-5}  & & 300 & best & \(\mathbf{848}\) & \(\mathbf{-4717}\) & \(\mathbf{6.7\)[\(2\) \\  & & average & \(\mathbf{905}\) & \(\mathbf{-4622}\) & / \\ \hline \multirow{4}{*}{25} & \multirow{2}{*}{100} & best & \(853\) & \(\mathbf{-4587}\) & \(\mathbf{45.8}\) \\  & & average & \(\mathbf{887}\) & \(\mathbf{-4319}\) & / \\ \cline{3-5}  & & 300 & best & \(848\) & \(\mathbf{-4810}\) & \(8.84\)[\(5.51\) \\  & & average & \(\mathbf{923}\) & \(\mathbf{-4545}\) & / \\ \cline{3-5}  & & 300 & best & \(\mathbf{848}\) & \(\mathbf{-4558}\) & \(7.8\)[\(1.34\) \\  & & average & \(914.2\) & \(\mathbf{-4497}\) & / \\ \cline{3-5}  & & 300 & best & \(848\) & \(\mathbf{-4822}\) & \(\mathbf{7.1\)[\(5.4\) \\  & & average & \(\mathbf{908}\) & \(\mathbf{-4561.5}\) & / \\ \hline \multirow{4}{*}{100} & \multirow{2}{*}{100} & best & \(848\) & \(\mathbf{-4642}\) & \(\mathbf{63.8}\) \\  & & average & \(\mathbf{896.3}\) & \(\mathbf{-4467}\) & / \\ \cline{3-5}  & & 300 & best & \(848\) & \(\mathbf{-4799}\) & \(12.7\)[\(4.6\) \\ \cline{3-5}  & & average & \(956\) & \(\mathbf{-4576}\) & / \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Comparison of function values of two rule-based populations. of this method is to find a rule-based initial population from good production planning, which can produce better Pareto solutions than the traditional stochastic methods.