## 4 The Hybrid Machine Learning and Population Knowledge Mining Method
### Rule Mining  
Rule mining refers to mining association rules between attribute set {operation feature, processing time, remaining time, due date} and attribute {priority}. The decision tree is an effective means of mining classification. Here, we can get 33 rules from the theory of entropy, which is shown in Supplementary Materials File S1. However, the mined rules may have different priorities for the same attribute set. To discriminate this difference and enhance the richness of excellent populations, the weight of a priority class [12] in this paper is used to mine the rules behind the training data. The minimum value of the weight we set here is 0.01, which is the lower bound of the weight of the priority class. When the weight of a rule set under a priority class is less than this value, the rule set is considered not to belong to the priority class. The obtained 37 dominant rules are shown in Table 4.  
The rules also could be expressed in the form of \"if-then\". For example, Rule 3 is given as:  
If (operation feature = \"first\", and processing time = \"middle\", and remaining time = \"long\", and due date = \"slack\")  
Then, (priority = \"0\", weight = \"0.71\"; priority = \"1\", weight = \"0.28\"; priority = \"2\", weight = \"0.01\")  
It should be mentioned that there may be a case where the sum of weights is not equal to 1, which is due to rounding and does not affect the results of rules.  
\begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \hline \multirow{2}{*}{**Id**} & \multirow{2}{*}{**Rule Set**} & \multicolumn{8}{c}{**Priority**} \\ \cline{3-10}  & & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline
0 & first long long slack & 0.67 & 0.15 & 0.14 & 0.05 & & & & & & \\
1 & first long middle tight & 0.80 & 0.20 & & & & & & & \\
2 & first middle long slack & 0.71 & 0.28 & 0.01 & & & & & & \\
3 & first middle long tight & 0.98 & 0.02 & & & & & & & \\
4 & first middle middle tight & 0.82 & 0.18 & & & & & & & \\
5 & first short long slack & 1.00 & & & & & & & & \\
6 & first short long tight & 0.33 & 0.48 & 0.12 & 0.07 & & & & & \\
7 & last long short slack & & & & & & 0.02 & 0.01 & 0.09 & 0.11 & 0.78 \\
8 & last long short tight & & & & & & 0.08 & 0.76 & 0.17 & 0.00 & 0.00 \\
9 & last middle short slack & & & & & & 0.07 & 0.02 & 0.17 & 0.75 \\
10 & last middle short tight & & & & & & 0.08 & 0.21 & 0.39 & 0.32 \\
11 & last short short slack & & & & & & & 0.03 & 0.27 & 0.70 \\
12 & last short short tight & & & & & & 0.06 & 0.16 & 0.02 & 0.14 & 0.63 \\
13 & later long short slack & & & & & 0.01 & 0.08 & 0.09 & 0.06 & 0.19 & 0.39 & 0.19 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Dominant rules obtained from knowledge mining.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Operation**} & \multirow{2}{*}{**Operation**} & \multirow{2}{*}{**Processing**} & \multirow{2}{*}{**Remaining**} & \multirow{2}{*}{**Due Date**} & \multirow{2}{*}{**Priority**} \\ \cline{1-1} \cline{6-6}  & & & **Feature** & & & **Time** & & **Time** \\ \hline
1 & 40 & first & long & middle & tight & 0 \\
2 & 90 & first & middle & long & slack & 0 \\
3 & 90 & first & middle & long & slack & 0 \\
4 & 90 & first & middle & long & slack & 0 \\
5 & 40 & first & long & middle & tight & 0 \\
6 & 40 & first & long & middle & tight & 0 \\
7 & 80 & first & short & long & slack & 0 \\
8 & 80 & first & short & long & slack & 0 \\
9 & 00 & first & middle & long & tight & 0 \\ \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\
6594 & 99 & last & middle & short & slack & 9 \\
6595 & 79 & last & middle & Short & slack & 9 \\
6596 & 99 & last & middle & short & slack & 9 \\
6597 & 89 & last & short & short & slack & 9 \\
6598 & 69 & last & long & short & slack & 9 \\
6599 & 69 & last & long & short & slack & 9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Sample data of the trained data.