## 6 Conclusions  
In this paper, in order to increase the convergence speed of the evolutionary algorithm and to improve rule understandability while using fewer features, we proposed a feature selection mechanism to design dispatching rules for the DJSS with improved gene expression programming (IGEP). An improved GEP approach, employing an adaptive variable neighborhood search method, was developed to search for competitive dispatching rules in a large heuristic search space for different scheduling scenarios. Based on the optimal rules obtained using the IGEP algorithm, and considering the fitness of the rules and feature contribution to the rules, the subset of features that played an important role in mining dispatching rules were selected from the original terminal set using a weighted voting ranking method. Finally, based on the evolutionary information from the improved GEP and selected features, the proposed approach successfully achieved effective and interpretable rules for DJSS. The proposed algorithm (FS-IGEP) was compared to two algorithms (GEP, IGEP) in an MS scenario, MFT scenario, and MWT scenario, with respect rule performance, rule length, and efficiency. The experimentally obtained results demonstrated the effectiveness of the proposed approach for designing more effective and interpretable rules while reducing computational time considerably. Considering the distribution of features in the best-evolved rules, the FS-IGEP algorithm obtained compact rules with a smaller selected terminal. Based on the rule analysis, it was revealed that the FS-IGEP had the ability to find more building blocks for improving the rule quality. In addition to the compact structure, the FS-IGEP rules presented overall improvement in the three considered scenarios, compared to the other rules designed using other two algorithms (GEP, IGEP). When working with complex production systems and a large number of features from jobs and machines, feature selection becomes a crucial task in the automated design of dispatching rules. More research ought to be conducted in the future, to increase the accuracy of the feature selection. The feature selection mechanism will also receive more attention in our feature studies so that we can better grasp when to use it and how to \begin{table}
\begin{tabular}{c c} \hline \hline
**Scenario** & **Key Feature Set** \\ \hline MS scenario & PT, NPT, WINQ, WKR, NOINQ, NOR, OWT \\ MFT scenario & PT, NPT, WINQ, WKR, NOINQ \\ MWT scenario & PT, W, WINQ, NOINQ, NPT, DD \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The key feature set for the three dynamic job-shop scenarios. Figure 6: The matrix plot of the feature selection results of the proposed algorithm in the three scenarios: (**a**) selected features using the FS-IGEP algorithm for the MS scenario; (**b**) selected features using the FS-IGEP algorithm for the MFT scenario; (**c**) selected features using the FS-IGEP algorithm for the MWT scenario. improve its effectiveness. It will be necessary to use various standard scheduling issues to demonstrate the significance of feature selection. In contrast to previous simple local search algorithms employed for the purpose of facilitating GEP, the suggested adaptive variable neighborhood search exhibited favorable characteristics for both exploration and exploitation. Therefore, it was not easily trapped at the local optima. Subsequent studies may delve deeper into the behavior of the heuristic with the goal of reducing the number of necessary parameters and enhancing its adaptability. Conceptualization, methodology, data curation, formal analysis, validation, writing--original draft, writing--review, and editing, A.S.; methodology, project administration, and supervision, Y.Y. ; resources and supervision, J.M. ; methodology and project administration, Y.L. and P.M. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (no.71961029), and the Xinjiang Scientific and Technology Project (no.