## 6 Conclusions  
In the field of scheduling problems, this paper suggested a novel hybrid learning method for parameter tuning metaheuristics.  
Since parameter tuning is so critical in the process of developing and implementing optimization techniques, the proposed hybrid approach was based on racing and CBR, with the goal of performing metaheuristic selection and tuning. While racing is used to assess a group of applicants in a refined and efficient manner, releasing those that tend to be less promising during the selection process, CBR uses previous similar cases to solve new cases, allowing for learning from experience. The metaheuristics used to generate scheduling plans can now be chosen and parameterized in the AutoDynAgents system.  
The aim of the computational analysis was to see how well the AutoDynAgents framework performed after learning modules were added. The findings of the hybrid racing + CBR method were compared to those obtained using racing and CBR separately, and to previously reported results that did not involve learning mechanisms.  
The statistical significance of all of the findings was investigated. The novel proposed racing + CBR solution was found to have a major statistical benefit. In comparison to previously reported findings, all of the proposed methods have enhanced the system's results. The hybrid racing + CBR method, on the other hand, yielded better results. Based on the findings, it was possible to draw the conclusion that there is statistical evidence for the benefit of incorporating learning into the metaheuristic parameter tuning method.  
Since each occurrence of events refers to a new case, the proposed module can also be extended to the resolution of complex scheduling problems with dynamic events, such as new orders, canceled orders and changes in deadlines. With the inclusion of this new hybrid learning method, the system becomes more stable, robust and effective in the resolution of scheduling problems with the existence of dynamic events.  
Future work includes extending the computational study to real scheduling problems with dynamic events and trying to achieve better results by exploring other learning techniques, such as artificial neural networks.  
Conceptualization, I.P. and A.M.; data curation, I.P.; formal analysis, I.P. and E.C.e5.; funding acquisition, A.M.; investigation, I.P. and A.M.; methodology, I.P. and A.M.; supervision, A.M.; validation, I.P., E.C.e5. and A.A.; writing--original draft, I.P.; writing--review and editing, I.P., A.M., E.C.e5. and A.A. All authors have read and agreed to the published version of the manuscript  
This work has been supported by FEDER Funds through \"Programa Operacional Factores de Competitividade-COMPETE\" and by National Funds through FCT \"Fundacao para a Ciencia e a Tecnologia\" through the project: FCOMP-01-0124-FEDER- PEst-OE/EEI/UI0760/2014.  
Not applicable.  
**Data Availability Statement:** Benchmark instances of job-shop scheduling problems extracted from OR-Library ([[http://people.brunel.ac.uk/~mastijb/jeb/info.html](http://people.brunel.ac.uk/~mastijb/jeb/info.html)]([http://people.brunel.ac.uk/~mastijb/jeb/info.html](http://people.brunel.ac.uk/~mastijb/jeb/info.html)), accessed on 7 February 2021) have been used.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Null Hypothesis** & **Alternative Hypothesis** & \(\mathbf{p}\)**-Value** \\ \hline \(\eta_{Previous}=\eta_{CBR}\) & \(\eta_{Previous}>\eta_{CBR}\) & \(0.0002214<0.05\) \\ \(\eta_{Previous}=\eta_{Taking}\) & \(\eta_{Previous}>\eta_{Racing}\) & \(2.611\times 10^{-5}<0.05\) \\ \(\eta_{Previous}=\eta_{Racing+CR}\) & \(\eta_{Previous}>\eta_{Racing+CRR}\) & \(3.392\times 10^{-6}<0.05\) \\ \(\eta_{CBR}=\eta_{Racing+CRR}\) & \(\eta_{CBR}>\eta_{Racing+CRR}\) & \(0.007589<0.05\) \\ \(\eta_{Racing}=\eta_{Racing+CRR}\) & \(\eta_{Racing}>\eta_{Racing+CRR}\) & \(1.05\times 10^{-5}<0.05\) \\ \hline \hline \end{tabular}
\end{table}
Table 13: Results for the paired-wise comparison.