## 7 Conclusions and Future Research  
In this work, we presented a technique to discriminate and cluster ordered permutation using ART-1 and Improved-ART-1 neural network-guided GA. In this process, two binary conversion techniques were introduced to convert ordered permutations to binary input vectors to use in ART-1 algorithms. The proposed binary conversion methods' performance, considering ART-1 and Improved-ART-1, was evaluated under three performance indicators: misclassification, cluster homogeneity, and average distance. Additionally, the empirical study was extended by varying the problem sizes. The investigation shows that the Improved-ART-1 neural network with the proposed binary conversion method-1 provides better results than ART-1 in every scenario.  
In addition, the detailed architecture of the proposed Improved-ART-1 guided GA was illustrated. A case study considering the flow shop scheduling problem was examined for small and large prototype problems based on the ANN-guided GA architecture. The empirical results show that the intervention of GA by ART-1 and SWCM prevents the algorithm from stagnating in a given region of the search space. Hence, the intervention promotes exploration of the solution space so that other clusters find the optimal solution. The Improved ART-1-guided GA has a better exploration ability than pure GA and can find an optimal solution by searching almost all the clusters. In addition, the performance result proves the competence of our proposed binary conversion method-1 with Improved-ART-1 neural-network-guided GA for any permutation-based combinational optimization with real-life applications.  
The Improved-ART-1 in the proposed ANN-guided GA architecture only deals with binary input vectors, which be applied to any problems in which the solutions are not ordered permutations. Since we considered a flow shop scheduling problem for our case study, future work could focus on applying the proposed binary conversion method-1-based Improved-ART-1-guided GA to other scheduling problems, such as job shop and open shop, whose solution may not be a pure ordered permutation. Moreover, the other metaheuristics algorithms, such as tabu search, ant colony, swarm intelligence, simulated annealing, etc., which are guided by ART-1, can be considered for scheduling problems and compared to our current technique. Our developed ANN-guided GA application area should not be limited to manufacturing scheduling problems; it can be considered for other application fields, such as image recognition, pattern recognition, mobile robot control, signature verification, medical diagnosis, etc.  
S.M.T.: Methodology, Investigation, Validation, Formal analysis, Writing--Original Draft, Data Curation; F.M.D.: Conceptualization, Methodology, Formal analysis, Software, Validation, Visualization, Writing--Review and Editing, Supervision. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Discovery Grant from NSERC, the Natural Science and Engineering Research Counsel of Canada ([[https://www.nserc-crsng.gc.ca/index_eng.asp](https://www.nserc-crsng.gc.ca/index_eng.asp)]([https://www.nserc-crsng.gc.ca/index_eng.asp](https://www.nserc-crsng.gc.ca/index_eng.asp))), accessed on 1 January 2020.  
Available upon request made to the corresponding author.  
We would like to thank all three anonymous reviewers for their suggestions that helped us to improve the paper.  
The authors declare no conflict of interest.