## 2 The Relaxed Flexible Flow Shop Problem Model with Sequence-Dependent Setup Times (RFFSP) Methods
### Simulated Annealing Algorithm
The above values indicate that (1) the implementation of the GA with hybrid local-search in the Morelos grid allows for the finding of better RFFSP solutions, and (2) the distribution of the jobs allows for the efficient usage of the computational resources, coupled with the effective use of the grid communication. The HGAG is an artificial intelligence heuristic algorithm. The convenience of the approach used in this work involves the combination of different search forms used to more effectively explore and exploit the solutions space, applying different procedures such as searches that allow the escape of optimal local solutions (simulated annealing), \begin{table}
\begin{tabular}{c|c|c} \hline \hline
[fj@cuexcomate \(\sim\)]8 mpiexec -ppn 1 -np 2./ping \\ I am process 0 of 2 running on :cuexcomate \\ I am process 1 of 2 running on :texcal \\ Smaller possible measurable time -0.953674 usec (Microseconds) \\ \hline \hline Bits (RTT) & Time & Transfer Rate \\  & uses & Mb /sec \\ \hline



\hline \end{tabular}
\end{table} 
Table 12: Round Trip Time (RTT) evaluation in the Morelos Grid. local searches with cooperation between individuals (ant colony), and also the search by exploration of the space of solutions that the genetic algorithm applies through the selection and crossover operators. Finally, exploration and exploitation in the search space is expanded in a reduced time by designing the HGAG algorithm for execution in a computational grid, applying the use of more than one computational cluster, where these clusters could be geographically distant. ## 6 Future Works

Future directions of this work are to implement hybrid programming using GPU-parallel programming in the Morelos Grid, since each grid cluster has GPU cards. This programming scheme will implement the hybrid local-search using SA and ACS. The genetic evolutionary process will remain in the master process to take advantage of the infrastructure's potential. These changes are intended to improve the HGAG speed up efficiency and reduce its total execution time. It is also essential to improve the search in the space for solutions by implementing new variable neighborhood structures in SA. Finally, using a multi-objective approach of the HGAG in the job shop scheduling problem can improve the generation of more compact feature schedules for benchmark problems published in the existing literature. Conceptualization, F.J.-P. and M.A.C.-C.; methodology, F.J.-P., M.A.C.-C. and R.R.-L.; software, F.J.-P. and M.A.C.-C.; validation R.R.-L., E.Y.A.-M. and M.L.E.-D.; formal analysis, E.Y.A.-M. and M.H.C.-R.; investigation, M.H.C.-R. and M.L.E.-D.; writing--original draft preparation, M.A.C.-C.; writing--review and editing, R.R.-L.; supervision, M.A.C.-C.; project administration, M.A.C.-C.; funding acquisition, M.A.C.-C. All authors have read and agreed to the published version of the manuscript. This research was funded by CONACYT grant number 317029. Not applicable. The authors declare no conflict of interest. ## References

* [PERSON] et al. (2019) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] _Handbook on Scheduling: From Theory to Practice_; Springer International Publishing: Cham, Switzerland, 2019. [CrossRef]
* [PERSON] et al. (2020) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Energy Efficient Communication and Computation Resource Slicing for eMBB and URLLC Coexistence in 5G and Beyond. _IEEE Access_**2020**, \(8\), 136024-136035. [CrossRef]
* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON] Two-objective stochastic flow-shop scheduling with deteriorating and learning effect in Industry 4.0-based manufacturing system. _Appl. Soft. Comput._**2018**, _68_, 847-855. [CrossRef]
* [PERSON] and [PERSON] (2020) [PERSON]; [PERSON] Automated task scheduling for automotive industry. In Proceedings of the 2020 IEEE 24 th International Conference on Intelligent Engineering Systems (INES), Reykjavik, Iceland, 8-10 July 2020; pp. 159-164.