# Embedded PSO for Solving FJSP on Embedded Environment (Industry 4.0 Era)
## 5 Proposed Technique: Embedded Two-Level PSO-FJSP
In the first case (Request_Period = 20%), the results show that there are total differences between the two variants on five benchmarks (\(U=0\) and \(p<0.05\)), significant differences in MK04 (\(U=10<23\) and \(p=0.0027<0.05\)), significant similarities in MK01 (\(U=30>23\) and \(p=0.1415>0.05\)) and total similarities on four benchmarks. In the second case (Request_Period = 50%), the results show that there are total differences between the two variants on three benchmarks (\(U=0\) and \(p<0.0001\)), significant similarity on four benchmarks (\(U>23\) and \(p>0.05\)) and a total similarity on three benchmarks. In the third case (Request_Period = 90%), the results show that there are no differences (total similarities) between the two variants on all benchmarks (\(U=50\) and \(p=0.9681\)). #### 6.2.4 Experiment #4 Robustness Analyses of Adaptive E2L-PSO

The results of the robustness measure comparing the outcomes of the second example (Table 11: adaptive E2L-PSO with medium reduction and E2L-PSO without CPU reduction needed) are shown in Table 14.

To resume, we can say that, in all the three scenarios and in the vast majority of cases, we have adequate robustness with improved makespan and shorter CPU times. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Beginning 20\%**} & \multicolumn{2}{c}{**Middle (50\%)**} & \multicolumn{2}{c}{**End (90\%)**} \\ \hline  & \(U\) & \(p\) & \(U\) & \(p\) & \(U\) & \(p\) \\ \hline MK01 & 30 & 0.1415 & 40 & 0.4175 & 50 & 0.9681 \\ MK02 & 0 & 0.0001 & 0 & 0.0001 & 50 & 0.9681 \\ MK03 & 50 & 0.9681 & 50 & 0.9681 & 50 & 0.9681 \\ MK04 & 10 & 0.0027 & 35 & 0.2713 & 50 & 0.9681 \\ MK05 & 0 & 0.0001 & 0 & 0.0001 & 50 & 0.9681 \\ MK06 & 0 & 0.0001 & 25 & 0.0643 & 50 & 0.9681 \\ MK07 & 0 & 0.0001 & 0 & 0.0001 & 50 & 0.9681 \\ MK08 & 50 & 0.9681 & 50 & 0.9681 & 50 & 0.9681 \\ MK09 & 0 & 0.0001 & 25 & 0.0643 & 50 & 0.9681 \\ MK10 & 50 & 0.9681 & 50 & 0.9681 & 50 & 0.9681 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Results of two-tailed Mann–Whitney tests. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Beginning 20\%**} & \multicolumn{2}{c}{**Middle (50\%)**} & \multicolumn{2}{c}{**End (90\%)**} \\ \hline  & \(MS\) & \(RM\) & \(MS\) & \(RM\) & \(MS\) & \(RM\) \\ \hline MK01 & 39 & 0 & 39 & 0 & 39 & 0 \\ MK02 & 28 & 10 & 27 & 6 & 26 & 5 \\ MK03 & 204 & 0 & 204 & 0 & 204 & 0 \\ MK04 & 60 & 1 & 60 & 1 & 60 & 1 \\ MK05 & 172 & 12 & 171 & 11 & 170 & 10 \\ MK06 & 64 & 6 & 62 & 4 & 62 & 4 \\ MK07 & 140 & 14 & 140 & 14 & 139 & 11 \\ MK08 & 523 & 0 & 523 & 0 & 523 & 0 \\ MK09 & 309 & 24 & 307 & 21 & 307 & 21 \\ MK10 & 205 & 0 & 205 & 0 & 205 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Robustness analyses of E2L-PSO with medium CPU reduction needed (40%) on Raspberry Pi B+. #### 6.2.5 Experiment #5 (Previous Metaheuristics Are Compared)

Since we have not found any previous work running metaheuristic algorithms to solve FJSP on Raspberry Pi B+ or STM32 cards, we compare our results (E2L-PSO without reduction) with previous works executed in another environment (PCs). Experiments are conducted with 50 particles and 100 iterations (5000 visited points). Table 15 presents the comparison against PSO-based metaheuristics: PSO [35], artificial bee colony (ABC) [36], quantum annealing based optimization (QAO) [37], genetic algorithm (GA) [38], human learning optimization algorithm and PSO (HLO-PSO) [39] and hybrid brain storm optimization algorithm and late acceptance hill climbing (hybrid PSO) [40] (-- denotes the data's unavailability). A bold value indicates that the E2L-PSO result is either optimal or the best. For all benchmarks, we note that the E2L-PSO performed on the Raspberry Pi B+ delivers the best makespan, except in two cases (MK02 and MK05), although the result is always close to the best of the alternatives.