# Embedded PSO for Solving FJSP on Embedded Environment (Industry 4.0 Era)
## 5 Proposed Technique: Embedded Two-Level PSO-FJSP
\begin{table}
\begin{tabular}{l c c c c c c} \hline Instance & \multicolumn{2}{c}{Basic PSO} & \multicolumn{2}{c}{One-Level PSO [32]} & \multicolumn{2}{c}{E2L-PSO without Reduction} \\  & \multicolumn{2}{c}{\(I=100\)\(S=50\)} & \multicolumn{2}{c}{\(I=100\)\(S=50\)} & \multicolumn{2}{c}{\(\mathbf{I_{1}}=20\)\(\mathbf{S_{2}}=10\)\(\mathbf{I_{2}}=5\)\(\mathbf{S_{2}}=5\)} \\ \cline{2-7}  & \(MS\) & CPU Time & \(MS\) & CPU Time & \(MS\) & CPU Time \\ \hline \(4\times 5\) & 12 &



The results in Tables 10-12 are determined under this assumption: reduction needed requests of 90%, 40% and 20%, respectively, occur every 20 s after the first request_Period. These tables present the simulation results of the E2L-PSO with hard, medium and soft particle reduction on the Raspberry Pi B+ card. From Table 10, we note that compared to the results in Table 9:

* Case 1: E2L-PSO gives acceptable results for \(MS\) with 26% to 70% of CPU time gain. * Case 2: E2L-PSO gives acceptable results for \(MS\) and best \(MS\) for 50% of benchmarks. E2L-PSO gives 15% to 44% of CPU time gain. * Case 3: E2L-PSO gives the best results for \(MS\) in all benchmarks, with 10% of CPU time gain. From Table 11, we note the following in comparison to the results in Table 9:
* Case 1: E2L-PSO gives acceptable results for \(MS\) and best \(MS\) for 60% of benchmarks. A 21% to 66% of CPU time gain is obtained. * Case 2: E2L-PSO gives acceptable results for \(MS\) and best \(MS\) for 80% of benchmarks. An 11% to 30% of CPU time gain is obtained. * Case 3: E2L-PSO gives best results for \(MS\) in all benchmarks, with 4% to 5% of CPU time gain. From Table 12, we note that, compared to the results in Table 9:
* Case 1: E2L-PSO gives the best \(MS\) for 100% of benchmarks. A 10% to 49% of CPU time gain is obtained. * Case 2: E2L-PSO gives the best \(MS\) for 100% of benchmarks with 6% to 9% of CPU time gain. * Case 3: E2L-PSO gives the best results for \(MS\) in all benchmarks, with a poor CPU time gain (1%). To conclude, we can say that the E2L-PSO give the best MS results with reduction in CPU time according to the flexibility of the problems, the CPU reduction needed and the request period. #### 6.2.3 Experiment #3 (Stability Analysis of Adaptive E2L-PSO)

The results of the two-tailed Mann-Whitney tests, 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 13.

The symbols \(U\) and \(p\) are the calculation of statistics, where \(U\) is the minimum value between the decisions variables of two groups and \(p\) is a non-parametric measure of the overlap between two distributions; it can take values between 0 and 1. We chose to work with a significance level = 0.05 and a number of samples (run) = 10, then the critical value of \(U\) at \(p<0.05\) is 23. To understand the results obtained, note that when the U-value increases (p increases), the difference between the two variants increases (i.e., high U-value = high similarity): \(U=0\) implies no similarity and \(U=50\) implies total similarity. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Beginning 20\%** & \multicolumn{2}{c}{**Middle (50\%)**} & \multicolumn{2}{c}{**End (90\%)**} \\ \hline  & \(MS\) & **CPU** & \(MS\) & **CPU** & \(MS\) & **CPU** \\ \hline MK01 & 39 & 40.50 & 39 & 44.33 & 39 & 48.70 \\ MK02 & 26 & 73.15 & 26 & 130.66 & 26 & 142.55 \\ MK03 & 204 & 93.82 & 204 & 148.02 & 204 & 161.21 \\ MK04 & 60 & 81.77 & 60 & 86.12 & 60 & 90.01 \\ MK05 & 170 & 100.03 & 170 & 111.64 & 170 & 123.33 \\ MK06 & 62 & 188.4 & 62 & 207.01 & 62 & 249.46 \\ MK07 & 139 & 70.48 & 139 & 84.21 & 139 & 91.63 \\ MK08 & 523 & 260.70 & 523 & 300.65 & 523 & 368.01 \\ MK09 & 307 & 282.24 & 307 & 344.89 & 307 & 381.37 \\ MK10 & 205 & 310.70 & 205 & 399.57 & 205 & 446.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: E2L-PSO soft CPU reduction needed (20%).