## 5 Entanglement and Numerical Test of DE-MPFSC Algorithm Stability
### Numerical Test and Analysis of DE-MPFSC Algorithm
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{NP} & \multicolumn{4}{c}{\(DE\)} & \multicolumn{4}{c}{\(DE-MPFSC\)} \\ \cline{2-11}  & \(F\) & \(CR\) & \(\xi\) & \(\zeta\) & \(\varepsilon\)\% & \(F^{*}\) & \(CR^{*}\) & \(\xi\) & \(\zeta\) & \(\varepsilon\)\% \\ \hline
400 & 0.1 & 0.9 & 0.77 & 0.43 & \(\pm\)0.558 & 0.1 & 0.9 & 0.15 & 0.015 & \(\pm\)0.1 \\
400 & / & / & 0.85 & 0.29 & \(\pm\)0.341 & 0.4 & 0.5 & 0.25 & 0.02 & \(\pm\)0.08 \\
400 & / & / & 0.81 & 0.55 & \(\pm\)0.679 & 0.2 & 0.2 & 0.20 & 0.05 & \(\pm\)0.25 \\
400 & / & / & 0.80 & 0.63 & \(\pm\)0.787 & 0.2 & 0.3 & 0.30 & 0.042 & \(\pm\)0.14 \\
400 & / & / & 0.79 & 0.51 & \(\pm\)0.645 & 0.2 & 0.3 & 0.22 & 0.02 & \(\pm\)0.09 \\ \hline \multirow{2}{*}{Average} & \multicolumn{4}{c}{\(DE\)} & \multicolumn{4}{c}{\(DE-MPFSC\)} \\ \cline{2-11}  & 0.1 & 0.9 & 0.804 & 0.482 & \(\pm\)0.602 & 0.22 & 0.44 & 0.224 & 0.0294 & \(\pm\)0.132 \\ \hline \multirow{2}{*}{Variance} & \multicolumn{4}{c}{\(DE\)} & \multicolumn{4}{c}{\(DE-MPFSC\)} \\ \cline{2-11}  & 0 & 0 & 0.00088 & 0.01672 & \(\pm\)0.02802 & 0.012 & 0.078 & 0.00313 & 0.00024 & \(\pm\)0.00487 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical Analysis of Entanglement Degree \(\frac{1}{\xi}\) and Entanglement Degree Error \(\zeta\) of the DE algorithm and the DE-MPFSC algorithm 400 times. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{NP} & \multicolumn{4}{c}{\(DE\)} & \multicolumn{4}{c}{\(DE-MPFSC\)} \\ \cline{2-11}  & \(F\) & \(CR\) & \(\xi\) & \(\zeta\) & \(\varepsilon\)\% & \(F^{*}\) & \(CR^{*}\) & \(\xi\) & \(\zeta\) & \(\varepsilon\)\% \\ \hline
600 & 0.1 & 0.9 & 0.69 & 0.38 & \(\pm\)0.550 & 0.1 & 0.9 & 0.15 & 0.015 & \(\pm\)0.1 \\
600 & / & / & 0.70 &and the dynamic crossover probability \(CR\) of the DE-MPFSC algorithm and analyze the data tables one by one. In summary, when the number of individuals is 200, 400, 600, 800 or 1000, the range of entanglement error rate of the DE algorithm and the DE-MPFSC algorithm are respectively \(\varepsilon\in(\pm 0.714\%,\pm 0.904\%)\) and \(\varepsilon\in(\pm 0.133\%,\pm 0.578\%)\), which shows that the entanglement degree of the DE-MPFSC algorithm is significantly higher than that of the DE algorithm, and the stability of the DE-MPFSC algorithm is better. The range of entanglement degree of the DE algorithm and the DE-MPFSC algorithm are respectively \(\frac{1}{\xi}\in(0.65,0.9)\) and \(\frac{1}{\xi}\in(0.15,0.35)\), which shows that the entanglement degree of the DE-MPFSC algorithm is significantly higher than that of the DE algorithm and the DE-MPFSC algorithm is significantly higher than that of the DE algorithm, and the DE-MPFSC convergence of the algorithm is stronger. In addition, there IS an additional discovery during the experiment that the optimal dynamic mutation factor and the optimal dynamic crossover probability of the DE-MPFSC algorithm are \(F=0.2\) and \(CR=0.3\) respectively. In summary, the convergence, stability and effectiveness of the DE-MPFSC algorithm are higher than the DE algorithm, which has obvious advantages for the integration of individuals.