# A Novel Multi-Objective Five-Elements Cycle Optimization Algorithm
## 5 Simulation Experiment and Result Analysis
### Parameter Analysis and Comparison Experiments of MOFECO
#### 5.3.3 Comparison of Local-Global Update Probability \(P_{s}\)
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Functions** & \(P_{\mathbf{s}}\) **Is Nonlinear Variation** & \(P_{\mathbf{s}}\) **Is Linear Variation** & \(P_{\mathbf{s}}\) **= 0.5** \\ \hline ZDT1 & \(\mathbf{5.40\times 10^{-3}}\) & \(5.50\times 10^{-3}\) & \(5.60\times 10^{-3}\) \\ ZDT2 & \(\mathbf{5.40\times 10^{-3}}\) & \(5.60\times 10^{-3}\) & \(5.60\times 10^{-3}\) \\ ZDT4 & \(\mathbf{5.76\times 10^{-3}}\) & \(3.01\times 10^{-2}\) & \(5.80\times 10^{-3}\) \\ ZDT6 & \(4.70\times 10^{-3}\) & \(4.60\times 10^{-3}\) & \(\mathbf{4.30\times 10^{-3}}\) \\ DTLZ2 & \(7.49\times 10^{-2}\) & \(7.66\times 10^{-2}\) & \(\mathbf{7.10\times 10^{-2}}\) \\ DTLZ4 & \(\mathbf{1.21\times 10^{-1}}\) & \(4.29\times 10^{-1}\) & \(3.56\times 10^{-1}\) \\ DTLZ5 & \(\mathbf{6.70\times 10^{-3}}\) & \(7.00\times 10^{-3}\) & \(6.90\times 10^{-3}\) \\ DTLZ7 & \(\mathbf{2.88\times 10^{-1}}\) & \(3.60\times 10^{-1}\) & \(2.92\times 10^{-1}\) \\ WFG2 & \(\mathbf{5.11\times 10^{-1}}\) & \(6.26\times 10^{-1}\) & \(7.04\times 10^{-1}\) \\ WFG3 & \(\mathbf{1.60\times 10^{-1}}\) & \(2.61\times 10^{-1}\) & \(2.96\times 10^{-1}\) \\ WFG4 & \(7.89\times 10^{-1}\) & \(7.86\times 10^{-1}\) & \(7.74\times 10^{-1}\) \\ MaF1 & \(\mathbf{1.21\times 10^{-1}}\) & \(1.30\times 10^{-1}\) & \(1.62\times 10^{-1}\) \\ MaF2 & \(9.58\times 10^{-2}\) & \(9.49\times 10^{-2}\) & \(\mathbf{8.34\times 10^{-2}}\) \\ MaF12 & \(\mathbf{7.43\times 10^{-1}}\) & \(7.83\times 10^{-1}\) & \(7.43\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: \(IGD\) result of the local-global update probability \(P_{\mathbf{s}}\) of MOFECO algorithms on test functions. (The best result is bolded for each function). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Functions** & \(P_{\mathbf{s}}\) **Is Nonlinear Variation** & \(P_{\mathbf{s}}\) **Is Linear Variation** & \(P_{\mathbf{s}}\) **= 0.5** \\ \hline ZDT1 & \(\mathbf{1.40\times 10^{-4}}\) & \(1.72\times 10^{-4}\) & \(1.54\times 10^{-4}\) \\ ZDT2 & \(4.02\times 10^{-6}\) & \(4.05\times 10^{-6}\) & \(\mathbf{3.67\times 10^{-6}}\) \\ ZDT4 & \(\mathbf{2.39\times 10^{-5}}\) & \(2.70\times 10^{-3}\) & \(5.78\times 10^{-5}\) \\ ZDT6 & \(\mathbf{3.50\times 10^{-7}}\) & \(3.56\times 10^{-7}\) & \(3.53\times 10^{-7}\) \\ DTLZ2 & \(\mathbf{7.43\times 10^{-4}}\) & \(1.40\times 10^{-3}\) & \(1.20\times 10^{-3}\) \\ DTLZ4 & \(1.43\times 10^{-3}\) & \(\mathbf{2.86\times 10^{-4}}\) & \(3.87\times 10^{-4}\) \\ DTLZ5 & \(3.56\times 10^{-5}\) & \(1.18\times 10^{-2}\) & \(\mathbf{2.18\times 10^{-5}}\) \\ DTLZ6 & \(\mathbf{4.82\times 10^{-7}}\) & \(2.60\times 10^{-6}\) & \(1.73\times 10^{-6}\) \\ DTLZ7 & \(\mathbf{9.60\times 10^{-3}}\) & \(1.03\times 10^{-2}\) & \(1.50\times 10^{-2}\) \\ WFG2 & \(\mathbf{6.25\times 10^{-2}}\) & \(8.45\times 10^{-2}\) & \(9.51\times 10^{-2}\) \\ WFG3 & \(\mathbf{5.29\times 10^{-2}}\) & \(1.84\times 10^{-1}\) & \(1.36\times 10^{-1}\) \\ WFG4 & \(\mathbf{1.57\times 10^{-2}}\) & \(1.91\times 10^{-2}\) & \(1.83\times 10^{-2}\) \\ MaF1 & \(\mathbf{7.10\times 10^{-3}}\) & \(8.40\times 10^{-3}\) & \(1.28\times 10^{-2}\) \\ MaF2 & \(3.67\times 10^{-3}\) & \(5.30\times 10^{-3}\) & \(\mathbf{2.60\times 10^{-3}}\) \\ MaF12 & \(1.88\times 10^{-2}\) & \(2.00\times 10^{-2}\) & \(\mathbf{1.81\times 10^{-2}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: \(GD\) result of the local-global update probability \(P_{\mathbf{s}}\) of MOFECO algorithms on test functions. (The best result is bolded for each function).