# A Novel Multi-Objective Five-Elements Cycle Optimization Algorithm
## 5 Simulation Experiment and Result Analysis
### Parameter Analysis and Comparison Experiments of MOFECO
#### 5.3.2 Comparison of Conditions for Judging Whether to Update
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Functions** & **Method 1** & **Method 2** & **Method 3** \\ \hline ZDT1 & \(\mathbf{1.40\times 10^{-4}}\) & \(1.40\times 10^{-4}\) & \(2.61\times 10^{-4}\) \\ ZDT2 & \(\mathbf{4.02\times 10^{-6}}\) & \(4.02\times 10^{-6}\) & \(4.34\times 10^{-6}\) \\ ZDT4 & \(\mathbf{2.39\times 10^{-5}}\) & \(2.39\times 10^{-5}\) & \(1.26\times 10^{-2}\) \\ ZDT6 & \(\mathbf{3.50\times 10^{-7}}\) & \(3.50\times 10^{-7}\) & \(2.40\times 10^{-3}\) \\ DTLZ2 & \(\mathbf{7.43\times 10^{-4}}\) & \(1.10\times 10^{-3}\) & \(1.00\times 10^{-3}\) \\ DTLZ4 & \(1.43\times 10^{-3}\) & \(1.80\times 10^{-3}\) & \(\mathbf{9.39\times 10^{-4}}\) \\ DTLZ5 & \(3.56\times 10^{-5}\) & \(3.94\times 10^{-5}\) & \(\mathbf{3.48\times 10^{-5}}\) \\ DTLZ6 & \(\mathbf{4.82\times 10^{-7}}\) & \(9.11\times 10^{-5}\) & \(2.90\times 10^{-5}\) \\ DTLZ7 & \(9.60\times 10^{-3}\) & \(7.70\times 10^{-3}\) & \(1.44\times 10^{-2}\) \\ WFG2 & \(\mathbf{6.25\times 10^{-2}}\) & \(9.63\times 10^{-2}\) & \(6.68\times 10^{-2}\) \\ WFG3 & \(\mathbf{5.29\times 10^{-2}}\) & \(1.94\times 10^{-1}\) & \(1.80\times 10^{-1}\) \\ WFG4 & \(\mathbf{1.57\times 10^{-2}}\) & \(2.04\times 10^{-2}\) & \(1.94\times 10^{-2}\) \\ MaF1 & \(\mathbf{7.10\times 10^{-3}}\) & \(8.00\times 10^{-3}\) & \(7.90\times 10^{-3}\) \\ MaF2 & \(\mathbf{3.67\times 10^{-3}}\) & \(6.60\times 10^{-3}\) & \(5.40\times 10^{-3}\) \\ MaF12 & \(1.88\times 10^{-2}\) & \(\mathbf{1.85\times 10^{-2}}\) & \(2.05\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(GD\) result of the three update conditions 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** & **Method 1** & **Method 2** & **Method 3** \\ \hline ZDT1 & \(\mathbf{5.40\times 10^{-3}}\) & \(5.40\times 10^{-3}\) & \(6.60\times 10^{-3}\) \\ ZDT2 & \(\mathbf{5.40\times 10^{-3}}\) & \(5.40\times 10^{-3}\) & \(7.00\times 10^{-3}\) \\ ZDT4 & \(\mathbf{5.76\times 10^{-3}}\) & \(5.76\times 10^{-3}\) & \(9.47\times 10^{-2}\) \\ ZDT6 & \(\mathbf{4.70\times 10^{-3}}\) & \(4.70\times 10^{-3}\) & \(4.90\times 10^{-3}\) \\ DTLZ2 & \(\mathbf{7.49\times 10^{-2}}\) & \(7.64\times 10^{-2}\) & \(7.55\times 10^{-2}\) \\ DTLZ4 & \(\mathbf{1.21\times 10^{-1}}\) & \(1.69\times 10^{-1}\) & \(2.68\times 10^{-1}\) \\ DTLZ5 & \(6.70\times 10^{-3}\) & \(\mathbf{6.60\times 10^{-3}}\) & \(8.30\times 10^{-3}\) \\ DTLZ6 & \(\mathbf{6.60\times 10^{-3}}\) & \(7.10\times 10^{-3}\) & \(7.80\times 10^{-3}\) \\ DTLZ7 & \(\mathbf{2.88\times 10^{-1}}\) & \(3.77\times 10^{-1}\) & \(3.76\times 10^{-1}\) \\ WFG2 & \(\mathbf{5.11\times 10^{-1}}\) & \(7.21\times 10^{-1}\) & \(1.21\times 10^{0}\) \\ WFG3 & \(\mathbf{1.60\times 10^{-1}}\) & \(2.79\times 10^{-1}\) & \(2.30\times 10^{-1}\) \\ WFG4 & \(7.89\times 10^{-1}\) & \(7.96\times 10^{-1}\) & \(7.86\times 10^{-1}\) \\ MaF1 & \(\mathbf{1.21\times 10^{-1}}\) & \(1.22\times 10^{-1}\) & \(1.21\times 10^{-1}\) \\ MaF2 & \(9.58\times 10^{-2}\) & \(9.78\times 10^{-2}\) & \(\mathbf{9.11\times 10^{-2}}\) \\ MaF12 & \(\mathbf{7.43\times 10^{-1}}\) & \(7.48\times 10^{-1}\) & \(7.65\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: \(IGD\) result of the three update conditions of MOFECO algorithms on test functions. (The best result is bolded for each function). From the experimental results of Tables 6-8, we can see that the \(GD\), \(IGD\), \(SP\) values obtained by the update condition of method 1 are smaller than method 2 and method 3, which shows that the MOFECO algorithm using the update condition of method 1 has better convergence and distribution. Therefore, we choose the method 1 as the update condition for the individuals in the MOFECO algorithm.