# A Novel Multi-Objective Five-Elements Cycle Optimization Algorithm
## 5 Simulation Experiment and Result Analysis
### Comparison with Other Optimization Algorithms
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Problems** & **MOFECO** & **NSGA-II** & **MOPSO** & **PESA-II** & **KnEA** & **NSLS** \\ \hline ZDT1 & \(8.70\times 10^{-3}\) & \(6.90\times 10^{-3}\) (-) & \(9.60\times 10^{-3}\) (+) & \(1.07\times 10^{-2}\) (+) & \(5.90\times 10^{-3}\) (-) & \(7.70\times 10^{-3}\) (-) \\ ZDT2 & \(7.60\times 10^{-3}\) & \(7.70\times 10^{-3}\) (+) & \(2.02\times 10^{-2}\) (+) & \(1.45\times 10^{-2}\) (+) & \(4.60\times 10^{-3}\) (-) & \(3.91\times 10^{-2}\) (+) \\ ZDT4 & \(7.40\times 10^{-3}\) & \(7.60\times 10^{-3}\) (+) & \(1.62\times 10^{-2}\) (+) & \(2.19\times 10^{-1}\) (+) & \(1.46\times 10^{-1}\) (+) & \(5.74\times 10^{-3}\) (-) \\ ZDT6 & \(6.80\times 10^{-3}\) & \(6.84\times 10^{-3}\) (+) & \(1.97\times 10^{-1}\) (+) & \(4.53\times 10^{-2}\) (+) & \(7.90\times 10^{-3}\) (+) & \(7.66\times 10^{-2}\) (+) \\ DTLZ2 & \(5.57\times 10^{-2}\) & \(5.85\times 10^{-2}\) (+) & \(5.13\times 10^{-2}\) (-) & \(5.16\times 10^{-2}\) (-) & \(7.16\times 10^{-2}\) (+) & \(3.43\times 10^{-2}\) (-) \\ DTLZ4 & \(4.33\times 10^{-2}\) & \(5.48\times 10^{-2}\) (+) & \(4.89\times 10^{-2}\) (+) & \(5.23\times 10^{-2}\) (+) & \(9.10\times 10^{-2}\) (+) & \(4.84\times 10^{-2}\) (+) \\ DTLZ5 & \(9.70\times 10^{-3}\) & \(9.30\times 10^{-3}\) (-) & \(1.52\times 10^{-2}\) (+) & \(1.33\times 10^{-2}\) (+) & \(1.80\times 10^{-2}\) (+) & \(7.40\times 10^{-3}\) (-) \\ DTLZ6 & \(9.40\times 10^{-3}\) & \(1.12\times 10^{-2}\) (+) & \(1.69\times 10^{-2}\) (+) & \(2.04\times 10^{-2}\) (+) & \(1.03\times 10^{-2}\) (+) & \(6.40\times 10^{-2}\) (-) \\ DTLZ7 & \(6.50\times 10^{-2}\) & \(7.18\times 10^{-2}\) (+) & \(6.69\times 10^{-2}\) (+) & \(6.14\times 10^{-2}\) (-) & \(4.97\times 10^{-2}\) (-) & \(4.25\times 10^{-2}\) (-) \\ WFG2 & \(3.37\times 10^{-1}\) & \(4.88\times 10^{-1}\) (+) & \(3.62\times 10^{-1}\) (+) & \(3.40\times 10^{-1}\) (+) & \(4.37\times 10^{-1}\) (+) & \(3.64\times 10^{-1}\) (+) \\ WFG3 & \(1.42\times 10^{-1}\) & \(3.43\times 10^{-1}\) (+) & \(2.01\times 10^{-1}\) (+) & \(1.79\times 10^{-1}\) (+) & \(4.06\times 10^{-1}\) (+) & \(1.99\times 10^{-1}\) (+) \\ WFG4 & \(4.26\times 10^{-1}\) & \(5.23\times 10^{-1}\) (+) & \(4.87\times 10^{-1}\) (+) & \(4.32\times 10^{-1}\) (+) & \(7.24\times 10^{-1}\) (+) & \(4.29\times 10^{-1}\) (+) \\ MaF1 & \(7.31\times 10^{-2}\) & \(8.36\times 10^{-2}\) (+) & \(7.06\times 10^{-2}\) (-) & \(6.23\times 10^{-2}\) (-) & \(1.05\times 10^{-1}\) (+) & \(7.18\times 10^{-2}\) (-) \\ MaF2 & \(6.27\times 10^{-2}\) & \(6.28\times 10^{-2}\) (\(\sim\)) & \(6.08\times 10^{-2}\) (-) & \(5.39\times 10^{-2}\) (-) & \(8.64\times 10^{-2}\) (+) & \(3.21\times 10^{-2}\) (-) \\ MaF12 & \(4.31\times 10^{-1}\) & \(5.18\times 10^{-1}\) (+) & \(4.53\times 10^{-1}\) (+) & \(4.33\times 10^{-1}\) (+) & \(7.17\times 10^{-1}\) (+) & \(6.85\times 10^{-1}\) (+) \\ + & / & 12 & 12 & 11 & 12 & 7 \\ - & / & 2 & 3 & 4 & 3 & 8 \\ \(\sim\) & / & 1 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 18: \(HV\) result of the six compared algorithms on test functions. (“+”, “\(\sim\)” and “-” respectively represent that MOFECO is better than, similar to and inferior to the other five algorithms).