## 5 Numerical Experiments
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & _UF1_ & _UF2_ & _UF3_ & _UF4_ & _UF5_ & _UF6_ & _UF7_ & _UF8_ & _UF9_ & _UF10_ \\ \hline _GDES_ & \(5.34\times 10^{-2}\) & \(1.20\times 10^{-2}\) & \(1.06\times 10^{-1}\) & \(2.65\times 10^{-2}\) & \(3.93\times 10^{-2}\) & \(2.51\times 10^{-1}\) & \(2.52\times 10^{-2}\) & \(2.49\times 10^{-1}\) & \(8.25\times 10^{-2}\) & \(4.33\times 10^{-1}\) \\ _MOEADGM_ & \(6.20\times 10^{-3}\) & \(6.40\times 10^{-3}\) & \(4.90\times 10^{-2}\) & \(4.76\times 10^{-2}\) & \(1.79\) & \(5.56\times 10^{-1}\) & \(7.60\times 10^{-3}\) & \(2.45\times 10^{-1}\) & \(1.88\times 10^{-1}\) & \(5.65\times 10^{-1}\) \\ _MTS_ & \(6.46\times 10^{-3}\) & \(6.15\times 10^{-3}\) & \(5.31\times 10^{-2}\) & \(2.36\times 10^{-2}\) & \(\mathbf{1.49\times 10^{-2}}\) & \(5.92\times 10^{-2}\) & \(4.08\times 10^{-2}\) & \(1.13\times 10^{-1}\) & \(1.14\times 10^{-1}\) & \(5.53\times 10^{-1}\) \\ _DMOEAD-DD_ & \(1.04\times 10^{-2}\) & \(6.79\times 10^{-3}\) & \(3.34\times 10^{-2}\) & \(4.27\times 10^{-2}\) & \(3.15\times 10^{-1}\) & \(6.67\times 10^{-2}\) & \(1.03\times 10^{-2}\) & \(6.84\times 10^{-2}\) & \(4.90\times 10^{-2}\) & \(3.22\times 10^{-1}\) \\ _NSGA-II-LS_ & \(1.15\times 10^{-2}\) & \(1.24\times 10^{-2}\) & \(1.06\times 10^{-1}\) & \(5.84\times 10^{-2}\) & \(5.66\times 10^{-1}\) & \(3.10\times 10^{-1}\) & \(2.13\times 10^{-2}\) & \(6.83\times 10^{-2}\) & \(7.19\times 10^{-2}\) & \(8.45\times 10^{-1}\) \\ _OWMOsDE_ & \(1.22\times 10^{-2}\) & \(8.10\times 10^{-3}\) & \(1.03\times 10^{-1}\) & \(5.13\times 10^{-2}\) & \(4.30\times 10^{-1}\) & \(1.92\times 10^{-1}\) & \(5.85\times 10^{-2}\) & \(9.45\times 10^{-2}\) & \(9.83\times 10^{-2}\) & \(7.43\times 10^{-1}\) \\ _Clustering MOGA_ & \(2.99\times 10^{-2}\) & \(2.28\times 10^{-2}\) & \(5.49\times 10^{-2}\) & \(5.85\times 10^{-2}\) & \(2.47\times 10^{-1}\) & \(8.71\times 10^{-2}\) & \(2.23\times 10^{-1}\) & \(2.38\times 10^{-1}\) & \(2.93\times 10^{-1}\) & \(4.11\times 10^{-1}\) \\ _AMGA_ & \(3.59\times 10^{-2}\) & \(1.62\times 10^{-2}\) & \(7.00\times 10^{-2}\) & \(4.06\times 10^{-2}\) & \(9.41\times 10^{-2}\) & \(1.29\times 10^{-1}\) & \(1.57\times 10^{-2}\) & \(1.71\times 10^{-1}\) & \(1.89\times 10^{-1}\) & \(3.24\times 10^{-1}\) \\ _MOEP_ & \(5.96\times 10^{-2}\) & \(1.89\times 10^{-2}\) & \(9.90\times 10^{-2}\) & \(4.27\times 10^{-2}\) & \(2.25\times 10^{-1}\) & \(1.03\times 10^{-1}\) & \(1.97\times 10^{-2}\) & \(4.23\times 10^{-1}\) & \(3.42\times 10^{-1}\) & \(3.62\times 10^{-1}\) \\ _OOGA-II_ & \(8.56\times 10^{-2}\) & \(3.06\times 10^{We also conducted a specific comparison of our algorithm with Archive-guided memory to _MPSO_ (_AgMOPSO_) [14] just to see the performance gains achievable over an algorithm that, as with _AgMOPSO_, applies decomposition of the original problem into subproblems to search the solution space of a _MOP_. The results (_IGD_ metric) are listed in Table 5 for the comparison of _MOWOATS_ against _AgMOPSO_, _MMOPSO_, _D\({}^{2}\)MOPSO_, and _EAG-MOEA/D_, obtained from 30 independent runs [14]. These experiments were performed on tri-objective _DTLZ_ and _CEC2009_ benchmark test functions. Here, the results show once again that _MOWOATS_ achieves the best mean and standard deviation values for all test functions except (_ZDT1_, _ZDT2_, _ZDT3_, _ZDT6_, _DTLZ6_, and _DTLZ7_) test functions. The second-best standard deviation values are attained by our algorithm for _ZDT2_ and _DTLZ6_, and the third best results for _ZDT3_ and _ZDT6_. While not uniformly better, these results indicate that even when it is not the best, _MOWOATS_ yields results with comparable quality to the best _SI_-based algorithms proposed in the literature, and that its variability across the different _MOPs_ is small.