## 5 Numerical Experiments
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Problem** & **MOWOATS** & _AgMOPSO_ & _MMOPSO_ & _D\({}^{2}\)MOPSO_ & _EAG-MOEA/D_ & _NSGA-II_ \\ \hline _ZDT1_ & _mean_ & \(\mathbf{1.303\times 10^{-3}}\) & \(3.701\times 10^{-3}\) & \(3.936\times 10^{-3}\) & \(1.038\times 10^{-2}\) & \(3.757\times 10^{-3}\) & \(4.976\times 10^{-3}\) \\  & _std_ & \(7.450\times 10^{-4}\) & \(\mathbf{2.83\times 10^{-5}}\) & \(3.456\times 10^{-5}\) & \(6.07\times 10^{-3}\) & \(1.02\times 10^{-4}\) & \(1.73\times 10^{-4}\) \\ _ZDT2_ & _mean_ & \(\mathbf{7.318\times 10^{-4}}\) & \(3.828\times 10^{-3}\) & \(2.414\times 10^{-2}\) & \(4.904\times 10^{-1}\) & \(2.113\times 10^{-2}\) & \(5.102\times 10^{-3}\) \\  & _std_ & \(2.955\times 10^{-4}\) & \(\mathbf{3.15\times 10^{-5}}\) & \(1.11\times 10^{-1}\) & \(2.45\times 10^{-1}\) & \(8.19\times 10^{-2}\) & \(1.79\times 10^{-4}\) \\ _ZDT3_ & _mean_ & \(\mathbf{2.872\times 10^{-3}}\) & \(4.367\times 10^{-3}\) & \(4.413\times 10^{-3}\) & \(1.404\times 10^{-2}\) & \(3.142\times 10^{-2}\) & \(6.408\times 10^{-3}\) \\ _std_ & \(2.691\times 10^{-3}\) & \(5.23\times 10^{-5}\) & \(\mathbf{4.28\times 10^{-5}}\) & \(4.34\times 10^{-3}\) & \(3.73\times 10^{-2}\) & \(5.41\times 10^{-3}\) \\ _ZDT4_ & _mean_ & \(\mathbf{2.850\times 10^{-4}}\) & \(7.942\times 10^{-3}\) & \(2.342\times 10^{-2}\) & \(3.203\) & \(2.357\times 10^{-2}\) & \(7.654\times 10^{-3}\) \\  & _std_ & \(\mathbf{7.729\times 10^{-5}}\) & \(2.23\times 10^{-2}\) & \(4.42\times 10^{-2}\) & \(2.06\) & \(3.18\times 10^{-2}\) & \(2.45\times 10^{-3}\) \\ _ZDT6_ & _mean_ & \(\mathbf{8.922\times 10^{-4}}\) & \(2.997\times 10^{-3}\) & \(3.635\times 10^{-3}\) & \(1.423\times 10^{-2}\) & \(3.132\times 10^{-3}\) & \(9.088\times 10^{-3}\) \\ _std_ & \(3.476\times 10^{-4}\) & \(\mathbf{9.51\times 10^{-5}}\) & \(2.31\times 10^{-4}\) & \(8.14\times 10^{-3}\) & \(2.13\times 10^{-4}\) & \(1.00\times 10^{-3}\) \\ _DTLZ1_ & _mean_ & \(\mathbf{3.760\times 10^{-4}}\) & \(2.183\times 10^{-2}\) & \(2.754\times 10^{-2}\) & \(1.515\) & \(2.582\times 10^{-2}\) & \(2.544\times 10^{-2}\) \\ _sdt_ & \(\mathbf{2.735\times 10^{-5}}\) & \(1.229\times 10^{-4}\) & \(2.56\times 10^{-2}\) & \(2.22\) & \(3.14\times 10^{-3}\) & \(3.02\times 10^{-3}\) \\ _DTLZ2_ & _mean_ & \(\mathbf{9.731\times 10^{-4}}\) & \(5.133\times 10^{-2}\) & \(6.354\times 10^{-2}\) & \(6.078\times 10^{-2}\) & \(5.93\times 10^{-2}\) & \(6.725\times 10^{-2}\) \\ _std_ & \(\mathbf{7.122\times 10^{-5}}\) & \(2.50\times 10^{-4}\) & \(1.82\times 10^{-3}\) & \(1.53\times 10^{-3}\) & \(1.73\times 10^{-3}\) & \(2.74\times 10^{-3}\) \\ _DTLZ3_ & _mean_ & \(\mathbf{2.242\times 10^{-3}}\) & \(3.619\times 10^{-1}\) & \(1.929\) & \(4.505\times 10^{1}\) & \(1.505\times 10^{-1}\) & \(1.525\times 10^{-1}\) \\ _sdt_ & \(\mathbf{6.181\times 10^{-4}}\) & \(5.79\times 10^{-1}\) & \(1.61\) & \(2.49\times 10^{1}\) & \(1.78\times 10^{-1}\) & \(2.52\times 10^{-1}\) \\ _DTLZ4_ & _mean_ & \(\mathbf{1.286\times 10^{-3}}\) & \(3.304\times 10^{-2}\) & \(6.325\times 10^{-2}\) & \(6.261\times 10^{-2}\) & \(1.872\times 10^{-1}\) & \(6.181\times 10^{-2}\) \\ _sdt_ & \(\mathbf{1.325\times 10^{-4}}\) & \(4.633\times 10^{-4}\) & \(4.55\times 10^{-3}\) & \(3.36\times 10^{-3}\) & \(1.47\times 10^{-1}\) & \(6.24\times 10^{-3}\) \\ _DTLZ5_ & _mean_ & \(\mathbf{4.365\times 10^{-5}}\) & \(3.868\times 10^{-3}\) & \(3.825\times 10^{-3}\) & \(6.072\times 10^{-3}\) & \(3.876\times 10^{-3}\) & \(5.217\times 10^{-3}\) \\ _sdt_ & \(\mathbf{1.507\times 10^{-5}}\) & \(8.12\times 10^{-5}\) & \(9.45\times 10^{-5}\) & \(1.12\times 10^{-3}\) & \(8.97\times 10^{-5}\) & \(2.69\times 10^{-4}\) \\ _DTLZ6_ & _mean_ & \(\mathbf{1.858\times 10^{-4}}\) & \(3.670\times 10^{-3}\) & \(3.756\times 10^{-3}\) & \(1.392\times 10^{-2}\) & \(3.730\times 10^{-3}\) & \(1.733\times 10^{-2}\) \\ _sdt_ & \(1.400\times 10^{-4}\) & \(1.653\times 10^{-4}\) & \(1.57\times 10^{-4}\) & \(2.06\times 10^{-3}\) & \(\mathbf{1.05\times 10^{-4}}\) & \(1.38\times 10^Another feature which strains the quality of solutions computed by a _MOP_ solver occurs when the _PF_ exhibits an irregular shape.