## 5 Numerical Experiments
### Results and Discussion
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline Problem & & _MOWOATS_ & _R2 HMOPSO_ & _R2 HMOPSO_ & _MOEA/D_ & _NSGA-II_ & _dMOPSO_ & _R2 MOPSO_ \\ \hline _ZDT1_ & _mcm_ & \(\mathbf{1.549\times 10^{-3}}\) & \(3.904\times 10^{-3}\) & \(3.943\times 10^{-3}\) & \(7.544\times 10^{-3}\) & \(4.929\times 10^{-3}\) & \(3.899\times 10^{-3}\) & \(3.928\times 10^{-3}\) \\ _std_ & \(2.648\times 10^{-3}\) & \(6.209\times 10^{-5}\) & \(8.593\times 10^{-5}\) & \(8.473\times 10^{-4}\) & \(2.043\times 10^{-4}\) & \(\mathbf{3.839\times 10^{-5}}\) & \(1.091\times 10^{-4}\) \\ _ZDT2_ & _mcm_ & \(\mathbf{8.951\times 10^{-4}}\) & \(3.834\times 10^{-3}\) & \(2.260\times 10^{-1}\) & \(2.503\times 10^{-2}\) & \(4.900\times 10^{-3}\) & \(6.442\times 10^{-2}\) & \(3.825\times 10^{-3}\) \\ _std_ & \(1.549\times 10^{-3}\) & \(\mathbf{4.907\times 10^{-3}}\) & \(2.969\times 10^{-1}\) & \(1.104\times 10^{-1}\) & \(2.074\times 10^{-1}\) & \(1.849\times 10^{-1}\) & \(3.336\times 10^{-5}\) \\ _ZDT3_ & _mcm_ & \(\mathbf{5.586\times 10^{-3}}\) & \(6.123\times 10^{-2}\) & \(6.840\times 10^{-3}\) & \(1.212\times 10^{-2}\) & \(7.254\times 10^{-3}\) & \(1.064\times 10^{-2}\) & \(1.017\times 10^{-2}\) \\ _std_ & \(3.631\times 10^{-3}\) & \(1.583\times 10^{-1}\) & \(\mathbf{6.058\times 10^{-4}}\) & \(5.585\times 10^{-3}\) & \(7.634\times 10^{-3}\) & \(7.098\times 10^{-4}\) & \(6.508\times 10^{-4}\) \\ _ZDT4_ & _mcm_ & \(\mathbf{9.755\times 10^{-5}}\) & \(4.518\times 10^{-3}\) & \(5.093\times 10^{-1}\) & \(2.452\times 10^{-1}\) & \(8.420\times 10^{-3}\) & \(5.992\) & \(8.374\times 10^{-2}\) \\ _std_ & \(\mathbf{4.180\times 10^{-5}}\) & \(3.733\times 10^{-3}\) & \(2.356\times 10^{-1}\) & \(1.571\times 10^{-1}\) & \(2.731\times 10^{-3}\) & \(4.477\) & \(9.787\times 10^{-2}\) \\ _ZDT6_ & _mcm_ & \(\mathbf{5.919\times 10^{-4}}\) & \(1.888\times 10^{-3}\) & \(1.868\times 10^{-3}\) & \(1.892\times 10^{-3}\) & \(2.696\times 10^{-3}\) & \(1.879\times 10^{-3}\) & \(1.865\times 10^{-3}\) \\ _std_ & \(6.917\times 10^{-4}\) & \(4.334\times 10^{-5}\) & \(2.227\times 10^{-5}\) & \(1.179\times 10^{-5}\) & \(4.111\times 10^{-5}\) & \(\mathbf{8.549\times 10^{-6}}\) & \(3.484\times 10^{-5}\) \\ _DTL21_ & _mcm_ & \(\mathbf{3.760\times 10^{-4}}\) & \(1.994\times 10^{-2}\) & \(1.724\times 10^{-2}\) & \(1.842\times 10^{-2}\) & \(1.935\times 10^{-2}\) & \(1.529\times 10^{-1}\) & \(1.745\times 10^{-1}\) \\ _std_ & \(\mathbf{2.735\times 10^{-5}}\) & \(2.800\times 10^{-3}\) & \(9.906\times 10^{-4}\) & \(4.773\times 10^{-4}\) & \(6.011\times 10^{-4}\) & \(1.180\times 10^{-1}\) & \(3.133\times 10^{-3}\) \\ _DTL22_ & _mcm_ & \(\mathbf{9.731\times 10^{-4}}\) & \(4.368\times 10^{-2}\) & \(5.555\times 10^{-2}\) & \(4.597\times 10^{-2}\) & \(5.5315\times 10^{-2}\) & \(4.716\times 10^{-2}\) & \(2.250\times 10^{-1}\) \\ _std_ & \(\mathbf{7.122\times 10^{-5}}\) & \(1.203\times 10^{-3}\) & \(3.302\times 10^{-3}\) & \(1.218\times 10^{-3}\) & \(2.373\times 10^{-3}\) & \(1.489\times 10^{-3}\) & \(1.526\times 10^{-2}\) \\ _DTL24_ & _mcm_ & \(\mathbf{1.266\times 10^{-3}}\) & \(5.198\times 10^{-2}\) & \(2.505\times 10^{-1}\) & \(5.160\times 10^{-2}\) & \(5.447\times 10^{-2}\) & \(1.175\times 10^{-1}\) & \(4.343\times 10^{-1}\) \\ _std_ & \(\mathbf{1.325\times 10^{-4}}\) & \(2.011\times 10^{-3}\) & \(1.262\times 10^{-1}\) & \(1.948\times 10^{-3}\) & \(1.727\times 10^{-3}\) & \(7.627\times 10^{-2}\) & \(5.111\times 10^{-2}\) \\ _DTL27_ & _mcm_ & \(\mathbf{6.314\times 10^{-2}}\) & \(7.036\times 10^{-2}\) & \(6.459\times 10^{-2}\) & \(1.271\times 10^{-1}\) & \(7.129\times 10^{-2}\) & \(1.265\times 10^{-1}\) & \(8.729\times 10^{-2}\) \\ _std_ & \(\mathbf{5.678\times 10^{-3}}\) & \(8.439\times 10^{-3}\) & \(9.521\times 10