## 4 Experimental Results and Discussions
### Experiment Comparison of Different COOBBO
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Benchmark**} & **Optimal** & **Comparison** & **COOBBO (Backward** & **COOBBO (Forward** & **COOBO (Circle)** \\  & **Solution** & **Criteria** & **Ellipse)** & **Ellipse)** & **COOBO (Circle)** \\ \hline \multirow{4}{*}{berlin52} & \multirow{4}{*}{7542} & BS & \(8321.864\pm 243.0838\) & \(\mathbf{8305.1157\pm 241.5853}\) & \(8333.591\pm 283.9502\) \\  & & CT & \(26.0636\pm 0.40613\) & \(26.2338\pm 0.43054\) & \(\mathbf{24.4901\pm 0.3307}\) \\  & & UR & \(17.7021\pm 1.5387\) & \(\mathbf{19.4787\pm 1.7205}\) & \(11.9418\pm 1.032\) \\  & & PD & \(23.4455\pm 1.7748\) & \(\mathbf{20.365\pm 0.99143}\) & \(31.0124\pm 0.58744\) \\ \hline \multirow{4}{*}{bier127} & \multirow{4}{*}{118282} & BS & \(\mathbf{18699.418\pm 11339.7602}\) & \(200390.2364\pm 9909.0866\) & \(190145.1356\pm 9264.6665\) \\  & & CT & \(77.5242\pm 1.7217\) & \(77.871\pm 1.8559\) & \(\mathbf{70.1001\pm 1.2754}\) \\  & & UR & \(\mathbf{10.0663\pm 0.94305}\) & \(9.4902\pm 0.93118\) & \(5.5513\pm 0.38539\) \\  & & PD & \(37.8905\pm 1.7826\) & \(\mathbf{34.7061\pm 1.3295}\) & \(47.5324\pm 1.3702\) \\ \hline \multirow{4}{*}{ch130} & \multirow{4}{*}{6110} & BS & \(\mathbf{10735.6857\pm 800.823}\) & \(12301.3115\pm 665.8969\) & \(11071.1291\pm 602.8048\) \\  & & CT & \(80.0928\pm 1.9244\) & \(80.2126\pm 1.7268\) & \(\mathbf{72.6642\pm 1.5963}\) \\  & & UR & \(\mathbf{11.046\pm 1.133}\) & \(10.2205\pm 0.96441\) & \(6.2528\pm 0.46867\) \\  & & PD & \(38.2925\pm 1.7171\) & \(\mathbf{33.9795\pm 1.2991}\) & \(52.0144\pm 1.1943\) \\ \hline \multirow{4}{*}{kroA150} & \multirow{4}{*}{26524} & BS & \(\mathbf{54089.9955\pm 4138.1095}\) & \(62213.9641\pm 3367.083\) & \(56154.8562\pm 3199.3826\) \\  & & CT & \(97.9435\pm 2.3961\) & \(97.909\pm 2.6651\) & \(\mathbf{87.9529\pm 1.6593}\) \\  & & UR & \(\mathbf{11.5362\pm 1.14}\) & \(10.7622\pm 0.91919\) & \(6.9752\pm 0.44009\) \\  & & PD & \(43.8533\pm 2.3142\) & \(\mathbf{39.1721\pm 1.9173}\) & \(61.6256\pm 1.7903\) \\ \hline \multirow{4}{*}{kroA200} & \multirow{4}{*}{29368} & BS & \(\mathbf{79433.7261\pm 5793.0264}\) & \(95434.8002\pm 4848.5489\) & \(93386.4811\pm 3698.4416\) \\  & & CT & \(146.7581\pm 3.6105\) & \(148.7677\pm 3.9271\) & \(\mathbf{130.3292\pm 3.1375}\) \\  & & UR & \(\mathbf{9.8554\pm 0.92318}\) & \(9.195\pm 0.88397\) & \(5.8667\pm 0.3423\) \\  & & PD & \(51.4226\pm 2.5032\) & \(\mathbf{46.2781\pm 2.5567}\) & \(74.8238\pm 3.0705\) \\ \hline \multirow{4}{*}{kroC100} & \multirow{4}{*}{20749} & BS & \(28786.3067\pm 2089.1848\) & \(32228.8304\pm 1988.7409\) & \(\mathbf{28124.5048\pm 1469.195}\) \\  & & CT & \(56.7792\pm 1.2044\) & \(57.3461\pm 1.2305\) & \(\mathbf{52.1812\pm 0.91162}\) \\ \cline{1-1}  & & UR & \(\mathbf{15.161\pm 1.4206}\) & \(14.8064\pm 1.5202\) & \(10.6852\pm 0.91019\) \\ \cline{1-1}  & & PD & \(36.5919\pm 2.2458\) & \(\mathbf{31.6739\pm 1.2889}\) & \(48.9681\pm 1.039\) \\ \hline \multirow{4}{*}{lin105} & \multirow{4}{*}{14379} & BS & \(\mathbf{20653.0943\pm 1528.6458}\) & \(22392.0575\pm 1610.5752\) & \(20786.2342\pm 1077.5567\) \\ \cline{1-1}  & & CT & \(60.3434\pm 1.2413\) & \(61.4\pm 1.2684\) & \(\mathbf{55.1161\pm 1.0321}\) \\ \cline{1-1}  & & UR & \(\mathbf{14.1988\pm 1.4196}\) & \(13.8791\pm 1.2581\) & \(10.4896\pm 0.95054\) \\ \cline{1-1}  & & PD & \(38.1673\pm 2.0066\) & \(\mathbf{34.3843\pm 1.4297}\) & \(50.6824\pm 1.088\) \\ \hline \multirow{4}{*}{lin318} & \multirow{4}{*}{42029} & BS & \(\mathbf{179974.0689\pm 11519.3106}\) & \(209648.546\pm 10977.459\) & \(241710.2118\pm 9377.1761\) \\ \cline{1-1}  & & CT & \(298.6361\pm 8.3882\) & \(305.7854\pm 8.8387\) & \(\mathbf{261.5351\pm 7.5882}\) \\ \cline{1-1}  & & UR & \(\mathbf{7.5774\pm 0.70079}\) & \(7.1332\pm 0.68193\) & \(4.073\pm 0.28234\) \\ \cline{1-1}  & & PD & \(67.1539\pm 3.9866\) & \(\mathbf{60.4984\pm 3.586}\) & \(97.8536\pm 5.4552\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison of different COOBBO.