## 5 Computational Experiments, Results, and Discussion
### Results for Small-Sized Instances
\begin{table}
\begin{tabular}{l r r r r r r r r r} \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{\(|\mathcal{P}|\)} & \multirow{2}{*}{\(\boldsymbol{HV\%(\mathcal{P})}\)} & \multicolumn{2}{c}{**NSGA-II**} & \multicolumn{4}{c}{**MOSS**} \\ \cline{3-10}  & & & \(|\widehat{\mathcal{D}}|\) & \(\overline{TGD}\) & \(\overline{\mathcal{H}}\) & \(\overline{\mathcal{D}}\) & \(\overline{\mathcal{D}}\) & \(\overline{\mathcal{D}}\) & \(\overline{TGD}\) & \(\overline{\mathcal{H}}\) \\ \hline DMOSP-S-1 & 8 & 64.66 & 5 & 5.8 & 6.459 & 1.10 & 7 & 7.7 & **1.499** & **0.06** \\ DMOSP-S-2 & 4 & 87.41 & **3** & **3.4** & 5.967 & **0.78** & 2 & 2.7 & **5.672** & 0.93 \\ DMOSP-S-3 & 4 & 73.90 & 3 & 3.3 & 4.425 & 0.50 & 4 & **4.0** & **3.823** & **0.10** \\ DMOSP-S-4 & 14 & 68.45 & 12 & 10.1 & 18.107 & 3.42 & 12 & 13.0 & **14.510** & **2.42** \\ DMOSP-S-5 & 1 & 50.85 & 1 & 1.0 & **0.000** & **0.00** & 1 & 1.0 & **2.213** & 0.31 \\ DMOSP-S-6 & 4 & 61.64 & 1 & 1.9 & 35.633 & 2.97 & **3** & **2.4** & **20.846** & **1.87** \\ DMOSP-S-7 & 2 & 62.35 & 2 & 2.2 & 35.462 & 4.12 & **4** & **3.6** & **29.367** & **2.95** \\ DMOSP-S-8 & 7 & 27.05 & 5 & 4.8 & **1.304** & **0.05** & 5 & **5.1** & 1.349 & 0.06 \\ DMOSP-S-9 & 7 & 88.42 & 4 & 4.9 & 39.315 & 5.16 & 7 & **7.2** & **23.246** & **3.73** \\ DMOSP-S-10 & 4 & 48.97 & **4** & **3.9** & 45.843 & 3.90 & 2 & 3.0 & **28.774** & **2.43** \\ DMOSP-S-11 & 10 & 60.05 & 4 & 5.0 & 15.560 & 2.79 & 8 & **7.2** & **10.890** & **2.17** \\ DMOSP-S-12 & 7 & 74.91 & 3 & 3.3 & 32.193 & 5.30 & 6 & **5.3** & **16.456** & **2.88** \\ DMOSP-S-13 & 16 & 45.03 & 7 & 8.3 & 14.125 & 2.00 & **16** & **13.7** & **9.219** & 0.76 \\ DMOSP-S-14 & 8 & 61.48 & 3 & 2.8 & 19.027 & 5.21 & 3 & **3.9** & **13.685** & 3.75 \\ DMOSP-S-15 & 17 & 60.08 & 10 & 10.2 & **17.895** & 4.70 & **11** & **11.6** & 19.774 & **4.18** \\ DMOSP-S-16 & 3 & 56.52 & 1 & 1.6 & 33.655 & 3.82 & **2** & **1.7** & **13.275** & **1.75** \\ DMOSP-S-17 & 11 & 44.01 & 6 & 6.8 & 25.253 & 2.81 & **10** & **9.4** & **20.979** & **1.44** \\ DMOSP-S-18 & 6 & 81.37 & 3 & 3.0 & 8.609 & 1.89 & **4** & **4.6** & **5.159** & **0.71** \\ DMOSP-S-19 & 3 & 17.89 & 3 & **3.4** & **14.222** & 0.48 & 3 & 3.0 & 14.829 & 0.39 \\ DMOSP-S-20 & 2 & 95.26 & 2 & 1.7 & 3.544 & 0.41 & 2 & **1.8** & **2.452** & **0.29** \\ DMOSP-S-21 & 11 & 74.69 & 6 & 7.5 & 17.498 & 5.76 & **11** & **8.8** & **9.765** & **3.03** \\ DMOSP-S-22 & 23 & 72.09 & 7 & 8.9 & 17.346 & 6.21 & **13** & **13** & **15.15** & **15.906** & **5.90** \\ DMOSP-S-23 & 1 & 59.50 & 1 & **1.3** & 17.666 & 1.23 & 1 & 1.1 & **15.108** & **1.05** \\ DMOSP-S-24 & 8 & 57.47 & 2 & 2.5 & 14.885 & **4.91** & **3** & **2.8** & **14.049** & 5.16 \\ DMOSP-S-25 & 5 & 64.32 & 5 & 4.8 & 16.416 & 4.04 & **8** & **6.6** & **8.074** & **1.46** \\ DMOSP-S-26 & 5 & 62.65 & 1 & 1.7 & 9.124 & 2.30 & **3** & **3.2** & **5.993** & **1.28** \\ DMOSP-S-27 & 2 & 93.03 & 2 & 2.0 & 27.869 & 1.59 & **3** & **2.5** & **24.542** & **1.54** \\ DMOSP-S-28 & 2 & 72.14 & 3 & 2.4 & 22.213 & 2.06 & 2 & **3.4** & **8.526** & **0.75** \\ DMOSP-S-29 & 2 & 96.87 & 2 & 2.0 & **1.856** & **0.14** & 2 & 2.2 & 2.028 & 0.26 \\ DMOSP-S-30 & 1 & 47.76 & 1 & **1.4** & 45.561 & 2.55 & 1 & 1.2 & **23.204** & **1.36** \\ \hline \end{tabular} Boldface highlights the best result.  
\end{table} 
Table 5: Summary of computational results statistics for small benchmark instances of both NSGA-II and MOS.