## 6 Results
### Pareto Set Quality Results
However, as indicated by the moderate non-dominance ratios, RAPTOR does generate strong albeit few solutions. More interestingly, we see that ML-TZSA Pareto set metric values improve with increasing transfer-zone sample size, which can be attributed to the larger and more diverse Pareto sets generated when the transfer-zone sample size is higher. ML-TZSA always has a non-dominance ratio close to one, indicating that its Pareto sets rarely contains solutions that are dominated on all criteria by any RAPTOR solution. Regarding reference set gap measures, RAPTOR results are independent of transfer-zone sample size and are hence displayed as constant in this comparison. The ML-TZSA reference set gap metrics tend to zero as the transfer-zone sample size approaches 500, even though ML-TZSA (500) only contributes around 15% of reference set solutions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Reference Set Contributions** & \multicolumn{2}{c}{**Non-Dominated Solutions per Method**} & \\
**Name** & **Total** & **Portion** & **Total** & **Portion Overall** & **Rank** \\ \hline ML-TZSA (200) & 7233 & 0.1167 & 19,479 & 0.0958 & 1 \\ ML-TZSA (500) & 6758 & 0.1090 & 26,774 & 0.1317 & 2 \\ ML-TZSA (250) & 6715 & 0.1083 & 21,048 & 0.1035 & 3 \\ ML-TZSA (350) & 6593 & 0.1064 & 24,277 & 0.1194 & 4 \\ ML-TZSA (450) & 6550 & 0.1057 & 25,298 & 0.1244 & 5 \\ ML-TZSA (400) & 6352 & 0.1025 & 23,495 & 0.1156 & 6 \\ ML-TZSA (300) & 6294 & 0.1015 & 22,866 & 0.1125 & 7 \\ ML-TZSA (150) & 5375 & 0.0867 & 15,619 & 0.0768 & 8 \\ ML-TZSA (100) & 3888 & 0.0627 & 11,286 & 0.0555 & 9 \\ ML-TZSA (50) & 2609 & 0.0421 & 7293 & 0.0359 & 10 \\ ML-TZSA (20) & 1731 & 0.0279 & 4151 & 0.0204 & 11 \\ ML-TZSA (10) & 1423 & 0.0230 & 1731 & 0.0085 & 12 \\ RAPTOR & 467 & 0.0075 & 1731 & 0.0085 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The reference Pareto set contributions of different solution methodologies (walking and public transport). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Reference Set Contributions** & \multicolumn{2}{c}{**Non-Dominated Solutions per Method**} & \\
**Name** & **Total** & **Portion** & **Total** & **Portion Overall** & **Rank** \\ \hline ML-TZSA (500) & 28,484 & 0.1450 & 77,812 & 0.1490 & 1 \\ ML-TZSA (350) & 23,269 & 0.1184 & 66,383 & 0.1271 & 2 \\ ML-TZSA (250) & 22,622 & 0.1151 & 56,294 & 0.1078 & 3 \\ ML-TZSA (400) & 22,359 & 0.1138 & 62,713 & 0.1201 & 4 \\ ML-TZSA (450) & 22,154 & 0.1128 & 68,815 & 0.1318 & 5 \\ ML-TZSA (200) & 21,930 & 0.1116 & 48,888 & 0.0936 & 6 \\ ML-TZSA (300) & 20,359 & 0.1036 & 59,183 & 0.1133 & 7 \\ ML-TZSA (150) & 14,599 & 0.0743 & 36,505 & 0.0699 & 8 \\ ML-TZSA (100) & 10,329 & 0.0526 & 24,265 & 0.0465 & 9 \\ ML-TZSA (50) & 5033 & 0.0256 & 12,537 & 0.0240 & 10 \\ ML-TZSA (20) & 3141 & 0.0160 & 6450 & 0.0124 & 11 \\ ML-TZSA (10) & 1682 & 0.0086 & 2314 & 0.0044 & 12 \\ RAPTOR-ES & 505 & 0.0026 & 2314 & 0.0044 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The reference Pareto set contributions of different solution methodologies (walking, public transport and e-scooters. Figure 11: Dominance ratio, non-dominance ratio, reference set gap average and standard deviation results for the case of walking and public transport. Figure 12: Dominance ratio, non-dominance ratio, reference set gap average and standard deviation results for the case of walking, public transport and e-scooters. Figure 13 displays the objective criteria scatter plots for the reference, ML-TZSA (500) and RAPTOR Pareto sets corresponding to the query depicted in Figure 10. The reference set consists of 628 solutions (small dots), ML-TZSA (500)'s Pareto set consists of 252 solutions (circles), 115 of which are reference set solutions, while RAPTOR's Pareto set consists of 2 solutions (asterixes), neither of which are in the reference set.