# Multicriteria Route Planning for In-Operation Mass Transit under Urban Data
## 4 Multicriteria Route Planning for Mass Transit
### The Algorithm
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**City** & **Source** & **DF** & **Unit PF** & **PF** & **Length** \\ \hline \multirow{6}{*}{Chicago} & Method & 6 & \(4.77\times 10^{-21}\) & \(3.27\times 10^{-5}\) & \(2.10\times 10^{-10}\) \\  & Area & 15 & \(3.09\times 10^{-44}\) & \(1.11\times 10^{-35}\) & \(1.10\times 10^{-17}\) \\ \cline{1-1} \cline{2-6}  & Method & 6 & \(1.00\times 10^{-14}\) & \(1.48\times 10^{-7}\) & \(2.46\times 10^{-17}\) \\  & Station & 11 & \(2.44\times 10^{-15}\) & \(7.34\times 10^{-80}\) & \(5.45\times 10^{-13}\) \\ \hline \multirow{6}{*}{Tianan} & Method & 6 & \(3.64\times 10^{-5}\) & \(1.56\times 10^{-6}\) & \(1.43\times 10^{-12}\) \\  & Area & 15 & \(1.96\times 10^{-39}\) & \(6.48\times 10^{-43}\) & \(2.13\times 10^{-23}\) \\ \cline{1-1} \cline{2-6}  & Method & 6 & \(1.66\times 10^{-24}\) & \(0.07\times 10^{-2}\) & \(3.50\times 10^{-16}\) \\ \cline{1-1}  & Station & 11 & \(6.22\times 10^{-15}\) & \(1.11\times 10^{-34}\) & \(3.34\times 10^{-10}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: \(p\)-Values in two-way ANOVA test for different methods towards all objectives. according to the performance towards unit PF. Based on the results of [PERSON]'s LSD test in Table 10, it seems that the unit PF obtained from BiasSpan is significantly better than those retrieved from other comparative methods. In other words, based on the fitness function of unit PF, BiasSpan is clustered on its own in the first-tier group for its performance in both datasets. On the other hand, _Dijkstra_'s and _Distance-A_* are both clustered in the second-tier group for their performance in both datasets, while _IDDFS_ and _Best-First_ are clustered in the last-tier group for both datasets. For the rest methods, _BFS_ and _PF-A_* turns out vary between the second tier and last tier depending on the datasets. This can be credited to the stability of effective exploration in grids for the route-planning algorithm itself. For instance, the decisions made by _Dijkstra_'s and _Distance-A_* tend to be attracted by the expected minimized cost in length, which seems to be a more reliable and less nonmonotonic feature compared to the other criterion. In contrast, _IDDFS_ and _Best-First_ aim to retain a better estimated profit in PF; however, they risk falling into local optimal or failing to secure a smooth path, which, in turn, leads these two methods together a worse performance. Similarly, the characteristics of _BFS_ and _PF-A_* also put some emphasis in searching for local optimal in the profit of PF, yet the cost is still considered in their mixed nature. This makes them fall in between these two types and end up with a mediocre position among all the tested algorithms. To further investigate the performance BiasSpan, the Wilcoxon signed-rank test for BiasSpan against other comparative methods towards all objectives is conducted with the results listed in Table 11. As a non-parametric alternative to the paired t-test, it shows that for the objective of length of fitness function (unit PF), BiasSpan turns out to retain significantly better performance compared to all other methods in both datasets. It is worth mentioning that, since the objective of length is to be minimized, a larger amount of negative ranks indicates that BiasSpan obtains a solution with better performance in the criterion of length against its competitor. Although comparative methods such as _BFS_ and _PF-A_* tend to retrieve a better performance in the objective of PF, especially in the Tainan dataset, the disadvantage is not that not significant according to the significance level as well as compared to its advantage in the other objective.