# 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 c c c} \hline \hline
**City** & **Objective** & **Indicator** & **Dijkstra** & **BFS** & **IDDFS** & **Best-First** & **Distance-A* & **PF-A* \\ \hline Chicago & Unit PF & \(p\)-value & 6.07 \(\times 10^{-6}\) & 8.67 \(\times 10^{-19}\) & 8.67 \(\times 10^{-19}\) & 8.67 \(\times 10^{-19}\) & 2.60 \(\times 10^{-9}\) & 8.67 \(\times 10^{-19}\) \\  & Positive ranks & 47 & 60 & 60 & 60 & 52 & 60 \\  & Negative ranks & 13 & 0 & 0 & 0 & 8 & 0 \\ \hline PF & \(p\)-value & 0.1225 & 0.0031 & 0.0067 & 0.0259 & 0.1831 & 0.0462 \\  & Positive ranks & 35 & 41 & 40 & 38 & 34 & 37 \\  & Negative ranks & 24 & 19 & 20 & 22 & 25 & 23 \\ \hline Length & \(p\)-value & 6.07 \(\times 10^{-6}\) & 8.67 \(\times 10^{-19}\) & 8.67 \(\times 10^{-19}\) & 8.67 \(\times 10^{-19}\) & 2.60 \(\times 10^{-9}\) & 8.67 \(\times 10^{-19}\) \\  & Positive ranks & 13 & 0 & 0 & 0 & 8 & 0 \\ \hline Tainan & Unit PF & \(p\)-value & 0.0031 & 8.67 \(\times 10^{-19}\) & 8.67 \(\times 10^{-19}\) & 8.67 \(\times 10^{-19}\) & 8.08 \(\times 10^{-8}\) & 8.67 \(\times 10^{-19}\) \\  & Positive ranks & 41 & 60 & 60 & 60 & 50 & 60 \\  & Negative ranks & 18 & 0 & 0 & 0 & 10 & 0 \\ \hline PF & \(p\)-value & 0.2595 & 0.0005 & 0.0259 & 0.0259 & 0.0775 & 0.0031 \\  & Positive ranks & 27 & 17 & 22 & 22 & 24 & 19 \\  & Negative ranks & 29 & 41 & 36 & 36 & 33 & 39 \\ \hline Length & \(p\)-value & 0.0031 & 8.67 \(\times 10^{-19}\) & 8.67 \(\times 10^{-19}\) & 8.67 \(\times 10^{-19}\) & 8.08 \(\times 10^{-8}\) & 8.67 \(\times 10^{-19}\) \\  & Positive ranks & 18 & 0 & 0 & 0 & 10 & 0 \\  & Negative ranks & 41 & 60 & 60 & 60 & 50 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Wilcoxon signed-rank test for BiasSpan against different methods towards all objectives. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**City**} & **Method** & \multicolumn{6}{c}{**Comparative Method**} \\ \cline{2-9}  & **BiasSpan** & **Dijkstra** & **BFS** & **IDDFS** & **Best-First** & **Distance-A*** & **PF-A* \\ \hline Chicago & BiasSpan & N.A. & **6.07\(\times\) 10\({}^{-6}\)** & **8.67\(\times\) 10\({}^{-19}\)** & **8.67\(\times\) 10\({}^{-19}\)** & **8.67\(\times\) 10\({}^{-19}\)** & **2.60\(\times\) 10\({}^{-9}\)** & **8.67\(\times\) 10\({}^{-19}\)** \\  & Dijkstra & D.A. & N.A. & 4.86 \(\times\) 10\({}^{-11}\) & 1.54 \(\times\) 10\({}^{-8}\) & 1.54 \(\times\) 10\({}^{-8}\) & 1.59 \(\times\) 10\({}^{-6}\) & 6.73 \(\times\) 10\({}^{-5}\) \\  & BFS & D.A. & D.A. & N.A. & 0.5513 & 0.4487 & D.A. & D.A. \\  & IDDFS & D.A. & D.A. & D.A. & N.A. & 0.0775 & D.A. & D.A. \\  & BestFirst & D.A. & D.A. & D.A. & D.A. & N.A. & D.A. \\  & Distance-A* & D.A. & D.A. & 3.84 \(\times\) 10\({}^{-10}\) & 1.54 \(\times\) 10\({}^{-8}\) & 6.07 \(\times\) 10\({}^{-6}\) & N.A. & 0.0002 \\  & PF-A* & D.A. & D.A. & 0.0067 & 0.0259 & 0.0002 & D.A. & N.A. \\ \hline Tainan & BiasSpan & N.A. & **0.0031** & **8.67\(\times\) 10\({}^{-19}\)** & **8.67\(\times\) 10\({}^{-19}\)** & **8.67\(\times\) 10\({}^{-19}\)** & **8.08\(\times\) 10\({}^{-8}\)** & **8.67\(\times\) 10\({}^{-19}\)** \\  & Dijkstra & D.A. & N.A. & 5.19 \(\times\) 10\({}^{-12}\) & 4.54 \(\times\) 10\({}^{-13}\) & 5.19 \(\times\) 10\({}^{-12}\) & 0.0005 & 2.60 \(\times\) 10\({}^{-9}\) \\  & BPS & D.A. & D.A. & N.A. & 0.0259 & 0.3494 & D.A. & 0.1225 \\  & IDDFS & D.A. & D.A. & D.A. & N.A. & D.A. & D.A. \\  & BestFirst & D.A. & D.A. & D.A. & 0.0462 & N.A. & D.A. & D.A. \\  & Distance-A* & D.A. & D.A. & 1.54 \(\times\) 10\({}^{-8}\) & 1.59 \(\times\) 10\({}^{-6}\) & 8.08 \(\times\) 10\({}^{-8}\) & N.A. & 8.08 \(\times\) 10\({}^{-8}\) \\  & PF-A* & D.A. & D.A. & D.A. & 0.1225 & 0.0031 & D.A. Nevertheless, according to the reported analysis, BiasSpan successfully holds a performance significantly outperforming other comparative methods. #### 5.3.5 Summary

To conclude, BiasSpan ends up retaining the Pareto-optimal for route planning that connects must-visit sites and recommended ones.