# Multicriteria Route Planning for In-Operation Mass Transit under Urban Data
## 4 Multicriteria Route Planning for Mass Transit
### The Algorithm
that the BiasSpan is able to secure the Pareto optimal under the concerns in the nature of objective itself. #### 5.3.4 Statistical Analysis for BiasSpan

For the statistical analysis of BiasSpan against other comparative methods, the one-way analysis of variance (ANOVA), two-way ANOVA, Fisher's least significant difference (LSD), and Wilcoxon signed-rank tests are adopted with a significance level of 0.05. The results for two-way ANOVA test for different methods and constraints towards unit PF performance are listed in Figure 3:4 Meanwhile, the \(p\)-values in two-way ANOVA test for different methods towards all objectives are depicted in Figure 3:5 To be more specific, the two-way ANOVA is based on the fitness function of unit PF in Table 7, and all targeted criteria (PF, length, unit PF) for Figure 3:6 As the \(p\)-values demonstrated, it seems that there is a significant difference between the solutions generated by various methods and under different constrained settings. This result first supports the complexity as well as heterogeneity of the problem space, where different formations of constrained settings indeed affect the constitutions and performance of the possible solutions. Furthermore, it seems that the solutions generated by different methods have different efficacy between each other based on the reported results. To better interpret the different efficacies among various algorithms, the one-way ANOVA test is applied based on the unit PF performance and its results are depicted in Figure 3:7 Next, [PERSON]'s LSD test is applied to examine the cluster of different methods \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**City** & **Source** & **DF** & **SS** & **MS** & **F-Value** & \(p\)**-Value** \\ \hline \multirow{6}{*}{Chicago} & Method & 6 & 0.361537984 & 0.060256331 & 33.77470726 & \(4.77\times 10^{-21}\) \\  & Area & 15 & 2.021735304 & 0.134782354 & 75.54782186 & \(3.09\times 10^{-44}\) \\  & Error & 90 & 0.160566003 & 0.001784067 & & \\  & Total & 111 & 2.543839291 & & & \\ \cline{2-6}  & Method & 6 & 0.240735177 & 0.040122529 & 23.67341257 & \(1.00\times 10^{-14}\) \\  & Station & 11 & 0.318606133 & 0.028964194 & 17.08968306 & \(2.44\times 10^{-15}\) \\  & Error & 66 & 0.111859114 & 0.001694835 & & \\  & Total & 83 & 0.671200423 & & & \\ \hline \multirow{6}{*}{Tianan} & Method & 6 & 0.016672738 & 0.002778790 & 5.828486175 & \(3.64\times 10^{-5}\) \\  & Area & 15 & 0.411747878 & 0.027449859 & 57.57582978 & \(1.96\times 10^{-39}\) \\ \cline{1-1}  & Error & 90 & 0.042908409 & 0.000476760 & & \\ \cline{1-1}  & Total & 111 & 0.471329025 & & & \\ \cline{1-1} \cline{2-6}  & Method & 6 & 0.006929104 & 0.001154851 & 58.45235695 & \(1.66\times 10^{-24}\) \\ \cline{1-1}  & Station & 11 & 0.003567283 & 0.000324298 & 16.41425121 & \(6.22\times 10^{-15}\) \\ \cline{1-1}  & Error & 66 & 0.001303970 & \(1.98\times 10^{-5}\) & & \\ \cline{1-1}  & Total & 83 & 0.011800358 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Two-way ANOVA test for different methods and constraints towards unit PF performance.