## 5 Discussion
### Dynamic Adjustment Evaluation  
This section focuses on evaluating the results of the dynamic adjustment stage by measuring the variations in the value of objectives, with the initial and dynamic adjustment stages implemented with INSGA-II. For each tourist, three kinds of initial reference solutions (three-spot, four-spot, and five-spot routes) are selected from the final non-dominated solutions of initial routes, according to the tourist's needs (in Equation (24)). The initial reference solutions are used to access the dynamic adjustment stage proposed, which avoids overcrowded attractions by providing alternative attractions. Among these initial routes (including 20 three-spot routes, 20 four-spot routes, and 18 five-spot routes), the proposed method provides dynamic route adjustments for 8, 10, and 9 of them, respectively. The effect of the adjustment is measured by the relative change rate (\(RCR\)), which is calculated as follows:  
\[RCR=\frac{m_{adjusted}-m_{initial}}{|m_{initial}|}\times 100\% \tag{26}\]  
where \(m_{initial}\) and \(m_{adjusted}\) denote different metrics of the initial and adjusted reference routes, which include the real-time crowding objective, value objective, distance objective, and total time spent. The adjustment strategy aims to avoid the sudden increase in crowding while minimizing the three objectives; thus, the reduction of the objective values (reflected with negative \(RCR\)) is expected. Figure 14 shows the \(RCR\) of route adjustment for all tourists. It can be seen that the adjustment achieves avoiding the sudden crowding increase and reduces the  
Figure 13: The comparison of average, maximum and minimum DRP value for 20 different tourists (INSGA-II, NSGA-II, MOPSO, MOACO, and WSM). \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Method**} & **Frequency of Lowest** & **Frequency of the Minimum** \\  & **Average DRP** & **DRP** \\ \hline INSGA-II & 14 (70\%) & 19 (95\%) \\ NSGA-II & 4 (20\%) & 4 (20\%) \\ MOPSO & 1 (5\%) & 0 (0\%) \\ MOACO & 1 (5\%) & 1 (5\%) \\ WSM & 0 (0\%) & 0 (0\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The frequency of lowest average DRP and minimum DRP in 20 tourists by INSGA-II, NSGA-II, MOPSO, MOACO, WSM. objective of real-time crowding (calculated with the real-time crowd flow indicators on 4 October) at the price of the increase in other objectives. Considering the crowd-avoiding goal in this paper, if this price is within the tolerable range, the goal of dynamic adjustment of the route is achieved. In Table 6, further statistical results are analyzed with Figure 14. After the adjustment, 85.19% of the adjusted routes have a reduction in the real-time crowding, while 85.19% of them increase in the value objective, which indicates that the adjustment is implemented at the expense of the value objective in most cases. Surprisingly, the distance and total time spent decreased in most cases. In terms of \(RCR\), the dynamic adjustment results in an average reduction of 7% in the crowding, with an average reduction of 7.95% and 6.74% in the distance and total time and an average increase of 10.87% in the value objective. Therefore, it can be concluded that the obtained value is mainly affected by the dynamic adjustments. Overall, the route adjustment in this paper achieves the purpose of avoiding crowds and providing real-time guidance and adjustment at an acceptable price. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Metrics**} & **Count of Reduced** & **Count of Increased** & **Average RCR** \\  & **Cases** & **Cases** & **Average RCR** \\ \hline Real-time crowding & 23 (85.19\%) & 4 (14.81\%) & \(-\)7.00\% \\ Value objective & 4 (14.81\%) & 23 (85.19\%) & 10.87\% \\ Distance objective & 20 (74.07\%) & 7 (25.93\%) & \(-\)7.95\% \\ Total time & 23 (85.19\%) & 4 (14.81\%) & \(-\)6.74\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The RCR of four metrics after the adjustment.