## 4 Experiment and Results
### Algorithm Parameters  
Several parameters affect the performance of INSGA-II, including operational population size (\(P\)), archival population size (\(P_{A}\)), crossover probability (\(P_{c}\)), mutation probability (\(P_{m}\)), and maximum number of iterations (\(G\)). In this paper, the value of \(G\) is empirically set to 2000; \(P_{A}\) is a multiple of \(P\) set to ten times of \(P\). Eight sets of controlled trial experiments are designed to determine the appropriate values for the remaining parameters, including \(P\), \(P_{c}\), and \(P_{m}\). In Table 2, E1, E2, E3, and E4 are the experiments designed for the parameter \(P\), E2, E5, and E6 for parameter \(P_{c}\), and E2, E7, and E8 for parameter \(P_{m}\). Ten independent experiments are conducted for each set of parameters using the same dataset from Dalian.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment** & **P** & \(P_{c}\) & \(P_{m}\) \\ \hline E1 & 30 & 0.7 & 0.2 \\ E2 & 50 & 0.7 & 0.2 \\ E3 & 70 & 0.7 & 0.2 \\ E4 & 100 & 0.7 & 0.2 \\ E5 & 50 & 0.5 & 0.2 \\ E6 & 50 & 0.9 & 0.2 \\ E7 & 50 & 0.7 & 0.1 \\ E8 & 50 & 0.7 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Eight comparative experiments were performed to test the appropriate parameter.  
Figure 6: Derived results of crowd dynamics from tourism activity chains: (**a**) an example of tourism activity chain; (**b**) interaction network of attractions; (**c**) crowd flow indicator of attractions; (**d**) similarity of crowd structure of attractions.  
The algorithm's performance can be compared in terms of efficiency and effectiveness. Efficiency can be measured by the number of iterations and CPU time. For effectiveness, the algorithm can be evaluated using the hypervolume metric (\(HV\)), which can reassure convergence, distribution, and diversity of a solution set [62]. A larger value of HV indicates better performance.  
\[HV(X,P)=\bigcup_{x\in X}^{X}v(x,P) \tag{23}\]  
The comparison results of controlled trial experiments are shown in Figure 7. As \(P\) increases, the average number of iterations decreases. However, the average CPU time consumed for iterative convergence increases, which indicates that the increase in population size could significantly increase the computation time per generation. The mean HV value of E2 (\(P\) = 50) is significantly larger than that of E1 (\(P\) = 30) and E3 (\(P\) = 70) and slightly lower than that of E4 (\(P\) = 100). Considering the cost of calculation, it is more reasonable to set \(P\) to 50. For \(P_{c}\), E2 (\(P_{c}\) = 0.7) performs better than E5 (\(P_{c}\) = 0.5) for all three evaluations. Although E2 (\(P_{c}\) = 0.7) has a larger average number of convergent generations than E6 (\(P_{c}\) = 0.9), E2 (\(P_{c}\) = 0.7), it can reach convergence faster than E6 (\(P_{c}\) = 0.9). For \(P_{m}\), E2 (\(P_{m}\) = 0.2) is significantly more advantageous than E7 (\(P_{m}\) = 0.1) and E8 (\(P_{m}\) = 0.3). Therefore, considering the efficiency and effectiveness simultaneously, we set the parameters of our approach to the values listed in Table 3.  
Figure 7: Algorithm evaluation results under different parameters. The three vertical columns are the controlled trial experiments on different kinds of parameters, including \(P\), \(P_{c}\), and \(P_{m}\). The three horizontal rows demonstrate the indicators of the experiment results to evaluate the algorithm’s performance under different parameters, including average iteration times, average CPU time, and average HV.