## 3 Experiments
### Result and Discussion  
Based on the U.S. regional datasets, we set the cost of each view image to be the same (i.e., \(c_{j}=1\)), resulting in a cost of 1786 for the pre-screening data. The optimal solution cost of Experiment A is 340, and the result is the same every time. When Experiment C also uses the same column pruning process as Experiment B, the minimum cost is 299, which takes 3497.77 s. From Table 3, the column pruning process of Experiment C consumes about 80.89% of the time. After we completely deleted this process, the minimum cost is 315, which takes 1647.24 s. If we only perform column pruning after constructing the initial population, we obtain the minimum cost of 307, which takes 2007.69 s, where the column pruning process consumes 15.38% of the time. From the above experimental results, we can see that column pruning operation is crucial to the optimization of the algorithm. However, considering the influence of time, we choose to carry out the column pruning operation only after generating the initial population, at which time the experimental optimal result is 307, which is reduced by 8-22 compared to Experiment B, and the time consumed is significantly reduced, which is exactly what was adopted for Experiment C recorded in Table 4.  
The running results of Experiment BCD are shown in Table 4. We choose the convergence algebra and optimal solution cost in Experiment B and Experiment C to plot the scatter plot. As shown in Figure 5, the initial population constructed by the tent chaotic map has a richer diversity and more uniform distribution, i.e., it is easier to escape from the local optimum, and at the same time, it has a better optimization performance. In Experiment D, we obtain a minimum cost of 300, which takes 1821.54 s. We plotted a 3D surface map based on the different parameter settings of Experiment BCD, with each parameter combination corresponding to a surface, as shown in Figure 6. It can be seen that the experimental results of the improved algorithm are better. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experimental Group** & **Greedy Algorithm** & **Tent Chaotic Map** & **Column Pruning** & **DE Algorithm** \\ \hline Experiment A & ✓ & & & \\ Experiment B & ✓ & & ✓ & \\ Experiment C & & ✓ & ✓ & \\ Experiment D & & ✓ & ✓ & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Implementation of key experimental steps (�means that the experimental group contains the step). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Step** & **Local Search** & **Charge and Force Calculation** & **Move the Particle** & **Column Pruning** \\ \hline Proportion & 8.423\% & 0.093\% & 10.594\% & 80.89\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time proportion of each step in the algorithm (The experimental results of performing the column pruning operation every time a new solution is generated in Experiment C). To further explore the effect of population size on the experimental results, we increased the initial population number to 30, and chose the set of parameter configurations that contained the largest number of optimal solutions, i.e., we chose a pop value of 0.85 for the experiment. As shown in Table 5, when the initial population size is doubled, the minimum cost of 298 is obtained, which takes 4091.61 s. The cost of the optimal solution shows a decreasing trend in general, but the decrease is not significant, while at the same time, the corresponding running time increases significantly.