## 5 Discussion  
In this paper, we proposed MSPDDE, a differential evolution algorithm suitable for finding the optimal values of the rendering parameters of the 3 DTiles model. The MSPDDE algorithm increases the search space and improves the convergence speed by constructing a pool of mutation strategies using multiple mutation strategies and, at the same time, handles the discrete variables in a probabilistic discretization strategy so that the algorithm has the capability of solving the constrained mixed-variable optimization problem and can thus accomplish the optimization of rendering parameters for 3 DTiles models. This article mainly conducted two experiments: performance evaluation and ablation experiments. The experimental conclusions are as follows:  
1. The effectiveness of the MSPDDE algorithm is evaluated by comparing the rendering times of three parameter configurations: the optimization results of the MSPDDE algorithm, the progressive loading on demand strategy parameter configuration, and the default parameter configuration of Cesium. The results show that the average reduction in the rendering time for the three cases using the MSPDDE algorithm's optimization results is 28.84%, 27.89%, and 13.32%. This suggests that the MSPDDE algorithm can be used as an effective method for optimization of rendering parameters for 3 DTiles models. 2. The results of the mutation strategy ablation experiments show that the mutation strategy pool significantly outperforms other mutation strategies in finding the optimal values of the rendering parameters of the 3 DTiles model. The reason is that the mutation strategies pool fully utilizes the advantages of DE/rand/k, DE/best/k (k = 1,2), which speeds up the convergence while guaranteeing the global search ability and reducing the probability of falling into local optimality. 3. The results of the discrete strategy ablation experiments show that the rendering time achieved by the probabilistic discretization strategy is 11.36% lower than that of  
Figure 5: Box plots of rendering time for Qishan Park cases under two discrete strategies optimization results. \begin{table}
\begin{tabular}{c c c c} \hline
**Discrete Strategy** & **_RT Max(s)_ & **_RT Min(s)_** & **_RT Average(s)_** \\ \hline rounding discretization strategy & 19.05 & 17.02 & 17.96 \\ probabilistic discretization strategy & 17.02 & 14.83 & 15.92 \\ \hline \end{tabular}
\end{table} 
Table 8: The rendering time of Qishan Park case under the optimization results of two discrete strategies. the rounding discretization strategy, which is explained by the fact that probabilistic discretization avoids the repair of illegal values of multiple mutant individuals to the same value, which prevents the mutation operation of the next generation from being blocked and the evolution stopping. The MSPDDE algorithm enables the automated optimization of Cesium 3 DTiles rendering parameters. Compared to the manual tuning approach used in current studies, it significantly reduces optimization costs, minimizes the risk of falling into local optimality, and enhances the accuracy of the optimization results. However, the research methodology proposed in this paper also has some shortcomings. Firstly, the MSPDDE algorithm requires using Cesium to render the 3 DTiles model for each fitness evaluation, which increases the time and resource consumption during the optimization process. To address this, future research could employ machine learning [34] or statistical models [35] to simulate the results of 3 DTiles rendering. Secondly, most of the Cesium 3 DTile rendering parameters have certain synergistic effects and mutual constraints, so all the parameters are optimized in this paper, which leads to the high dimensionality of the optimization problem in this paper. To solve this problem, the importance of parameters for rendering can be explored in the future.