###### Abstract  
Cesium is an open-source 3D virtual earth engine based on WebGL and one of the most widely used 3D GIS engines. The 3 DTiles rendering parameters in Cesium improve rendering efficiency but involve numerous data types and complex interdependencies, making simultaneous optimization challenging. In this paper, we proposed a multi-strategy probabilistic discrete differential evolution algorithm (MSPDDE) for finding the optimal values of the rendering parameters of Cesium 3 DTiles model, which increases the search space and improves the convergence speed by introducing multiple mutation strategies. These strategies effectively reduce the probability of falling into local optimality due to too many parameters and deal with discrete variables in the rendering parameters by applying a probabilistic discretization strategy to the discrete variables so that MSPDDE is able to find all the rendering parameter optima of Cesium 3 DTiles. Under three different sizes of 3 DTiles model cases, the rendering model time using the optimal parameter configurations found by the algorithm is reduced by 28.84%, 27.89%, and 13.32%, respectively, compared with the default parameter configurations of Cesium, which shortens the time of rendering 3 DTiles models by Cesium. mutation strategies pool; probabilistic discretization strategy; differential evolutionary algorithms; cesium 3 DTiles +
Footnote †: journal: Applied sciences  
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parameters of Cesium 3 DTiles, the existing studies can be classified into two categories: increasing the maximum screen space error and optimizing the 3 DTiles rendering strategy. [PERSON] [11] and [PERSON] [12] et al. successfully shortened the rendering time of the 3 DTiles model by increasing the maximum screen space error, but the increase in the maximum screen space error reduced the rendering time of the 3 DTiles model. However, increasing the maximum screen space error reduces the rendering quality of the model. Therefore, many scholars have chosen to reduce the rendering time by tuning the parameters to optimize the rendering strategy of 3 DTiles. [PERSON] et al. manually optimized three rendering parameters and summarized a progressive loading on demand strategy to realize the fast rendering of the overall scene of the 3 DTiles model [13]. [PERSON] et al. illustrated that when Cesium renders the 3 DTiles model, it can jump traverse the tiles with a screen error that is smaller than the base screen space error until it finds the tile with a screen error that is smaller than the maximum screen space error. They pointed out that the value of base screen space error can be adjusted according to the 3 DTiles model, which can effectively reduce the amount of data and rendering time [14]. Both parameter optimization methods use manual tuning, but the manual tuning method is time-consuming and labor-intensive, and the optimization results are less accurate. Additionally, all current studies have only tuned a limited set of parameters and failed to account for the synergistic effects between them, and the optimization process overlooks the differences between parameter types. In this paper, in order to find the optimal values of rendering parameters of 3 DTiles model provided by Cesium, which is faced with the problems of many rendering parameters, both continuous and discrete variables, as well as the existence of constraints on the values and conditions of the parameters, we proposed a multi-strategy probabilistic discrete differential evolution algorithm (MSPDDE). This algorithm adopts multiple mutation strategies to make full use of the advantages of various mutation strategies, taking into account the quality of the solution and convergence speed and reducing the probability of the algorithm falling into local optimality due to the large number of rendering parameters.