## 6 Conclusions  
In previous studies on slope displacement, many algorithms have been applied to engineering examples. However, most of these algorithms suffer from defects such as slow convergence speed and low convergence accuracy. To optimize the performance of the algorithms, this paper introduces adaptive weight factors and irrational escape strategies to optimize the sparrow search algorithm, thus improving the convergence speed and accuracy. The IESSA algorithm is then applied to function verification and engineering examples, leading to the following conclusions:  
1. In function verification, the IESSA algorithm performs well in 30 tests of nine benchmark functions, with eight best means and seven smallest standard deviations compared to GWO, SSA, PSO, and CSSOA. In three low-dimensional functions, it has the two best means and the two smallest variances. The root mean square error is the smallest, and the fit is closer to one, indicating that the IESSA algorithm has high accuracy and stability;
2. In contrast, the SSA, GWO, PSO, and CSSOA algorithms are prone to fall into local optimal solutions during the iterative process of function verification, making it difficult to perform a global search. The IESSA algorithm proposed in this paper can jump out of the local optimal solution. The iterative adaptation change curve shows that the convergence speed of the IESSA algorithm is much better than the other four algorithms, thus improving the efficiency of function computation;
3. In terms of engineering examples, this paper selects five years of rainfall, water level, and slope displacement data of two new beach slopes--xtGXT1 and xtGXT3--and applies the IESSA algorithm to obtain the slope displacement prediction. The comparison curves show that the IESSA algorithm outperforms the other four algorithms in terms of prediction accuracy. Its root mean square error is the smallest, and the fit is closer to one, indicating the feasibility and accuracy of the IESSA algorithm in engineering examples;
4. Considering factors such as convergence accuracy and speed, a comprehensive ranking of the four algorithms has been formulated and presented in the accompanying table. In the Friedman ranking test, the IESSA-LSSVM algorithm showcased distinctiveness from the remaining algorithms, with a figure exceeding 20 and a standard deviation of 3.18, which was the smallest. In the Nemenyi test, where pairwise comparisons were conducted, the significance of IESSA-LSSVM became even more pronounced. When incorporating convergence speed and accuracy into the assessment, the algorithms can be ranked in the following order: IESSA-LSSVM > GWO-LSSVM > SSA-LSSVM > LSSVM. Overall, the application of IESSA in slope displacement prediction is still at the preliminary exploration stage. More external factors need to be considered to test and optimize the algorithm to verify its feasibility in actual slope displacement prediction. **Author Contributions:** Conceptualization, G.S. and Y.L. ; Methodology, G.S. and Y.L. ; Software, G.S. ; Validation, G.S. ; Formal Analysis, G.S. ; Investigation, G.S. ; Resources, G.S. ; Data Curation, Y.L. ; Writing--Original Draft Preparation, G.S. ; Writing--Review and Editing, H.Y. ; Visualization, G.S. ; Supervision, H.Y. ; Project administration, H.Y. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. This dataset was provided by \"National Cryosphere Desert Data Center/National Service Center for Speciality Environmental Observation Stations\". Deformation monitoring data of Xin Tan landslide in Zigui County, Three Gorges reservoir area of Yangtze River from 2007 to 2012, are from the National Field Scientific Observation and Research Station of Yangtze River Three Gorges Landslide in Hubei, China. National Field Scientific Observation and Research Station. The authors would like to thank Three Gorges University for providing the data. No data are available to validate an optimization algorithm like IESSA-LSSVM.