## 4 Engineering Example Application  
### Hydrogeological Conditions of Xin Tan Landslide  
According to meteorological data, annual rainfall in the area of the Xin Tan landslide is relatively abundant, averaging up to 1016 mm. The maximum recorded annual average rainfall reached 1430 mm. The rainfall in the area is particularly abundant during the rainy season, averaging up to 2 mm. The maximum rainfall recorded during the rainy season reached 1107 mm. The rainy season is mainly concentrated between May and September.  
The Xin Tan landslide is located on the north bank of the Yangtze River, 26 km away from the Three Gorges Dam site. The body of the Xin Tan landslide is in the shape of a long tongue, the terrain is high in the north and low in the south, and it has a gentle slope inclined to the Yangtze River, with an overall slope degree of 23\({}^{\circ}\). The back edge is located at the foot of Guangjia Cliff, with an elevation of 910 m, and the front edge is located below the water level of 135 m, with a length of 1600 m in the north-south direction, a width of 500 m in the east-west direction, and an average thickness of about 30 m. The landslide surface is the contact surface between the accumulation body and the underlying bedrock. The lithology of the underlying bedrock is Silurian sand-mud shale.  
The steep terrain in the landslide area is primarily composed of the Yellow Cliff mountain. The exposed bedrock on the mountain consists mainly of Carboniferous diapiric tuff and Devonian sand and jade. Soluble rocks eroded by water become karst aquifers, while non-soluble rocks experience fissures due to tectonic geological actions, forming fissure aquifers. However, there are also insoluble rocks such as the Wujiaping Formation, Maanshan Section, and Silurian shale in the landslide area, creating a water barrier for the  
Figure 3: Comparison of iteration speed and accuracy of different algorithms. Unimodal test function: (a) F1, (b) F2, (c) F3. Multimodal test function: (d) F4, (e) F5, (f) F6. Fixed-dimension test functions: (g) F7, (h) F8, (i) F9.  
karst and fissure aquifers. Consequently, the groundwater in the aquifers lacks coherence. Moreover, due to the topographic control of the one-sided mountain, most of the surface water and groundwater can only flow into the river along the slope surface in a western direction after atmospheric rainfall reaches the surface. Only a small portion can penetrate into the slope body, resulting in limited recharge to the landslide.  
The material on the slope under the Jiangjia slope of the landslide consists mainly of crumbly stone and sandwiched soil formed by the avalanche slope deposit. This type of landslide body has high permeability due to its large porosity. It is widely distributed in the area, and its groundwater source mainly comes from the surface infiltration of atmospheric precipitation. It can also receive recharge from the surface and groundwater from the Huangyan mountain. Although the groundwater source in this area is relatively abundant, the slope body material is composed of gravel soil, which has a larger porosity for groundwater storage. Groundwater circulates through the pores in the slope body material, providing better drainage conditions. Consequently, groundwater does not accumulate significantly, with only a relatively small portion being stored in the grooves formed by impermeable rocks such as sand shale. Additionally, the flow of groundwater from the accumulation area to the river's front edge is relatively small during the dry season but increases during the rainy season.