### Establishment of Objective Function, Constraints, and Control Conditions
#### 2.1.1 Establishment of Objective Function of Optimization Model  
Using the objective function method, three objective functions are constructed, as shown in Equations (1) to (4):  
(1) Minimum total cost of dewatering  
The objective function is related to the number of wells and the pumping flow of the wells, and the pumping capacity and the number of pumping wells should be reasonably selected to ensure the lowest engineering cost.  
\[J_{1}=Z_{min}=\alpha_{1}\sum_{i=1}^{w}n_{i}+\alpha_{2}\sum_{i=1}^{w}q_{i}\ \ \ i=1,2,\ldots,w \tag{1}\]Among them, \(J_{1}\) is the minimum target of the total dewatering cost (\(Z_{min}\)); \(w\) is the total number of pumping wells; \(n_{i}\) is a binary variable, indicating whether the \(i\)-th well is in operation, with a value of 1 indicating operation and 0 indicating no operation; \(q_{i}\) is the flow of the \(i\)-th pumping well, m\({}^{3}\)/d; \(\alpha_{1}\) is the construction cost of the pumping well; \(\alpha_{2}\) is the cost per unit of pumping capacity; and \(\alpha_{1}\) and \(\alpha_{2}\) are different coefficients related to local market economic conditions.  
The minimum amount of land subsidence caused by dewatering  
Considering the influence of dewatering on the premise of meeting the allowable settlement value, it is required that the settlement of important building settlement control points should be the minimum; that is, the settlement influence coefficient should be the minimum. The settlement influence coefficient before optimization is 1, the optimization model can continuously reduce the amount of land subsidence, and the settlement influence coefficient decreases from 1.  
\[J_{2}=\left[C\right]_{min}=\frac{\sum_{g=1}^{n_{g}}\left[s\right]_{g}}{\sum_{g =1}^{n_{g}}\left[s\right]_{y}}\ \ g=1,2,\ldots,n_{g} \tag{2}\]  
Among them, \(J_{2}\) is the goal of minimizing the settlement influence coefficient ( \(\left[C\right]_{min}\)); \(n_{g}\) is the total number of settlement control points; \(\left[s\right]_{y}\) is the total allowable settlement, mm; and \(\left[s\right]_{g}\) is the optimized settlement of the \(g\)-th settlement control point, mm.  
The maximum drawdown of the water level in the center of the foundation pit  
When implementing the foundation pit dewatering, it is necessary to reduce the groundwater level as much as possible to ensure the safety of the foundation pit structure, but at the same time, it is necessary to ensure that the hydraulic gradient at the bottom of the pit is within the safe allowable range.  
\[H^{2}-h_{j}^{2}=\left(2H-S_{j}\right)S_{j}=\sum_{i=1}^{n_{g}}\frac{q_{i}}{\pi K }\ln\frac{R_{i}}{r_{ji}}j=1,2,\ldots,n_{j} \tag{3}\]  
\[J_{3}=H_{max}=\sum_{j=1}^{n_{j}}\frac{H-h_{j}}{n_{j}}\ \ \ j=1,2,\ldots,n_{j} \tag{4}\]  
Among them, \(H\) is the initial water level value of aquifer, m; \(h_{j}\) is the water level value of the \(j\)-th water level control point after pumping, m; \(S_{j}\) is the water level drawdown value at control point \(j\), m; \(n_{w}\) is the number of pumping wells; \(q_{i}\) is the flow rate of the \(i\)-th pumping well, m\({}^{3}\)/d; \(n_{j}\) is the number of water level control points; \(R_{i}\) is the influence radius of the pumping well, m; \(r_{ji}\) is the distance from the \(i\)-th well to the \(j\)-th water level control point, m; \(K\) is the permeability coefficient, m/d; \(J_{3}\) is the maximum target of groundwater drawdown at the center of the foundation pit (\(H_{max}\)), m.