## 5 Solving Pareto Optimal Solution Set and Analysis Decision
### Pareto Optimal Solution Set and Analysis of Running 26 Pumping Wells Schemes  
The multi-objective optimization model for foundation pit dewatering allows for the identification of Pareto optimal solutions and the generation of multiple dewatering schemes tailored to different objectives. The first working condition is set with 26 running wells, and the Gamultiobj program, based on the NSGA-II algorithm, is employed to obtain the Pareto optimal solution set and the operational status of the pumping wells. This information is depicted in Figure 5.  
It can be seen from Figure 5 that the optimization model maintains the running of all of the initial 26 pumping wells. After 30 iterations of the algorithm, the Pareto optimal solution set is obtained. The light green color ball in the solution set is the Pareto optimal solution. The red dot indicates the relationship between the total water inflow of the foundation pit and the settlement influence coefficient, the green dot indicates the relationship between the central water level drawdown of the foundation pit and the total water inflow, and the blue dot indicates the relationship between the central water level drawdown of the foundation pit and the settlement influence coefficient. Under the condition of meeting constraints and control conditions, the total water inflow ranges from 1.42 \(\times\) 10\({}^{5}\) to 1.56 \(\times\) 10\({}^{5}\) m\({}^{3}\)/d. The settlement influence coefficient is between 0.51 and 0.57, which is converted into the settlement value of 7.65-8.55 mm, which is less than the allow \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Foundation** & **K/(m/d)** & **Influence** & **\(\mathbf{q_{\text{max}}}\)/** **R/(m)** & **Number of** **Pumping Wells** & **Water Level Control Points** & **Settlement** **Total** **Q/(m\({}^{3}\)/d)** \\ \hline XZ0+326–XZ0+500 & 432 & 2242.5 & 6000 & 26 & 5 & 2 & 156,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculation parameters of initial design scheme. 15 mm. The drawdown of the water level in the center of the foundation pit is 0.2-10 m, meeting the drawdown requirements of more than 0 m. All Pareto solutions of 26 pumping wells under all running conditions are substituted into the dewatering multi-objective optimization evaluation system to calculate the evaluation score, which is arranged in descending order according to the weighted scores of the three objectives. The score results of Pareto solutions obtained by the scheme are shown in Table 5.  
It can be seen from Table 5 that the solutions in the Pareto optimal solution set are evaluated by AHP combined with the scoring method, and the Pareto solution with a high evaluation score is selected. So, the dewatering scheme with a weighted evaluation score of 90.545 is selected. The comparison of the optimization results of the three objectives is shown in Table 6, and the optimal results of decision variables are shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Schemes**} & \multirow{2}{*}{**Well Status**} & **Total Pumping** & **Settlement Value** & **The Distance Where Water Level in** \\  & & **Flow/(m\({}^{3}\)/d)** & **(mm)** & **the Center of the Foundation Pit Is** \\  & & & **Lower than the Bottom Plate/(m)** & **Gradient Value** \\ \hline Preliminary scheme & 26 wells in & 156,000 & \textless{}15 & \textgreater{}0 & \textless{}0.9 \\ The first optimized working condition & 26 wells in & 144,972 & 7.8 & 1.84 & 0.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Three objective optimization results of running 26 pumping wells. Figure 5: Pareto set distribution diagram and pumping well working state under the first optimized working condition.