## 4 Discussion
### Shield Tunneling Parameter Optimization Design Based on the Multi-Objective Optimization Algorithm  
The geometric parameters and geological conditions were fixed in the project discussed in this study. Therefore, optimizing tunneling parameters is essential to minimize subsequent soil layer disturbances and ensure safe shield tunneling operations. From the preceding analysis, the shield thrust, cutterhead torque, and tunneling speed were identified as the most influential and directly adjustable shield tunneling parameters affecting surface settlement. This selection was grounded in three engineering considerations: 1 Operational Adjustability: These parameters are directly controllable in real-time during tunneling (e.g., via shield hydraulic systems and cutterhead drives), unlike static factors like geological properties. 2 SHAP-Driven Criticality: As shown in Figure 15, shield thrust, cutterhead torque, and tunneling speed ranked highest in SHAP importance, collectively explaining >60% of settlement variance. 3 Practical Constraints: Thrust and torque are bounded by shield machine capacity (max thrust: 13,400 kN, max torque: 3531 kN\(\cdot\)m, as per Table 2), while tunneling speed is limited by soil stability--excessive rates risk face collapse in soft soils (e.g., silty clay). Balancing these constraints ensures feasibility. As a result, an improved Informer algorithm was employed as the objective function, and the above three parameters were selected as optimization variables.  
Surface settlement was used as the control objective to construct a multi-objective optimization algorithm for shield tunneling parameters. The problem was solved using the NSGA-III algorithm to obtain the optimized parameter set.  
The lower bound of the maximum surface settlement constraint was set as \(-10\) mm, and the range for the horizontal and vertical displacement objective functions for shield tunneling posture was set as \(20\) mm. The distribution range of the three tunneling parameter variables was optimized according to the 25 th and 75 th percentiles of the original dataset. Random sampling was employed for initial individual sampling. Specifically, the crossover and mutation probabilities were set as 0.85 and 0.45, respectively, and the maximum number of iterations was limited to 200.  
The computing process was evaluated using the convergence index, HV; the uniformity index, SP; and the diversity index, \(\Delta\)Line. As the number of iterations increased, HV initially rose and then stabilized, ultimately reaching 0.8940, indicating that the obtained solution set was of high quality. The SP value was 0.5761, suggesting that the solutions were relatively uniformly distributed in the objective space. There was no significant clustering or bias toward any single objective. The \(\Delta\)Line value of 0.2258 further confirmed the broad and diverse distribution of the solution set in the objective space, i.e., the solution set covers a wide range of potential solutions.  
The optimized parameter combinations are summarized in Table 8. Because there is no absolute superiority among the optimized parameters, the most suitable combination can be selected from the solution set according to specific project requirements to control shield tunneling effectively.  
Compared with the original tunneling parameters, the multi-objective optimized parameter combinations effectively controlled surface settlement. Comprehensive analysis of the optimized solution set revealed that, on average, the optimized tunneling parameters reduced surface settlement by 16.79%.