## 3 Results Analysis and Discussion
### Example Verification
#### 3.1.3 Engineering Applications  
Since Model 2 considers the coupling relationship between the three objectives of optimizing construction-period-cost-quality, which is relatively close to the actual situation of the project, Model 2 was applied to a single project concerning a concrete-face rockfill dam in a water conservancy project for application analysis. The system design of the concrete-face rockfill dam project is shown in Figure 8.  
This single project included 11 operations, and the relevant parameters and data can be found in Table 4.  
The concrete-face rockfill dam project's construction-period-cost-quality comprehensive balanced optimization model was constructed by using the second method proposed in section \"Quality Objective Function\". The relevant parameters in the model were: \(\lambda=0.5\) indicates that the decision-makers have no preference; the penalty coefficient \(\alpha\) for the delay was set at US$1,212,121/month; the reward coefficient \(\beta\) for early completion was set as US$606,060/month; the indirect cost coefficient \(IC\) was set at US$757,575/month; the planned construction period \(D\) was 42 months; and the cost budget \(B\) was set at US$90,909,090. The project's quality had to be above good. The SPSS21.0 software was used for nonlinear regression data analysis, and the estimated values of the parameters were \(a=-0.783\), \(b=0.001\), \(c=-0.146\), \(d=e=0\), and \(f=91.917\). The model was solved through the MATLAB program and PSO. The parameters of PSO were: the population size \(m=20\); maximum evolutionary generation \(Gen=100\); inertia weight \(\omega\) decreases linearly from 0.9 to 0.4; \(c_{1}=c_{2}=2\); \(v_{max}=0.5\). The solution results are shown in Table 5.  
The concrete-face rockfill dam project was made up of 11 operations, with an average of 2.4 execution modes for each operation. Therefore, the feasible solution space was 2.41, that is, there were 15217 combination schemes with different values of construction-period-cost-quality. PSO was used to find eight non-dominant solutions in a large search space, allowing decision-makers to choose from a narrower range of options. The optimized construction period of the concrete-face rockfill dam project, as shown in Table 5, is between [32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43] months, which meets the control requirements of the planned construction period of 42 months. The optimized cost was between [US$82,469,400-89,581,440], which is less than the budgeted cost of US$90,909,090, and meets the cost control require  
Figure 8: Project network plan for a concrete-face rockfill dam. Legend: 1—left-bank slope excavation; 2—right-bank slope excavation; 3—viewbed excavation; 4—consolidation grouting; 5—curtain grouping; 6—anti-seepage wall construction; 7—dam-body filling; 8—panel pouring; 9—wave-break wall construction; 10—dam-crest construction; 11—tail processing, data sorting and acceptance. ments. The optimized quality level is between [0.8032-0.8796]. Referring to the operation quality standard in Table 1, the optimized quality in this example reaches a good level, which meets the requirements of the engineering quality standards. As a result, the optimized construction-period-cost-quality of the concrete face rockfill dam project meets the project's actual requirements. The scheme can be selected by the decision-makers based on the specific requirements of the project construction, to serve as a reference basis for the decision-makers to carry out project planning and scheduling.