## 4 Empirical Analysis
### Fitness Modeling Simulation Based on NK Model  
Based on the DEMATEL calculation results, using Equation (10) with \(\omega\) = 0.7, \(\xi\) = 3.4935, the top four key performance indicators in centrality values (\(R_{i}\)) from Table 6 are identified as key performance indicators, namely, \(X_{6}\) (construction and implementation of safety management systems), \(X_{1}\) (personnel safety awareness and attitude), \(X_{14}\) (quality and safety status of prefabricated components), and \(X_{12}\) (construction site working environment). By integrating the DEMATEL method with the NK model, the number of key indicators 4 (\(S\) = 4) is converted to the parameter of the NK model (\(N\) = 4). Retaining the rows and columns of the key indicators in the comprehensive relation matrix \(Q_{16\times 16}\), the comprehensive relation matrix for the key indicators \(C\) = \([c_{a\beta}]_{4\times 4}\) is obtained, as shown in Table 7.  
An analysis of Table 7 shows that by aggregating the row and column elements in \(C\) = \([c_{a\beta}]_{4\times 4}\) and using Equation (11), the fitness value when implementing key indicator \(X_{1}\) alone is \(E_{1}\) = \([C_{14}]\)/\([\sum C_{a\star}\) + \(\sum C_{a\beta}]\) = 0.6368/(5.3694 + 5.3694)= 0.1186. Similarly, the fitness values \(E_{a}\) for other key indicators when implemented alone can be calculated (see the seventh column of Table 7). When multiple key indicators are implemented in combination and all the key indicators are interrelated, \(K\) = 4 - 1 = 3. If there are two scenarios (0 or 1) for implementing or not implementing each of the four key indicators, a total of 16 possible combinations are formed. Using Equations (11) and (12), the overall fitness values \(F_{d}\) (\(F_{1}\)-\(F_{16}\)) for the 16 combinations are calculated, with the results shown in Table 8.  
Based on the analysis of Table 8, the interaction between \(X_{1}\) and \(X_{6}\) results in an allele combination of (1, 1, 0, 0). This is discussed in two scenarios: when \(X_{1}\) acts on \(X_{6}\), the fitness value \(d_{1}\) = \(E_{1}\)\(\times\)\(\epsilon_{12}\) + \(E_{1}\) = 0.1186 \(\times\) 0.2299 + 0.1186 = 0.1459; when \(X_{6}\) acts on \(X_{1}\), the fitness value \(d_{2}\) = \(E_{2}\)\(\times\)\(\epsilon_{21}\) + \(E_{2}\) = 0.1372 \(\times\) 0.2672 + 0.1372 = 0.1739. The overall fitness value \(F_{6}\) = \(d_{1}\) + \(d_{2}\) = 0.3197. By merging key indicators \(X_{1}\) and \(X_{6}\) on the \(X\)-axis, and \(X_{12}\) and \(X_{14}\) on the \(Y\)-axis, and representing \(F_{d}\) on the \(Z\)-axis, an adaptive three-dimensional landscape climbing schematic is constructed to simulate the selection process of the improvement path for prefabricated building construction safety performance, as shown in Figure 2.  
Analyses of Figure 2 and Table 8 indicate that the global path optimization always starts from (0, 0, 0, 0), with an initial overall fitness value \(F_{1}\) = 0. First step: In Figure 2a, there are four scenarios (\(F_{2}\) to \(F_{5}\)) for the individual implementation of key indicators \(X_{1}\), \(X_{6}\), \(X_{12}\), and \(X_{14}\). Implementing the allele combination (0, 1, 0, 0) for \(X_{6}\) results in the highest overall fitness value \(F_{3}\) = 0.1372. In Figure 2b, this is represented by path 1, climbing from position ((0,0), (0,0), 0.0000) to ((0,1), (0,0), 0.1372). Thus, the first step should select key indicator \(X_{6}\). Therefore, (0,1,0,0) is both the endpoint of the first step and the starting