## 3 Methodology
### Simulation of Fitness Landscape Graph Based on NK Model  
By integrating the DEMATEL method with the NK model, key indicators are identified through centrality threshold values, constructing a fitness allele set for the key indicators, mapping them into three-dimensional space, and improving the selection of the optimal path for prefabricated building construction safety performance based on the simulation results. The main steps are as follows:  
(1) By setting a centrality threshold \(\xi\) to filter key indicators, the DEMATEL method and NK model can be integrated, converting the number of key indicators into the parameter \(N\) of the NK model. The calculation formula for \(\xi\) is as follows:  
\[\xi=\omega max\{W_{i}\}(i,j=1,2,\ldots,16) \tag{10}\]  
where \(\omega\) represents the maximum centrality percentage of the indicators, \(0<\omega\leq 1\), and the value of \(\omega\) depends on the historical experience of the project manager. A larger value of \(\omega\) indicates a higher centrality threshold \(\xi\) for extracting key indicators, resulting in fewer key indicators being ultimately extracted. (2) Quantify the safety performance improvement effect when implementing specific strategies individually. Retain the rows and columns of the key indicators \(X_{i}\) (\(i\) = 1, 2, \(\ldots\), 16) in the comprehensive relation matrix \(Q\) = \([q_{ij}]_{16\times 16}\) to obtain the comprehensive relation matrix \(C=[c_{\alpha\beta}]_{S\times S}\) for the key indicators, where \(\alpha\), \(\beta\)\(\in\)\(\{1,\,2,\,\ldots,\,S\}\). Aggregate the row and column elements of \(C=[c_{\alpha\beta}]_{S\times S}\) in the NK model to quantify the fitness value \(E_{\alpha}\) when implementing the key indicators individually [22]. The calculation formula for \(E_{\alpha}\) is as follows:  
\[E_{\alpha}=\frac{\left[\sum_{\alpha=1}^{S}c_{\alpha\beta}\right]_{\alpha\times 1 }}{\sum_{\alpha=1}^{S}c_{\alpha\beta}+\sum_{\beta=1}^{S}c_{\alpha\beta}}=\frac{ \left[C_{\alpha\right]}_{\alpha\times 1}}{\sum_{\alpha=1}^{S}c_{\alpha\beta}+\sum_{ \beta=1}^{S}c_{\alpha\beta}} \tag{11}\]  
(3) Quantify the safety performance improvement effect when implementing combination strategies comprehensively. In the NK model of \(C=[c_{\alpha\beta}]_{S\times S}\) (\(\alpha\), \(\beta\)\(\in\)\(\{1,\,2,\,\ldots,\,S\}\)), the interdependencies within the system are influenced by the interactions between the indicators. The fitness value \(d_{\alpha}\) of the key indicator combination strategy and the overall fitness value \(F\) can be quantified through the effect of the key indicator combination configuration. The calculation formulas for \(d_{\alpha}\) and \(F\) are shown in Equations (12) and (13):  
\[d_{\alpha}=E_{\alpha}+\sum_{\beta\in\{\beta|\zeta_{\beta}=1|\beta|\leq\mathrm{ k}\}}c_{\alpha}E_{\alpha},\alpha\
eq\beta \tag{12}\]  
\[F=\sum_{\alpha=1}^{S}d_{\alpha}\quad\quad\alpha,\beta\in\{1,2,\ldots,S\} \tag{13}\]  
For example, in the NK model [23], if there are four key indicators \(S\) = 4 and they all interact with each other, then \(N\) = 4 and \(K\) = 4 - 1 = 3. The fitness value when implementing the key indicator \(c_{1}\) individually is \(E_{1}=[c_{1}. ]/\left(\sum_{\alpha=1}^{A}c_{\alpha\beta}+\sum_{\beta=1}^{A}c_{ \alpha\beta}\right)\). The overall fitness value when \(c_{1}\) and \(c_{2}\) interact is as follows: when \(c_{1}\) acts on \(c_{2}\), the fitness value is \(d_{1}\) = \(E_{1\times}c_{12}+E_{1}\); when \(c_{2}\) acts on \(c_{1}\), the fitness value is \(d_{2}\) = \(E_{2\times}c_{21}+E_{2}\); and when \(c_{1}\) and \(c_{2}\) interact, the overall fitness value is \(F\) = \(d_{12}+d_{21}\). (4) In the NK model of \(C=[c_{\alpha\beta}]_{S\times S}\), if each key indicator makes a decision to implement or not (0 or 1), there are \(2^{S}\) configurations of 0 or 1 for the \(S\) key indicators.