# Supply-Demand Dynamic Matching in Cloud Manufacturing Based on Hypernetwork Model
## 4 Dynamic Matching Method
### Specific Mechanism of Rematching
To mitigate the impact of the inherent randomness in the multi-objective optimisation algorithm, each set of parameter samples was repeated 20 times, and the representative solution from the overall Pareto front was taken as the result for analysis. To quickly identify the key parameters that have the most significant impact on the model output, a local sensitivity analysis was first performed for each parameter indi

Figure 7: Comparison of methods with and without considering network resilience. (**a**) The comparison of average clustering coefficient. (**b**) The comparison of load balance. vidually. In this process, only one parameter's value was changed at a time, while the others remained at their default values, and the resulting changes in the objective functions \((U_{1},U_{2})\) were observed to assess the influence of each parameter on the model output [48]. Based on these findings, a global sensitivity analysis was then carried out to explore the main effects and interaction effects of the key parameters, providing a deeper understanding of the most critical parameters in the model and offering more precise requirements for the accuracy of real-time data collection in actual cloud manufacturing systems. 1. Local sensitivity analysis

A preliminary screening of the ten parameters was conducted, and a set of parameter samples was generated within the specified ranges. Each parameter was then perturbed by \(\pm 10\%\) based on the sample values, and the results of the two perturbations were recorded. Table 5 presents the outcomes of these two perturbations for all ten parameters, along with their sensitivity coefficients. From the results in the table, it can be observed that slight adjustments to some parameters lead to negative impacts on the output, indicated by negative sensitivity coefficients. A positive sensitivity coefficient suggests that the parameter has a beneficial effect on the model. Among these, the \(Et_{S}\) parameter shows some contradictory results in terms of the direction of impact on the \(U1\) objective after the two perturbations, which might be attributed to the inherent randomness of the algorithm. The sensitivity coefficient is calculated as in Equation (41). \[S1=\frac{\Delta U_{1}\%}{\Delta X\%},\hskip 14.226378 ptS2=\frac{\Delta U_{2} \%}{\Delta X\%}, \tag{41}\]

where \(S1\) and \(S2\) represent the sensitivity coefficients of parameter \(X\) to \(U_{1}\) and \(U_{2}\), respectively. \(\Delta U_{1}\%\) and \(\Delta U_{2}\%\) represent the change amplitude of \(U_{1}\) and \(U_{2}\), respectively, and \(\Delta X\%\) represents the disturbance amplitude of the parameters. The comprehensive sensitivity coefficient was obtained by summing the sensitivity coefficients from the two perturbations and then ranking them. As shown in Figure 8, it is evident that changes to the \(C_{T}\) and \(B_{T}\) parameters have a significant impact on the results, while adjustments related to time and reliability have a relatively low sensitivity in the model. Based on the local sensitivity analysis, the top three parameters were initially selected as the key influencing factors of the model, and these were carried forward into the next step for global sensitivity analysis. Figure 8: Ranking of the sensitivity coefficients of the parameters. (2) Global sensitivity analysis

Based on the preliminary screening results, we selected the three key parameters (\(C_{T}\), \(B_{T}\), and \(C_{S}\)) with the greatest impact on the objective function and conducted a global sensitivity analysis. Parameter combinations were generated through sampling using the SALib library, and the Sobol method [49] was employed to quantify the influence of each parameter and their interactions on the model output. Random sampling was performed for the key parameters within their distribution ranges. Due to resource limitations, 200 sample sets were generated, and multiple experiments were conducted using the Monte Carlo simulation idea.