# Supply-Demand Dynamic Matching in Cloud Manufacturing Based on Hypernetwork Model
## 4 Dynamic Matching Method
### Specific Mechanism of Rematching
Specific parameter settings for the experiment are shown in Table 3.

The edges in the network are generated randomly, and when an edge exists, its attributes, such as \(w_{ii}^{S}\) and \(w_{jj}^{T}\), are also calculated by the node attributes. The hyperedges generation method between tasks and services is based on the degree distribution of nodes in the multilayer network, which results in some service nodes being connected to more task nodes, creating a certain difference in the distribution of connectivity. For \(t>0\), four dynamic events occur independently with a probability of \(p=0.2\) at any given time. Each event randomly selects 1 to 10 nodes for increase or decrease operations. This process continues until the matching process is complete. If a dynamic event occurs, it is necessary to determine whether the event disrupts the original matching scheme. If it does, the sets \(DELETE_{S1}\), \(DELETE_{T1}\), and \(ADD_{T1}\) are generated to store the disrupted nodes at time \(t\). Subsequently, the matching scheme is adjusted based on different situations. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values** \\ \hline Population size & 20 \\ Crossover rate & 0.7 \\ Mutation rate & 0.1 \\ Maximum iteration & 400 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Algorithm parameter setting. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values or Range** \\ \hline \(\gamma_{e}\), \(\gamma_{t}\) & \(0.1\), \(-0.1\) \\ \(\gamma_{c}\), \(\gamma_{q}\) & \(-1\), \(1\) \\ \(\omega_{C}\), \(\omega_{L}\) & \(1\), \(0.01\) \\ \(\omega_{\varepsilon}^{S}\): \(\omega_{t}^{S}\): \(\omega_{T}^{S}\) & 1:1:1 \\ \(\omega_{T}^{T}\): \(\omega_{t}^{T}\): \(\omega_{T}^{T}\) & 1:1:1 \\ \(E_{S}^{i}\), \(E_{T}^{j}\) & [3; 20] \\ \(S_{S}^{i}\), \(S_{T}^{i}\) & [1; 5] \\ \(C_{S}^{i}\) & [0.1, 1] \\ \(C_{T}^{j}\) & [10; 150] \\ \(B_{S}^{i}\) & [50; 200] \\ \(B_{T}^{i}\) & [10; 100] \\ \(\eta_{S}^{i}\), \(\eta_{T}^{j}\) & [3; 10] \\ \(Q_{S}^{i}\), \(Q_{T}^{j}\) & [5; 10] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experiment parameter setting. ### Results and Analysis

We conducted a series of experiments to validate the ability and robustness of the SDM method considering network resilience in dynamic interruption scenarios. #### 5.2.1 Effectiveness of the Initial Matching Method on the SDM Problem

In this subsection, we examine the performance of the NSGA-II algorithm for the SDM problem. We chose the scenario with 60 task nodes and 100 service nodes for the experimental demonstration. This setup represents a typical medium-scale SDM system. The evolution of the non-dominated solutions at the 50 th, 100 th, 200 th, 300 th, 400 th, and 500 th generations is illustrated in Figure 3, with different colours representing different generations. As depicted, the solution gradually converges to the Pareto optimal frontier in the course of evolution. At the same time, most of these Pareto frontier solutions distribute uniformly and have a good diversity in the evolutionary process. These results demonstrate the efficiency and effectiveness of the NSGA-II algorithm in obtaining Pareto non-dominated solutions for system selection when addressing the SDM problem. Based on the validation of effectiveness discussed above, we compared the initial matching performance after 400 generations across four different task service proportions, as depicted in Figure 4. The analysis reveals that the 'U1' value decreases as the number of task nodes increases. This decline is attributable to the increasing scarcity of service resources as the number of tasks grows. Consequently, resource allocation becomes uneven, with certain service nodes becoming overloaded, leading to imbalanced loads. In the scenario with 80 tasks and 100 services, the 'U1' value shows a more pronounced decline due to the tight service resources. In contrast, the utility value of 'U2' increases proportionally with the number of tasks. Figure 4: Comparison of initial matching performance in different scenarios.