# Supply-Demand Dynamic Matching in Cloud Manufacturing Based on Hypernetwork Model
## 4 Dynamic Matching Method
### Specific Mechanism of Rematching
Figure 3: The evolution of the non-dominated solutions. #### 5.2.2 The Superiority of the NSGA-II Algorithm for SDM Problem

In the previous subsection, we validated that the NSGA-II algorithm exhibits good convergence performance in solving SDM problems. In this subsection, we further compare NSGA-II with other multi-objective optimisation algorithms, focusing on the performance of NSGA-II, MOEA/D, and MOPSO [47] in addressing SDM problem. Specifically, we compare the Pareto solution sets obtained from three algorithms with 400 iterations in the scenario of 60 task nodes and 100 service nodes, with the results illustrated in Figure 5.

The figure clearly demonstrates that the Pareto solutions generated by the NSGA-II algorithm are closer to the Pareto front than those of the MOPSO and MOEA/D algorithms. However, it is worth noting that when the number of Pareto solutions is similar, the Pareto solutions generated by the MOEA/D algorithm may be more uniform and concentrated. #### 5.2.3 The Adaptability of Matching Method Considering Network Resilience

In this section, we conduct repeated experiments and perform statistical analysis on the rematching schemes output at the final matching time \(t=50\). We compare the performance of the new schemes generated by two matching methods with and without considering the network resilience, where scheme generation without considering network is similar to that in [27]. In 30 repeated experiments, we compared the fault recovery time, operational utility, network connectivity, and load balance of the adjustment schemes of the two methods. We conducted statistical significance tests on the data collected from these repeated experiments in different scenarios. Table 4 presents the specific data for the rematching schemes under dynamic event disturbances for two matching methods across four scenarios. The method that does not consider network resilience is called the operation-only method, with the corresponding data listed under 'OPE' in the table. The method that considers network resilience is called the operation and network resilience method; the data are organised under the 'OPE-NR' column. Based on the data presented in the table, for all metrics, including recovery time, operational utility, clustering coefficient, and load balance, the \(p\)-values of two methods are both significantly less than 0.05. This indicates that there are significant differences between the two methods in these four metrics. Figure 5: Comparison of multi-objective algorithms. Meanwhile, we compared the effectiveness of the adjustment schemes obtained from two methods under different task service proportions, as shown in Figures 6 and 7. According to Figure 6a, it is evident that, regardless of whether service resources are abundant or scarce, the 'network' sample has a lower system recovery time during dynamic events compared to the 'operate'. This suggests that the method considering network resilience produces an initial scheme that can more rapidly achieve rematching solutions in response to market fluctuations, thereby restoring normal operations more quickly. In larger-scale manufacturing matches, this advantage in recovery time may become even more pronounced. The overall operational utility of the matching scheme obtained through adjustment is depicted in Figure 6b. It is obvious that in most cases, the rematching scheme considering the network has higher operational utility. This indicates that the matching method proposed in this paper can achieve better cooperation between consumers and service providers in dynamic environments. Upon analysing Figure 7a, it is evident that the 'network' samples have larger average clustering coefficients. This suggests that the scheme is considering the network resilience