## 7 Conclusions  
This study combined the complex network with multi-agent simulation to propose a new analysis method for the structural robustness and process robustness of the CMS. To target the frequent failure of resource nodes in the cloud manufacturing environment, three resource substitution strategies were proposed to better ensure the stability and robustness of the system. First, a multi-agent simulation model was constructed to study the dynamic process robustness of the CMS. Here, RoS was proposed as a robustness measure, and the behavior characteristics and modeling methods of several key types of CMP agents were detailed. Second, a complex network model of cloud manufacturing resources was established through the order-task relationship and task-resource relationship to study the static topological robustness of the CMS. Here, the maximum connectivity subgraph was proposed as a robustness measure. Regarding attack strategies, four failure modes (i.e., ID, IB, RD, and RB) were defined, and regarding robustness enhancement strategies, three resource substitution strategies (i.e., internal replacement, external replacement, and internal-external integration replacement) were proposed. Third, a case study of a cloud manufacturing project of a new energy vehicle was conducted. The results of this show that (1) the proposed RoS index was effective at portraying the variations of CMP robustness, (2) the three resource substitution strategies could improve both the structural robustness and process robustness of the CMS (with the internal-external integration strategy being most effective, followed by the external substitution strategy, and then the internal substitution strategy), and (3) the two node failure modes based on the recalculated topology were more destructive to the robustness of the CMP than the two node failure modes based on the initial topology. However, for all four failure modes, all three resource substitution strategies could protect the robustness of the CMS to some degree.  
In combining the complex network with multi-agent simulation, the robustness analysis object of the CMS is extended from the CMN to the CMP, which provides a new perspective with two dimensions (i.e., structure and process). Moreover, the three proposed recovery strategies (elastic measures) are designed based on the idea of adding redundant nodes, which is of great significance to the implementation and deployment of cloud manufacturing projects. This research will be furthered by investigating the robustness of cloud path interruption, cloud logistics interruption, city lockdowns, and other phenomena, to provide a quantitative and dynamic decision-making basis for improving the robustness of the CMS.  
Conceptualization, [PERSON] ([PERSON]); methodology, [PERSON] ([PERSON]).; software, [PERSON] ([PERSON]); formal analysis, [PERSON] ([PERSON]); investigation, [PERSON] ([PERSON]); resources, [PERSON] ([PERSON]); data curation, [PERSON] ([PERSON]) and Y.W.; writing--original draftpreparation, [PERSON] ([PERSON]); writing--review and editing, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); visualization, [PERSON] ([PERSON]) and Y.W.; supervision, [PERSON] ([PERSON]); project administration, [PERSON] ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China (No. 71871018).  
Not applicable.  
The used and analyzed datasets during the present study are available from the corresponding author on reasonable request.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.