## 1 Introduction  
The worldwide pandemic of the COVID-19 virus has forced people to change the way they live, socialize, and work. To maintain social distance, more human activities than ever have migrated online. In December 2021, [PERSON] et al. [1] estimated that approximately 56% of the U.S. workforce could move to online or remote work. McKinsey Consumer Pulse [2] demonstrates that the shares of e-commerce in the major countries increased at two to five times the rate before COVID-19. Compared to the pre-lockdown levels, the usage of Internet services increased from 40% to 100% [3]. The usage of video-conferencing services, such as Zoom, has increased ten times [4]. In addition, to contain the pandemic, massive amounts of residential and medical data were sent to data centers for analysis. For example, China uses health QR codes nationwide to monitor and manage population movements with big data. Behind these large-scale digital activities, the support of cloud computing data centers (CDCs) is inseparable. To meet the corresponding computing power needs, people have now embraced cloud computing in all aspects. With the explosive increase in the use of cloud computing, cloud service providers (CSPs) are also facing severe challenges in the management of CDCs. The problem mainly comes from two aspects: the cost of maintaining the operation of the CDC and the guarantee of Quality of Service (QoS) for users. With the surge in the number of users, to maintain the business needs of existing users and satisfy new users' experience of cloud services, CSPsmust increase investment in their CDCs. For example, SaaS service provider Salesforce increased the cost of its data center by 43% in 2022, which is USD 284 million, to meet higher customer service requirements [5]. Such a large financial investment is a great economic burden for the operation of an enterprise. Therefore, a feasible way to alleviate the economic pressure is to optimize the management of the CDC and improve the utilization of various computing resources in the CDC. The problem, however, brought about when resource utilization is improved is that the competition for different computing resources among the virtualized computing devices of users is enhanced. When the competition on the host with limited resources is intense to a certain extent, it will inevitably lead to a situation in which the user's QoS drops significantly. It can be said that there is a certain contradiction between reducing the operating cost of the CDC and ensuring the QoS of users. We need to design a feasible way to achieve the tradeoff between the two. Users run a wide variety of services in the CDC, and the corresponding virtual machine (VM) workloads are constantly changing due to the dynamic changes in services over time. During peak business hours, VMs have increased demands on computing resources such as CPU, memory, disk, and network. During periods of slack in business, the demand for these computing resources by VMs is also greatly reduced. To adapt to the dynamic changes of such workloads, the commonly used solution for managing hosts and VMs in CDCs is to perform server consolidation periodically [6]. By leveraging VM live migration, server consolidation migrates some VMs on hosts with high resource usage to other hosts with low resource usage to achieve load balancing in the CDC as much as possible. On the other hand, SLA is used to quantitatively describe the QoS for the use of VMs [7]. Hence, to ensure QoS, SLA needs to be taken into account to a certain extent when performing server consolidation. In general, a round of server consolidation is divided into three sub-steps to implement. The first is host workload detection, which picks out overloaded and underloaded hosts in the cluster. Next is VM selection for overloaded hosts. To achieve the goal of reducing the workload on these hosts and the occurrence of SLAV, suitable VMs need to be selected for migration.