## 1 Introduction  
Cloud computing is an elastic and scalable model of providing Information Technology (IT) services to consumers, where they can conveniently access resources, platforms, or software on demand [1]. It has become a critical computing paradigm in recent years because it offers virtualized resources, reduced capital outflow, and improved computing efficiency without revealing platform and implementation details [2]. As a result, cloud service providers can offer parallel computing resources and achieve large-scale storage at a relatively low cost [3]. The global cloud computing market has been steadily expanding since 2022, and cloud-based applications are gaining popularity. In the cloud environment, users are provided with cloud services based on their requirements. However, existing services often cannot fully satisfy users' needs, so composite services that combine several services are commonly used to provide value-added functionality. Service composition is a fundamental concept in the field of service-orientedcomputing. It involves the integration of multiple services to provide a comprehensive solution that meets the specific needs of customers [4]. These services may originate from a single provider or multiple providers. The purpose of service composition is to provide a more complete and personalized service to better meet the needs of the customers. In practice, service composition takes various forms that cater to different customer needs. For example, it may involve selecting and combining the most appropriate services to create a solution. Alternatively, it may entail providing customers with customized service packages or plans that correspond to their unique preferences and constraints. Personalized recommendation services based on data analytics and behavioral analysis are also becoming increasingly prevalent in modern service composition systems. With the rapid development of cloud computing, numerous cloud service providers offer many services with similar functions but different quality of service (QoS) attributes. QoS is a critical attribute in the service composition process, serving as a means to assess the quality of service delivery by service providers. Typically, QoS pertains to the non-functional attributes of a service, including latency, throughput, reliability, security, and availability, among others [2]. These metrics can accurately describe and measure a service's performance and ultimately impact the user experience. Therefore, selecting appropriate cloud services and combining them to meet users' QoS expectations, a process known as QoS-aware cloud service composition (QoS-CSC) [4], has become a significant issue for cloud service provision. Considering the significance and necessity of QoS attributes in multi-cloud service composition, it can provide users with more reliable and efficient services. By taking into account QoS attributes, service composition can provide better quality assurance and meet the users' needs, thus improving user satisfaction. QoS-CSC is a combinatorial optimization problem. However, due to fierce competition in the market, technical similarity, customer needs, and the growing number of similar cloud services, QoS-CSC has become an NP-hard problem. Over the past decade, QoS-CSC has become a crucial research topic in the academic community. In QoS-CSC, users' needs are broken down into multiple subtasks, and suitable cloud services are selected from the cloud service pool for each subtask. These services are then combined to create a composite service that meets users' needs while obtaining the optimal QoS value. However, finding an optimal cloud service composition has become particularly challenging with the proliferation of clouds, the entry of more service providers to the market, and the dynamic nature of multi-cloud environments that cause cloud services to change with time, season, or other complex factors.