## 3 Problem Formulation
### Energy Consumption Model  
In a multi-cloud environment, the energy consumption model is a crucial concept because the energy consumption of cloud services directly affects the overall operating costs and environmental issues, such as energy conservation and cloud platform emission reduction. We believe that the energy consumption of cloud services in a multi-cloud service composition is composed of two parts, the energy consumption generated by the execution of the cloud service itself and the energy consumption generated by file \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**QoS** & **Sequential** & **Parallel** & **Conditional** & **Loop** \\ \hline
**Cost** & \(\sum\limits_{i=1}^{n}cost_{i}\) & \(\sum\limits_{i=1}^{n}cost_{i}\) & \(\sum\limits_{i=1}^{n}prob_{i}\times cost_{i}\) & \(k\times cost_{i}\) \\
**Reliability** & \(\prod\limits_{i=1}^{n}rel_{i}\) & \(\min_{i=1}^{n}(rel_{i})\) & \(\sum\limits_{i=1}^{n}prob_{i}\times rel_{i}\) & \((rel_{i})^{k}\) \\
**Response time** & \(\sum\limits_{i=1}^{n}rt_{i}\) & \(\max_{i=1}^{n}(rt_{i})\) & \(\sum\limits_{i=1}^{n}prob_{i}\times rt_{i}\) & \(k\times rt_{i}\) \\
**Energy** & \(\sum\limits_{i=1}^{n}EC_{i}\) & \(\sum\limits_{i=1}^{n}EC_{i}\) & \(\sum\limits_{i=1}^{n}prob_{i}\times EC_{i}\) & \(k\times EC_{i}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The aggregation formula for QoS attributes based on different workflow patterns. \(n\) is the number of abstract services; \(k\) is the number of iterations, and \(prob\) is the conditional probability [25]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cloud** & & & **Cloud Services** \\ \hline \(cd_{1}\) & \(cs_{1,1^{\prime}}^{1},cs_{1,2^{\prime}}^{1},cs_{1,3}^{1}\) & \(cs_{2,1^{\prime}}^{1},cs_{2,2}^{1}\) & \(cs_{3,1^{\prime}}^{1},cs_{3,2^{\prime}}^{1},cs_{3,3^{\prime}}^{1},cs_{3,A}^{1}\) \\ \hline \(cd_{2}\) & \(cs_{1,1^{\prime}}^{2},cs_{1 transmission between cloud services [30; 49]. For any cloud service, its execution energy consumption can be calculated based on two parameters, execution time and energy consumption efficiency. The file transmission energy consumption between cloud services can be calculated based on the time required for the file transmission and the power required for transmitting files. Cloud services consume energy during execution. For example, some programs may frequently call hardware devices, such as network cards and disks, which result in additional energy consumption and burden. For the energy consumption of the \(i\)-th cloud service execution in a cloud service composition, we can define it as follows:  
\[EC_{i}^{exec}=t_{i}^{exec}\times EF_{i}^{exec} \tag{1}\]  
where \(EC_{i}^{exec}\) represents the energy consumption generated by the execution of the \(i\)-th cloud service in a cloud service composition; \(t_{i}^{exec}\) represents the execution time of the \(i\)-th cloud service, and \(EF_{i}^{exec}\) represents the efficiency of energy consumption during the execution of the \(i\)-th cloud service. We know that efficiency multiplied by time equals workload, so the execution time of a cloud service multiplied by its energy consumption efficiency equals the energy consumption generated during the execution of the cloud service. The problem of cloud service composition in a multi-cloud environment presents unique challenges, including an increase in data transfer and computation between cloud services compared to a single-cloud environment. In a multi-cloud environment, the additional expenses incurred by data transfer energy consumption can be attributed to the following three reasons:  
1. Different cloud services may be stored in distinct physical locations, necessitating data transfer operations when processing data;
2. In a multi-cloud environment, each cloud service may process a considerable amount of data, resulting in a significant amount of data transfer and network communication.