# Task-Driven Virtual Machine Optimization Placement Model and Algorithm
## 5 Experiment Results and Analysis
### Evaluation of the CE-VMP Method
#### 5.4.2 Efficiency  
The CE-VMP method proposed in this study aimed to balance the interests of cloud service providers and users, considering the energy consumption of the cloud data center and the makespan and user rental costs. In most studies [7; 8; 9; 10], the makespan and user rental cost have not been considered as optimization objectives. In this study, the energy consumption, makespan, and user rental costs are compared to evaluate the efficiency of the presented CE-VMP method. Figure 6 depicts the experiment results on energy consumption of the proposed CE-VMP method and the other compared methods. As the number of tasks increases, the total active time of the VMs increases as the number of tasks undertaken by each VM increases. Meanwhile, PM resource utilization rises, leading to an increase in PM energy consumption  
Figure 5: Comparison of metrics. and total energy consumption. As can be seen from Figure 6, for instances \(T2,T3,\ldots,T12\), the CE-VMP method has the lowest EC value. This is because the CE-VMP considers EC as one of the optimization objectives, and it also takes into account the impact of task loading on VM placement, which results in tasks being loaded to VMs more efficiently, shortening the task scheduling time, and indirectly reducing the activity time of the PMs which in turn reduces EC. For \(T1\), when the number of tasks is small, the needed VMs are fewer, and the EC of the PM is relatively small, in this case, the optimization policy does not have a significant impact on the EC, resulting in an average performance of CE-VMP. The EEACS-VMP is the second best, as it considers each VM as an energy-consuming block, taking into account its individual energy requirements. EEACS-VMP ranks the PMs in descending order based on their energy efficiency and optimizes both server selection and pheromone updating rules within the ACS. Since the FFD-VMP places VMs in order of the size of their resource requirements, it does not take into account the optimization of EC and thus performs the worst. Figure 6: Comparison of EC. Typically, the better the convergence of an algorithm for solving the TLVMP problem, the closer the solution set generated by the algorithm is to the true Pareto front. This achieves the optimal balance between makespan, user rental costs, and the energy consumption of cloud data centers. To assess the effectiveness of the proposed CE-VMP method in terms of makespan and user rental costs, we evaluated it indirectly by comparing the convergence of the primary model-solving algorithms within the CE-VMP method. Here, five algorithms, OMOPSO [21], SMPSO [22], NSGA-III [23], F-NSGAIII [25] and FAME [26] are selected as model-solving algorithms within the CE-VMP method and are compared and evaluated against the CE-NSGAIII. Figures 7 and 8 presents the Pareto front experimental results of the six compared algorithms on 12 instances, covering the optimization results for the makespan, user rental costs, and cloud data center energy consumption. As depicted in Figure 7a,b, when the number of tasks is relatively small, the Pareto fronts of all methods are considerably close, with the CE-NSGAIII displaying only a slight advantage. As the number of tasks increases, the benefits of the CE-NSGAIII become more outperformed. This is because for intelligent optimization algorithms, when the number of tasks is high, the search space expands, requiring the algorithm to explore the possible solution space extensively. The proposed CE-NSGAIII casts the chaotic mapping mechanism, and the initial population it generates has high randomness and diversity, which is conducive to the global search of large-scale problems, and is not easy to fall into local optima prematurely; at the same time, the elite guidance strategy accelerates the search process of local optimal solutions. These factors help the CE-NSGAIII generate a better Pareto front, thereby allowing it to ensure a shorter makespan, lower user rental costs, and reduce the energy consumption of cloud data centers.