## 2 Related Work  
VMP focuses on optimizing resource utilization while minimizing energy consumption through several scheduling algorithms. Efficient VM placement is central to managing virtualized environments, directly impacting energy usage and system performance. It compromises between high resource utilization, lower energy consumption, and better overall system performance. Research in the area continuously develops heuristics and metaheuristics to solve the complex problems of VMP. Over time, researchers have proposed adaptive models [8], approaches from graph theory [9], and communication-aware metaheuristic algorithms [10]. These techniques target energy savings in network traffic and resource optimization while considering SLAs, communication patterns, and traffic exchange between VMs. Among heuristic algorithms, Particle Swarm Optimization (PSO) has been applied to VMP, modeling each solution as a particle moving toward optimal placement by learning from local and global experiences. The enhancement of VM placement while taking into consideration energy consumption and network bandwidth has been the application of these techniques [11; 12; 13]. However, PSO alone can be ineffective for large-scale VM placement because it often converges prematurely to local optima and is highly sensitive to parameter settings, making it difficult to maintain robust performance as the problem size grows. Simulated Annealing (SA), another metaheuristic algorithm, originates from a similar technique in metallurgy. It allows for the acceptance of uphill moves on occasion. Therefore, it can explore the solution space freely so that it does not get trapped in local optima. Although effective, SA's inherently slow convergence limits its applicability in real-time decision-making environments [14; 15; 16]. This limits the use of SA in real-time situations where decisions need to be made quickly. Evolutionary algorithms like Genetic Algorithms (GAs) have also been widely explored. GAs mimic evolutionary processes, applying selection, crossover, and mutation to evolve optimal placement strategies. An improved cluster-based GA was suggested in [17], which aimed to reduce the number of active PMs needed for VM hosting by enhancing population clustering, achieving improved crossover performance and energy efficiency. Another advanced version, I-GA [18], integrated a virtual hierarchy architecture into the GA framework to decrease energy consumption and increase resource availability. The simulated results illustrated that the energy efficiency of the datacenter improved remarkably, while high availability was maintained compared with benchmark results from other VMP algorithms. However, GA approaches are often computationally expensive, limiting their use in real-time dynamic cloud environments. Multi-objective evolutionary algorithms have also been studied. [PERSON] et al. [19] applied NSGA-III for energy-efficient VMP in distributed clouds, minimizing resource wastage, power consumption, and network transmission delay simultaneously. Yet, evolutionary methods often suffer from long convergence times and require careful parameter tuning. ACO algorithms emerge as a strong alternative for optimizing VM placement. These algorithms are known for their efficient information exchange, adaptability, and ability to handle multiple objectives. Such characteristics make ACO well suited for the changing conditions of datacenter environments, where VM placement must be flexible. ACOalgorithms can optimize VM placement by considering several factors, including energy consumption, communication costs, and quality-of-service requirements. MoOuACO [20] applies multi-objective ACO to minimize unused resources and communication costs by co-locating cooperating VMs. The results show improvements in both communication costs and energy consumption.