# A Multi-Objective Approach for Optimizing Virtual Machine Placement Using ILP and Tabu Search
## 4 Simulation Setup and Results
### Performance Comparison  
Figures 5-7 provide a comparative analysis of the various VM hosting algorithms considered in this study, based on three key performance metrics. The figures respectively illustrate the percentage of VMs hosted, residual resource wastage, and total power consumption, offering insights into the algorithms' efficiency and scalability. \begin{table}
\begin{tabular}{c c c c} \hline
**VM Type** & **CPU (Cores)** & **RAM (GB)** & **Storage (GB)** \\ \hline S & 3 & 4 & 50 \\ \hline M & 4 & 8 & 100 \\ \hline L & 5 & 12 & 150 \\ \hline XL & 6 & 24 & 250 \\ \hline \end{tabular}
\end{table} 
Table 4: VM types and resource requirements. Figure 4: Distribution of VM sizes for various values of \(N\). Figure 5: Average percentage of hosted VMs. Figure 6: Average residual resource wastage. Figure 5 shows the percentage of VMs successfully hosted as VM requests increase. All algorithms host all VMs when \(N\) is below 140, except FFD and WF, which start rejecting requests at \(N=140\). As \(N\) grows, rejections increase, with MOILP and MOTS consistently outperforming others. Under heavy loads, MOTS nearly matches MOILP, with only a 0.25% difference. Compared to MOACO and MOGA, MOTS achieves average gains of 2% and 3%, respectively, and performs significantly better than FF, FFD, and WF, hosting 11%, 32%, and 9% more VMs. FFD shows the poorest performance, especially at high \(N\). Figure 6 highlights average residual resource wastage as \(N\) increases. MOILP and MOTS demonstrate superior resource efficiency, especially at lower request levels, by hosting all VMs with minimal wastage. While MOACO and MOGA exhibit higher was due to less effective allocation, FF, FFD, and WF perform moderately but host fewer VMs. As \(N\) grows, MOILP and MOTS experience slightly increased wastage, reflecting their higher hosting rates. Overall, MOILP and MOTS are the most effective in reducing unused resources. Figure 7 depicts total power consumption across algorithms as \(N\) rises. MOILP and MOTS consume slightly more power due to their higher VM acceptance rates and associated CPU usage. Despite this, their energy efficiency stems from better resource utilization. In contrast, FF, FFD, and WF exhibit inefficient resource use, resulting in comparable or higher power consumption relative to MOILP and MOTS. MOTS consumes 1% more energy than MOACO, MOGA, and FF on average, with differences rising to 2% and 6% compared to WF and FFD, respectively, as the latter two accept fewer VMs. To summarize, MOILP and MOTS excel in resource utilization and energy efficiency due to their optimization techniques. MOILP leverages integer linear programming to achieve precise, globally optimized allocations, particularly effective under high demand. MOTS, with its TS heuristic, delivers near-optimal solutions quickly, making it ideal for large-scale scenarios. Both algorithms minimize resource wastage and prevent over-provisioning, leading to lower energy consumption. In contrast, MOACO and MOGA, while hosting fewer VMs than MOILP and MOTS, are less energy-efficient due to their heuristic nature, which can result in suboptimal allocations under heavy loads. Figure 7: Average total power consumption. In Figures 8-11, we present the average percentage of accepted VMs of types S, M, L, and XL, respectively, as a function of \(N\), for the various algorithms evaluated. The MOILP model and the MOTS algorithm achieve the highest acceptance rates for VMs of types S, M, and L, with nearly 100% acceptance for types S and M, even under a heavy load. However, as the number of VM requests increases, the acceptance rates for type L drop to 92% for MOILP and 82.5% for MOTS. Both MOILP and MOTS outperform the other algorithms in hosting VMs of types S, M, and L. In contrast, Figure 11 shows that MOILP and MOTS have the lowest acceptance rates for XL VMs. Specifically, the acceptance rate for XL VMs drops to 7.5% for MOILP and 15.5% for MOTS when \(N\) reaches 240.