# Task-Driven Virtual Machine Optimization Placement Model and Algorithm
## 5 Experiment Results and Analysis
### The Effectiveness of the Presented CE-NSGAIII  
The effectiveness of the presented CE-NSGAIII is evaluated by using IGD and HV metrics. To assess the effectiveness of the improvements made to the NSGA-III, comparisons are made with the D-NSGAIII, which incorporates only adaptive crossover and mutation operations, and the D-E-NSGAIII, which includes both adaptive crossover and mutation operations and elite guidance.  
The results of the statistical tests on the IGD and HV values for the 12 instances (mean and standard deviation) are shown in Table 4, in which the compared algorithm obtaining the best performance is marked with dark gray shading and the second best is highlighted with light gray shading. Here, the Wilcoxon rank-sum test is adopted to compare the results at a significance level of 0.05. Symbols \"+\", \"\(-\)\" and \"\(\approx\)\" mean that the competing algorithm is significantly better than, significantly worse than, and statistically tied by CE-NSGAIII respectively.  
\begin{table}
\begin{tabular}{l l l l l l} \hline
**PM** & **CPU** & **MIPs** & **PE** & **Memory (GB)** & **Bandwidth (Mbps)** \\ \hline \multirow{2}{*}{PH1} & Intel Core 2 & \multirow{2}{*}{27079} & \multirow{2}{*}{2} & \multirow{2}{*}{24} & \multirow{2}{*}{20} \\  & Extreme X6800 & & & & \\ \multirow{2}{*}{PH2} & Intel Core i5-2500K & 83000 & 2 & 24 & 20 \\ \multirow{2}{*}{PH3} & Intel Core i7–920 & 82300 & 4 & 32 & 20 \\ \multirow{2}{*}{PH4} & Intel Core i7-875K & 92100 & 4 & 32 & 20 \\ \hline \end{tabular}
\end{table}
Table 2: The PM parameter settings.  
\begin{table}
\begin{tabular}{l l} \hline
**Parameters** & **Value Range** \\ \hline CPU (\(\times 10^{4}\) MIPS) & [2; 8] \\ Memory (GB) & [1; 4] \\ Bandwidth (Mbps) & [2; 10] \\ PE & [1; 4] \\ \hline \end{tabular}
\end{table}
Table 3: The VM parameter settings.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Instance** & \multicolumn{2}{c}{**ICD**} & \multicolumn{2}{c}{**DV**} & \multicolumn{2}{c}{**DV**} \\ \cline{2-7}  & **D-NSC4 AIII** & **D-L-N5 AIII** & **CI-N5 AIII** & **D-NSC4 AIII** & **CI-N5 AIII** \\ \hline T1(200 x8) & 1.04\(\times  
As presented in Table 4, the CE-NSGAIII exhibits the best overall performance in terms of the IGD and HV metrics. D-NSGAIII exhibits the worst performance, and D-E-NSGAIII is ranked second. This is because the CE-NSGAIII incorporates an elite guidance strategy that employs elite solutions to guide the entire population toward the Pareto front, thereby enhancing the algorithm's global search capability and improving the quality of the solutions. In addition, the chaotic mapping mechanism introduced in the CE-NSGAIII generates sequences with high randomness and ergodicity. This characteristic aids in the creation of a diverse initial population at the early stages of the algorithm [15]. The PBI distance is used to associate reference points and aids in fairly evaluating the crowding degree of individuals, thus better balancing convergence and diversity during the selection process. However, in smaller instances, the HV values of the CE-NSGAIII are slightly lower than those of the other two algorithms being compared. This is because the complex dynamic characteristics of chaotic mapping are not necessarily required for small-scale TLVMP problems and can even lead to reduced convergence owing to over exploration of the solution space.