## 5 Simulation
### HS Parameter Tuning Using Adaptive HS  
An experiment was conducted to determine the optimal parameters for the HS for comparison with existing studies. We compared the optimal parameter results with the traditional HS and adaptive HS, which changes the parameters dynamically. The original HS used the parameters of the best and worst results as the basis. The Bitbrain dataset used in the simulation is the actual DC operation environment data without considering VM consolidation. The nature of this data showed that VM migrations occur more at the beginning than towards the end of the simulation. Comparative experiments to find the optimal parameters for the HS and adaptive HS compared VM placement results based on the PM-VM assignment at the beginning of the simulation, and the iterations were performed a total of 30 times for 10,000 times each.  
For the original HS, the HMCR was set between 0.5 and 0.9 and PAR was set between 0.3 and 0.7. The parameter values with the best experimental result were 0.9 for the HMCR and 0.5 for the PAR. The parameter values with the worst experimental results were 0.5 for the HMCR and 0.6 for the PAR. Experimental results for each parameter combination; the high values of the HMCR showed better results than the low values. This can be interpreted as generating meaningful solutions (MC) referring to the previous solution obtaining better results than generating solutions randomly. However, the PAR showed a tendency for better results with values in the middle of the range, but not proportional to the parameter values. This can be interpreted as a non-excessive and appropriate neighborhood solution search that is effective for finding better solutions.  
The results of the original and adaptive HS were then compared. For the adaptive HS, the worst and best values of the original HS were set as the upper/lower limits of the dynamically changing parameter from start to end of the experiment. The experimental results in Figure 7 and Table 4 show that each average value of the adaptive HS result was better than the worst result of the original HS, and the best result was the average value of the NS-HS. Based on the average values, the adaptive HS algorithms showing better results than the original were NS-HS and PSF-HS.  
Based on the best results, all the adaptive HS algorithms showed better results than the original HS. Figure 8 shows the graph of the solution search process for each algorithm based on the worst result. From the point of view of hill climbing, which aims to create significant neighborhood solutions to obtain the global optimum, an algorithm can be evaluated with good quality using the numbers of the solution improvement frequencies. Adaptive HS seeks diversity through a wide solution search area at the beginning and reduces the search area to obtain the optimal solution. Experimental result show that the solution improved at the beginning of the algorithm, but the solution did not improve towards the end for the original HS. However, the adaptive HS showed that the solution improved even towards the end. Accordingly, the adaptive HS is an efficient algorithm to determine the optimal solution in terms of exploration and results.  
Figure 8: Comparison of improvements in HS and adaptive HS by iteration.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & **Mean** & **Worst** & **Best** & **Std Dev.** \\ \hline Original HS (Best) & 0.503383 & 0.740271 & 0.236577 & 0.144973 \\ Original HS (Worst) & 0.640093 & 0.889 & 0.337712 & 0.180478 \\ PSF-HS & 0.345021 & 0.557234 & 0.21522 & 0.087343 \\ NS-HS & 0.328725 & 0.540743 & 0.181 & 0.125616 \\ I-HS & 0.509136 & 0.771547 & 0.312424 & 0.132324 \\ PA-HS & 0.451241 & 0.620795 & 0.274073 & 0.103505 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparative experimental results for HS and adaptive HS.  
Figure 7: Comparative experimental results for original HS and adaptive HS.