# Heuristic Global Optimization for Thermal Model Reduction and Correlation in Aerospace Applications
## 4 Results
### Heuristic Methods Benchmark Results
#### 4.3.1 Parameters Optimization Results
\begin{table}
\begin{tabular}{c l c c c c c c} \hline \hline \multicolumn{1}{c}{**Method**} & \multicolumn{1}{c}{**Parameters**} & \multicolumn{1}{c}{**Min**} & \multicolumn{1}{c}{**First**} & \multicolumn{1}{c}{**Average**} & \multicolumn{1}{c}{**Median**} & \multicolumn{1}{c}{**Third**} & \multicolumn{1}{c}{**Max**} \\ \hline \multirow{4}{*}{GA} & Population Size & 12 & 39 & 43 & 49 & 51 & 51 \\  & Crossover Rate & 0.690 & 0.754 & 0.778 & 0.781 & 0.799 & 0.864 \\  & Mutation Rate & 0.164 & 0.289 & 0.299 & 0.305 & 0.312 & 0.364 \\  & Mutation Magnitude & 0.352 & 0.502 & 0.582 & 0.575 & 0.610 & 0.977 \\ \hline MLR & Population Size & 25 & 31 & 38 & 41 & 43 & 46 \\ \hline \multirow{4}{*}{SA} & Initial Temperature & 101 & 433 & 428 & 494 & 506 & 510 \\  & Cooling Rate & 0.022 & 0.028 & 0.039 & 0.038 & 0.041 & 0.080 \\  & Min Temperature & 0.121 & 0.656 & 0.630 & 0.672 & 0.680 & 0.700 \\ \hline TS & Tabu Tenure & 11 & 48 & 49 & 54 & 55 & 57 \\ \hline Alienor & Subdivision Factor & 0.673 & 2.619 & 2.695 & 3.123 & 3.165 & 3.225 \\ \hline \multirow{4}{*}{Noising} & Population Size & 23 & 47 & 45 & 48 & 49 & 49 \\  & Noising Rate & 0.135 & 0.211 & 0.242 & 0.249 & 0.262 & 0.346 \\  & Noise Magnitude & 0.019 & 0.420 & 0.441 & 0.494 & 0.506 & 0.578 \\ \hline \multirow{4}{*}{CA} & Population Size & 14 & 48 & 49 & 55 & 55 & 55 \\  & Crossover Rate & 0.596 & 0.703 & 0.735 & 0.746 & 0.778 & 0.811 \\  & Mutation Rate & 0.190 & 0.254 & 0.271 & 0.258 & 0.265 & 0.477 \\  & Mutation Magnitude & 0.263 & 0.554 & 0.557 & 0.595 & 0.605 & 0.614 \\  & Cultural Population Size & 25 & 26 & 29 & 26 & 31 & 47 \\ \hline \multirow{4}{*}{PSO} & Population Size & 13 & 39 & 40 & 45 & 45 & 46 \\  & c1 & 1.077 & 1.127 & 1.243 & 1.135 & 1.383 & 1.859 \\  & c2 & 0.830 & 1.091 & 1.134 & 1.179 & 1.227 & 1.237 \\  & w & 0.417 & 0.686 & 0.686 & 0.698 & 0.706 & 0.800 \\ \hline \multirow{4}{*}{ACU} & Population Size & 10 & 21 & 21 & 23 & 23 & 23 \\  & Crossover Rate & 0.618 & 0.766 & 0.775 & 0.787 & 0.808 & 0.815 \\  & Mutation Rate & 0.077 & 0.182 & 0.183 & 0.201 & 0.208 & 0.258 \\  & Mutation Magnitude & 0.506 & 0.701 & 0.706 & 0.711 & 0.729 & 0.807 \\ \hline GRASP & Alpha & 0.171 & 0.424 & 0.458 & 0.489 & 0.531 & 0.559 \\ \hline \multirow{4}{*}{ACO} & Num Ants & 12 & 28 & 28 & 30 & 30 & 31 \\  & Evaporation Rate & 0.466 & 0.490 & 0.541 & 0.504 & 0.550 & 0.796 \\  & Alpha & 1.067 & 1.418 & 1.423 & 1.428 & 1.451 & 1.579 \\  & Beta & 0.784 & 2.881 & 2.817 & 2.948 & 2.966 & 3.529 \\ \hline \multirow{4}{*}{DE} & Population Size & 12 & 20 & 22 & 25 & 25 & 25 \\  & Mutation Factor & 0.428 & 0.624 & 0.643 & 0.646 & 0.682 & 0.820 \\  & Crossover Probability & 0.332 & 0.588 & 0.604 & 0.638 & 0.648 & 0.762 \\ \hline \multirow{4}{*}{AIS} & Population Size & 10 & 23 & 21 & 24 & 24 & 24 \\  & Clone Factor & 3.594 & 5.176 & 5.234 & 5.380 & 5.482 & 6.689 \\  & Mutation Rate & 0.215 & 0.220 & 0.268 & 0.257 & 0.273 & 0.442 \\  & Mutation Magnitude & 0.611 & 0.619 & 0.667 & 0.639 & 0.660 & 0.917 \\ \hline \multirow{4}{*}{HS} & Harmony Memory Size & 12 & 23 & 24 & 26 & 26 & 27 \\  & Harmony Memory Consideration Rate & 0.558 & 0.655 & 0.693 & 0.671 & 0.708 & 0.866 \\ \cline{1-1}  & Pitch Adjustment Rate & 0.155 & 0.232 & 0.274 & 0.297 & 0.302 & 0.390 \\ \cline{1-1}  & Harmony Memory Size & 12 & 23 & 24 & 26 & 26 & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._Next, Figure 9 shows the average time per generation/iteration for each method. The data indicate that some methods are faster than others (e.g., Simulated Annealing and Alienor). On average, each generation/iteration takes approximately 45 s when using the minimum parameter values from Table 7. If the maximum parameter values are used, the time per generation increases by roughly 2.5 times, reaching approximately 108 s. These differences can be significant in correlation processes that involve hundreds of generations or iterations. In addition to computation time, memory usage was also evaluated.