## 3 Optimization of Alternator Heatsink
### Optimization  
In this section, the alternator heatsink was optimized with six different optimization algorithms and the optimization methods were compared. An objective surrogate model was developed by using the artificial neural network (ANN). Finally, the methods are compared both quantitatively and qualitatively. In Figure 11, the convergence curves of each optimization method run twenty times are given. When the curves are examined, it is seen that each method exhibits different characteristics. In general, it can be said that method 6 converges very quickly. While convergence occurred with a small change after approximately 50 iterations in the AOA, the initial values in the Aquila, AVOA, EO and PSO algorithms started from worse values in some runs. The GA started from the best point in all runs and converged very quickly. Optimization was performed on a computer with an AMD Ryzen 7 3750H processor, a Radeon Vega Mobile Gfx 2.30 GHz graphics card and 16 GB of RAM. In Figure 12, the convergence curves of the best objective function of each optimization are given. In the graph, the fastest convergence occurs in the AVOA, GA and PSO, followed by the EO with a very small delay. Although PSO converges very quickly, its optimum value is worse than other methods. Aquila and the AOA have good optimum values, although they converge somewhat late. Figure 11: Convergence curves of each optimization algorithm. In Table 4, the best value, mean value, standard deviation and total CPU time results obtained by running each optimization 20 times are presented. For the alternator heatsink optimization problem, the standard deviations of all optimization algorithms are very low, which shows that they converge to the same value every time. In terms of the best value, other methods except PSO gave the same optimum value. When the total CPU times were examined, the Aquila optimizer gave the longest time, followed by PSO. The remaining four methods gave very close times. Considering both speed and accuracy, the AOA, AVOA, EO and GA are the most suitable methods for the alternator heatsink optimization problem. In Table 5, the best values of each optimization and the results of the finite element analysis performed at these values are compared. According to the results, the largest relative error is 1.672%. Also, the largest relative error is 1.350% for the MATLAB Simulink model which was created by [PERSON]. A 10% error is an acceptable margin of error in engineering studies [36]. Thus, it can be said that the use of metamodels created by the ANN method in optimization gives results with sufficient accuracy. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Best Value** & **Mean Value** & **Worst Value** & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} &
\begin{tabular}{c} **Total CPU** \\ **Time** \\ \end{tabular} \\ \hline AOA & 728.902224 & 728.901906 & 728.900627 & \(4.20\times 10^{-4}\) & 00:43:19 \\ Aquila & 728.902226 & 728.902211 & 728.902135 & \(2.14\times 10^{-5}\) & 01:24:46 \\ AVOA & 728.902226 & 728.902226 & 728.902226 & \(0.00\times 10^{0}\) & 00:43:26 \\ EO & 728.902226 & 728.902226 & 728.902226 & \(0.00\times 10^{0}\) & 00:43:35 \\ GA & 728.902226 & 728.902225 & 728.902225 & \(2.87\times 10^{-7}\) & 00:43:33 \\ PSO & 728.467356 & 728.467356 & 728.467356 & \(1.17\times 10^{-13}\) & 00:47:01 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison of the optimization algorithms. Figure 12: Best convergence curve of each optimization.