## 4 Simulation Result  
At this stage, we have set the temperature range for the thermal source layout design at [335 K, 350 K]. Simulation results indicate that the temperature range falls within [341.87 K, 345.89 K], meeting the design requirements. However, to further optimize the layout effectiveness, we will use the established automated optimization system to refine the experiential layout. After 40 rounds of iteration, the results of applying the automatic optimization system framework to MCM are presented based on the PCB board temperature extreme index and temperature uniformity index, as shown in Figure 8. Figure 8 displays the indices of all individuals in the 40 rounds of iteration and their exponential trend fitting, while the Figure 8 displays the same information. The exponential fitting results are shown in Formulas (2) and (3). The following results can be obtained: the temperature range of all solution sets is within [344.06 K, 346.05 K], and the temperature uniformity index is within [0.73 K, 3.93 K]. As the iterations progress, the fitness values of both indices show a continuous convergence trend, with the optimal temperature index reaching 344.06 K and the optimal uniformity index reaching 0.73 K.  
\[T_{max}:y=344.39e^{-4E-07x}\mathrm{R}^{2}=0.3318 \tag{5}\]  
\[T_{avg}:y=1.2878e^{-2E-04x}\mathrm{R}^{2}=0.3276 \tag{6}\]  
The solution to the MCM layout problem is a bi-objective optimization process, where the two indices are not independent but coupled, leading to a Pareto problem. In the IOF system, the 40 individuals generate a total of 2400 solution sets after 40 rounds of iteration. By correcting the solution sets with the constraint (8) and removing solutions that do not meet the constraints of the two indices, the Pareto front of MCM and the bi-objective Pareto feasible solutions are plotted, as shown in Figure 9,b. The Pareto front consists of seven selected optimal solution sets that meet the engineering application constraints, with the temperature index within [344.06 K, 344.17 K], and the uniformity index within [0.73 K, 0.88 K]. Figure 8: Optimization result: (**a**) optimization index \(\mathbf{T_{max}}\) iteration diagram; (**b**) optimization index \(\mathbf{T_{avg}}\) iteration diagram. The correctness of the optimization system's automatic writing of variables and its optimization results were verified by solving the transient temperature field using NS/SST with the optimal solution for the indicators. The comparison was made with the layout based on the empirical rule of placing high-power heat sources in edge positions. Three MCM layouts and the transient temperature cloud maps are shown in Figures 10 and 11. It can be observed from the figures that, when the indicators are optimal, the range of the PCB transient temperature field is [343.14 K, 344.09 K], with a temperature difference of 0.95 K. When the indicators are optimal, the range of the PCB transient temperature field is [343.39 K, 344.21 K], with a temperature difference of 0.82 K. In the case of an empirical layout, the range of the PCB transient temperature field is [341.87 K, 345.89 K], with a temperature difference of 4.02 K.  
Compared to the empirical layout, the temperature difference for the indicators decreased by 76.36% and the temperature difference for the indicators decreased by 79.60%. It can be seen that the system has a significant effect on improving the uniformity of the substrate temperature. Additionally, it is worth noting that we can observe a certain difference between the temperatures of the PCB substrate obtained by the simulation software when the indicators are optimal and when the Pareto optimal solutions are considered. This is because the temperature cloud maps obtained by the simulation software are transient, representing the temperature distribution at a specific moment, while the temperature indicators in the Pareto solution set are the average values of the PCB substrate temperature after it has stabilized.