# Heuristic Global Optimization for Thermal Model Reduction and Correlation in Aerospace Applications
## 3 Heuristic Methods on a Simple Thermal Model Reduction and Correlation
### Global Optimization Method Implementation  
To improve the thermal model correlation between the DTMM and RTMM, it is necessary to add adjustable variables\"KGL\" and \"KGR\", labelled as KGL\({}_{0,10}\), KGL\({}_{10,20}\), KGL\({}_{20,30}\), KGR\({}_{10}\), KGR\({}_{20}\), and KGR\({}_{30}\), which are incorporated into the RTMM, as illustrated in Figure 6.  
To optimize these \"KGL\" and \"KGR\" values for achieving the lowest possible FF, a heuristic global optimization method (as summarized in Table 5) must be implemented. By refining these parameters, the RTMM can be correlated more closely with the DTMM. The implementation of a global optimization method to optimize the \"KGL\" and \"KGR\" variables in RTMM--namely,  
\[\text{KGL}_{0,10},\quad\text{KGL}_{10,20},\quad\text{KGL}_{20,30},\quad\text{ KGR}_{10},\quad\text{KGR}_{20},\quad\text{and}\quad\text{KGR}_{30},\]  
is shown in Figure 6.  
Each heuristic global optimization methods listed in Table 5 to determine which approach is most effective for the Thermal Model Reduction and Correlation Process between DTMM and RTMM. However, before directly comparing these methods, we first need to adjust each method's configuration \"parameters\" (e.g., population size, mutation rate, initial temperature, cooling rate, etc.). To that end, we used a Genetic Algorithm to optimize the parameters of each method within a 20-generation loop, enabling stabilization of each method's configuration parameters and thereby making them comparable. In each iteration of this 20-generation loop, every method was run for 50 iterations/generations. Because running all methods for a large number of iterations is time-consuming, 20 iterations/generations was selected as the most balanced compromise. Consequently, each optimized algorithm was run for a total of 400 iterations/generations overall. However, several methods were excluded from this benchmark for the following reasons:  
1. Broyden: This method primarily depends on the \"tolerance\" and \"Max Iterations\" parameters. The \"tolerance\" was already set to a very low value (\(\sim\)10\({}^{-3}\)), which is not easily optimized. Additionally, \"Max Iterations\" must be set relatively high because the method requires initializing a Jacobian matrix, making it more difficult to compare  
Figure 6: RTMM with adjustable variables “KGL” and “KGR”—resistance network. with other methods. However, this method could be revised and implemented in later complex models. 2. Memetic Algorithm (MA): This algorithm is essentially based on the Genetic Algorithm (GA), making it redundant to run separately. 3. Distributed Search (DS): The DS method uses the GA as a baseline, adding parallel agents to search for other local minima. Since the GA has already been analyzed, DS was not implemented. 4. Multi-Objective Optimization (GA based): Although similar to the GA, this approach requires more than one fitness function to be effective, which was beyond the scope of this study. 5. Monte Carlo Hybrid Algorithm: This method proved to be significantly more time-consuming than the others. One key limitation of the Monte Carlo approach is that it lacks the adaptive learning mechanisms present in other optimization algorithms. Instead, it performs a blind search around the current best solution using a fixed \"search radius\" parameter. If this radius is too small, the method fails to explore the solution space adequately, if it is too large, it often samples poor-quality regions, reducing efficiency. An adaptive or dynamic adjustment of the search radius could potentially improve performance, but due to constraints in computational resources and time, it was not feasible to explore such enhancements or run the method for a sufficient number of iterations to ensure convergence. 6. Machine Learning: Machine learning itself is not a heuristic global optimization method, but it frequently employs such methods for optimization tasks; however it will not be used in this study. This method will be implemented in future studies.