## 2 Materials and Methods
### Elimination of Invalid Configurations in the Solution Space  
In dual-adaptive structures, there is one more row than the adaptive panels in the single-adaptive architecture. As can be seen in Figure 5, the second adaptive panel group has caused the number of rows of adaptive panels to be twice as many. The matching of fixed panels with adaptive panels is calculated again by permutation over the total number of adaptive ones, and as in the logic of the scanning algorithm [25], each fixed panel is matched with all adaptive panels. The important thing here is that the adaptive panels that match the fixed ones must have appropriate matches. In other words, not every connection in the entire connection space is a correct match. Cases such as an adaptive panel matching more than one fixed panel or an adaptive panel not matching any fixed panel should be eliminated. Therefore, the first problem to overcome here is to create correct connections between the fixed panels and the adaptive panels. In a single-adaptive and \(m\)-row architecture, there are \(m^{m}\) correct connections in the entire connection space. For example, if the number of rows is, e.g., \(m=3\), only \(3^{3}=27\) connections are suitable connections in 336 connections. In a dual-adaptive and \(m\)-row architecture, there are \(m^{m\times 2}\) correct connections in the entire connection space. For example, if the number of rowsis \(m=3\), there are 3\({}^{3\chi 2}\) = 729 connections in 249,984 connections in the dual-adaptive structure. This means that trying to find the correct connections that are suitable in the entire connection space is the most important element of the problem. Table 2 provides examples for checking the suitability of fixed-adaptive matching. Algorithm 1 includes the pseudo codes of the validation process. Algorithm 1 takes the chromosome representing the configuration whose suitability will be tested and the sequence numbers of adaptive and fixed panels as parameters. The algorithm is based on the logic that adaptive panels should be used only once each when matching with fixed panels. The 1s in the chromosome indicate the presence of the adaptive panel, while the 0s indicate its absence. Therefore, when the chromosome values that match each fixed panel are collected bit by bit and multiplied by each other, if the result is 1 (_product_), the tested configuration is a valid configuration. It is important for the success of the system to perform the operation by detecting only valid configurations within the entire space. ```
Input: chromosome, adaptive_panel_array_length(\(N\)), fixed_panel_array_length(\(ROW\)) Output: valid
1: Set\(f\) array\(\leftarrow\)zero_values, \(k\)\(\leftarrow\)1 // The elements of the adaptive parts connected by the // fixeds having the same index are collected. 2:loop\(i\) = 1 to N*\(ROW\)
3: f(\(k\))\(\leftarrow\)f(\(k\))+ chromosome



### GA-Based Controller

Metaheuristic algorithms are general-purpose solution search techniques that aim to find optimum or approximate solutions in complex and large solution spaces. These algorithms are more flexible than traditional heuristic approaches and can be applied to different types of problems instead of adhering to rigid rules developed for a problem. Metaheuristic algorithms generally prevent local minima or maxima in global optimization problems and aim to reach the best solution by exploring large solution spaces. Inspired by natural events, biological processes, social dynamics and physical processes, these algorithms use evolutionary processes, swarm behaviors or random search methods. The problem discussed in this article is an optimization aimed at finding the most appropriate solution in a very large solution space that falls into the category of high-dimensional discrete optimization. The solution space consists of thousands or even millions of bit sequences, each of which has a fixed length such as 32 bits or 256 bits. This problem can be directly defined as a global optimization problem.