## 2 Materials and Methods
### Cuckoo Search Algorithm  
The Cuckoo Search Algorithm (CSA) is based on how cuckoo birds reproduce. For this, it uses other birds' nests and places its eggs in them, hoping that the other birds \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Description** \\ \hline Population size & 200 & \begin{tabular}{c} Number of individuals \\ (random solutions) \\ \end{tabular} \\ \hline Termination condition: fitness & \(\leq\)40,000 & \begin{tabular}{c} Maximum number of times \\ the fitness function is \\ evaluated \\ \end{tabular} \\ \hline Biological pressure & 85\% & \begin{tabular}{c} Percentage of individuals that \\ reproduce \\ \end{tabular} \\ \hline Elitism & 10\% & \begin{tabular}{c} Percentage of best individuals \\ whose reproduction is \\ guaranteed \\ \end{tabular} \\ \hline Mutation probability & 30\% & \begin{tabular}{c} Probability that an individual \\ will mutate \\ A random point in a parent is \\ selected to combine the two \\ parents \\ \end{tabular} \\ \hline Selection method & Rank selection & \begin{tabular}{c} The individual with the best \\ performance has the best rank; \\ the individual with the best \\ rank has a higher probability \\ of reproducing \\ \end{tabular} \\ \hline Coefficient search range & [0–1] & \
\begin{tabular}{c} Float limits values for each \\ coefficient \\ \end{tabular} \\ \hline Exponent search range & [0–5] &
\begin{tabular}{c} Integer limits values for each \\ exponent \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Search parameters used for the genetic algorithm. will raise their young. Of course, some eggs will be discovered, but the more the foreign eggs resemble the host bird's eggs, the more likely they will hatch. This behavior has been successfully adapted to a metaheuristic algorithm, an egg being in a nest being a possible solution. The CSA has been widely used and has shown significant improvement combined with the Levy flight. In this work, we decided to use this algorithm to verify that the hyperparameters used in the genetic algorithm did not affect the performance of the final model. The advantage of the CSA is that it contains only one specific parameter, which is the probability that the impostor egg will be discovered. It should also be considered that it was not the objective of this study to demonstrate the superiority of one algorithm over another. In fact, according to the no free lunch theorem, all optimization algorithms have the same average performance [65]. This supposition implies that if an algorithm was more efficient in one task, it will be worse for another task. Therefore, tests must be carried out with at least two algorithms, for which the CSA was chosen to compare the results with the GA. The complete process of the algorithm is shown in the pseudo-code in Algorithm 2, and the search parameters are shown in Table 3.  
```
1:Begin
2:Create random initial population of n host nests (vectors with coefficients and exponents)
3:whilefitness evaluations consumed limit <40,000 do
4: Obtain a cuckoo randomly by Levy flights and evaluate fitness \(\mathcal{F}_{i}\)
5: Choose a nest among n (say, j) randomly
6:if\(\mathcal{F}_{i}\)>\(\mathcal{F}_{j}\)then
7: Replace j with the new solution
8:endif
9: Abandon a fraction \(\mathcal{P}_{a}\) of the worse nests and build new ones at the new values via Levy flights
10: Rank the solutions and find the current best
11:endwhile
12: Save the best vector
13:end
```  
**Algorithm 2** Cuckoo search algorithm  
The same general parameters and same fitness evaluations consumed were used to make a fairer comparison between the algorithms [66; 67; 68].