## 3 Proposed RBAVO-DE for GS
### The Complete RBAVO-DE Algorithm  
To handle the GS strategy, the steps of the recommended RBAVO-DE algorithm are described in the following subsections. The pseudo-code for the proposed RBAVO-DE algorithm is provided in Algorithm 1. A flowchart of the proposed RBAVO-DE algorithm is shown in Figure 1, illustrating its main steps. Figure 1: Flowchart of the RBAVO-DE algorithm. ```
1:\(N\)--total number of positions (size of population)
2:\(G_{max}\)--maximum number of permitted iterations
3:\(D\)--problem's dimensional space
4:\(L_{B}\)--lower bounds of variables
5:\(U\)\(B\)--upper bounds of variables
6:\(C_{B}\)--crossover rate
7:\(W_{M}\)--mutation weighting factor
8:Output:
9:\(X_{base}\)--the global best volume's position found while searching
10:\(fit(X_{Max})\)--the global best fitness function value found, which should be lessened
1:Start
11:Apply the Relief approach for selecting the related features and filtering them, as demonstrated in Section 3.1;
12: Initialize a population of \(N\) positions, and provide the values of the necessary parameters (\(L_{1}\), \(L_{2}\), \(w\), \(P_{1}\), \(P_{2}\), and \(P_{3}\));
13: Set a random position \(X\) in the initial population;
14: Evaluate the fitness values \(fit(X)\) for each position in the initial population;
15: Arrange the positions in ascending order depending on their fitness function \(fit(X)\);
16:\(g\gets 1\); \(\triangleright\) Current number of iterations
17:while\(g<G_{max}\)do
18: Assign the positions of both the first-best volume \(X_{Max_{1}}^{g}\) and the second-best volume \(X_{Sus



timization (BHHO) [55]. The optimizers undergo evaluation through training and testing benchmarks, with conclusive results derived from the average values of the evaluation metrics. The benchmarks employed for assessing the performance of the proposed model are detailed in Section 4.1. The parameters used in the operational environments are outlined in Section 4.2. The metrics used for evaluation are described in Section 4.3. The analysis of the experimental outcomes is discussed in Section 4.4. ### Dataset Description

In-depth experimental approaches and various wrapper algorithms were applied to twenty-two datasets of gene descriptions; the data comprise normalized Level 3 RNA-Seq gene expression data for twenty-two kinds of tumors from the Broad Institute. These data are publicly accessible and can be found in [56]. We adhered to the methodology described in [36] and observed discrepancies between the data referenced from GitHub in the paper and the figures reported within the document, which were sourced from the website. The website's data included a mix of tumor and standard samples, whereas the paper treated the data uniformly as tumor samples. Consequently, we conducted a detailed examination of the data. Initially, the website offered various formats of the identical dataset we intended to analyze. Upon delving into the data, we encountered the following challenges:

* Certain genes are identified by ID but lack an associated symbol. * Some genes are absent from the annotation file. * There is a mix-up of samples, including both normal and tumor types. Consequently, pre-processing was necessary to segregate and identify samples, distinguish between normal and tumor samples for use in binary classification, and streamline the GS process. We addressed the challenges above in the following manner:

* We looked up the corresponding gene symbol for each ID found in the annotation file. * After cross-referencing with the annotating file, over one hundred genes were eliminated. * Based on the sample report, every Excel sheet's row was organized according to the kind of sample for binary classification. Moreover, the Relief approach, as detailed in Section 3.1, was utilized in the pre-processing stage to calculate the weight of each gene within the benchmark. These weights were subsequently ordered from highest to lowest. Genes with lower weights were then removed. The Relief approach was useful for discarding genes that do not contribute to classification.