## 3 Proposed RBAVO-DE for GS
### The Complete RBAVO-DE Algorithm
Following the pre-processing phase, the data were refined and ready for the GS process. Contrary to the approach used in [36], which tackled the multi-classification of all types of cancer together, we opted to analyze every cancer type individually for greater specificity. Table 1[57] presents a comprehensive overview of all twenty-two tumor types and their respective sample counts. The number of features utilized in the benchmark datasets is 32,000 features (genes). \begin{table}
\begin{tabular}{l l c c} \hline \hline \# & **Cancer** & **Normal** & **Tumor** \\  & & **Records** & **Records** \\ \hline
1 & Bladder Urothelial Carcinoma (BLCA) & 19 & 408 \\
2 & Thyroid Cancer (THCA) & 59 & 501 \\
3 & Cervical and Endocervical Cancers (CESCs) & 3 & 304 \\
4 & Cholangiocarcinoma (CHOL) & 9 & 36 \\
5 & Colon Adenocarcinoma (COAD) & 41 & 458 \\
6 & Esophageal Cancer (ESCA) & 13 & 184 \\
7 & Glioblastoma Multiforme (GBM) & 5 & 153 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Datasets employed in this paper [57]. ### Parameter Setting

The proposed RBAVO-DE algorithm was compared against binary variants of different meta-heuristic optimizers, such as BABC, BSSA, BPSO, BBA, BGWO, BWOA, BBSA, BGOA, BHHO, BASO, and BHGSO. The critical parameters for the ML models employed in this study are detailed in Table 2.

Within the proposed framework, the validity of the results was verified using a 10-fold cross-validation approach to ensure the reliability of the outcomes. This involved randomly dividing each dataset into two distinct subsets: 80% for training and the remaining 20% for testing. The training portion was employed to train the presented classifiers using optimization techniques, while the testing portion was used to evaluate the selected genes' effectiveness. The parameters most commonly applied across all compared algorithms are summarized in Table 3. To execute all experiments in this paper, Python was utilized in a computational environment with a Dual Intel(r) Xeon(r) Gold 5115 2.4 GHz CPU and 128 GB of RAM on the Microsoft Windows Server 2019 operating system. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**\#** & **Cancer** & **Normal** & **Tumor** \\  & & **Records** & **Records** \\ \hline
8 & Thymoma (THYM) & 2 & 120 \\
9 & Head and Neck Squamous Cell Carcinoma & & \\  & (HNSC) & 44 & 520 \\
10 & Kidney Chromophobe (KICH) & 25 & 66 \\
11 & KIRC & 72 & 533 \\
12 & Kidney Renal Papillary & 32 & 290 \\  & (KIRP) & & \\
13 & Liver Hepatocellular Carcinoma (LIHC) & 50 & 371 \\
14 & LUAD & 59 & 515 \\
15 & LUSC & 51 & 501 \\
16 & Pancreatic Adenocarcinoma (PAAD) & 4 & 178 \\
17 & UCEC & 35 & 176 \\
18 & Pheochromocytoma and & 3 & 179 \\  & Paraganglioma (PCPG) & & \\
19 & Rectum adenocarcinoma (READ) & 10 & 94 \\
20 & Sarcoma (SARC) & 2 & 259 \\
21 & Skin Cutaneous Melanoma (SKCM) & 1 & 103 \\
22 & STAD & 37 & 415 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._ \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **Parameters** \\ \hline SVM & Polynomial kernel \(=2\) \\ \(k\)-NN & Euclidean distance metric \(k=5\)[21; 58; 59] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The key parameters of the employed ML models. \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **Parameters** \\ \hline SVM & Polynomial kernel \(=2\) \\ \(k\)-NN & Euclidean distance metric \(k=5\)[21; 58; 59] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter configurations of all utilized optimizers. ### Evaluation Criteria

To evaluate the proposed RBAVO-DE's effectiveness relative to other methods, each strategy was independently tested thirty times on each benchmark to ensure statistical validation of the results. For this purpose, the following established performance metrics for the GS issues were employed:

* **Mean classification accuracy** (\(Mean_{AC}\)): This measure represents the accuracy of correctly classifying data, calculated by running the algorithm independently thirty times.