## 5 Results and Discussion  
The subsequent discussion examines the results from the parallelization of the metaphorless optimization algorithms discussed in this article in the GPU architecture. The primary emphasis lies in evaluating the attained speedup gains, understanding their behavior concerning increases in the problem dimension, and exploring different GPU hardware configurations. This aims to unravel the implications of leveraging parallel computational resources for optimizing algorithmic performance. The speedup factor quantifies the performance improvements resulting from the parallel implementation and is defined as the ratio of the sequential to the parallel computation time. It is important to note that the speedup values presented in this analysis were calculated using the full computational times without rounding up. Test data are systematically organized into tables, wherein test problems are categorized by dimension (i.e., population size and number of variables). The mean sequential computational times are presented in the column labeled _CPU_, while the results for parallel computation are organized into distinct columns based on the GPU hardware used for testing. All reported computational times pertain to the comprehensive execution of the algorithm, encompassing the entire duration from initiation to completion. The primary emphasis in parallel computation is on data obtained with the RTX 3090 and A100 GPUs, which are presented in columns bearing the same names. The selection of the RTX 3090 GPU aligns with its consistent use in previous parallelization of the majority of algorithms discussed in this article, while the A100 GPU represents a highly relevant hardware option in the professional sector, and it is employed here to illustrate the scalability of the parallel implementations and its adeptness in harnessing additional GPU resources without necessitating adjustments to the underlying parallelization strategy. Data obtained from the analysis of mean computational times for both sequential and parallel implementations, along with the corresponding speedup gains for each studied algorithm, were organized into tables and grouped based on similarities in algorithmic structure. Consequently, Table 1 presents computational results for the Jaya and EJAYA algorithms; the three Rao algorithms are showcased in Table 2, while the outcomes of the tests conducted with the BWP and MaGI algorithms are displayed in Table 3. Although Jaya and EJAYA are presented side by side, it is important to highlight that the EJAYA algorithm possesses a distinct structure compared to the other algorithms. Findings reveal the superior efficiency of GPU-based algorithms compared to their corresponding sequential implementations. In all algorithms, the speedup gains increased proportionally with the growth of the problem dimension. Consequently, the lower speedup gains were observed in the smallest dimensions, while the most pronounced speedups were achieved in the largest dimensions. This expectation is rooted in the parallelization strategy employed for GPU-based algorithms, wherein the allocation of GPU processing capabilities (expressed in terms of the number of CUDA cores, the block size, and thenumber of blocks) is adjusted automatically according to the problem dimensionality and inherent characteristics of the GPU. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & \multicolumn{3}{c}{**Jaya**} & \multicolumn{3}{c}{**EJAYA**} \\ \cline{3-8}
**Pop. ** & **Prob. ** & **CPU** & **RTX 3090** & **A100** & **CPU** & **RTX 3090** & **A100** \\ (**Vars) & **No. ** & **Time** & **Time (Gain)** & **Time (Gain)** & **Time (Gain)** & **Time (Gain)** & **Time (Gain)** \\ \hline  & 1 & 39.90 & 0.59 (**67.6**) & 0.33 (**121.9**) & 54.98 & 1  
Regarding the GPU hardware, the A100 GPU demonstrated speedup gains ranging from a minimum of 34.4\(\times\) in the EJAYA algorithm to a maximum of 561.8\(\times\) in Rao-3, achieving a global mean speedup (across all algorithms, problems, and dimensions) of 231.2\(\times\).