## 5 Results and Discussion
Conversely, Rao-2 and Rao-3 required approximately 147.9% more time on average than Rao-1 to complete identical tests, with a respective duration of 460.08 s and 502.96 s.  
In a comparative evaluation, the GPU-based implementations demonstrated superior scalability amidst the increasing complexity of the Rao algorithms when juxtaposed with their sequential counterparts. With the RTX 3090 GPU, the Rao-1 algorithm yielded a global average of 2.06 s, while Rao-2 and Rao-3 exhibited an increase of approximately 26.7% (2.60 s for Rao-2 and 2.61 s for Rao-3). Employing the A100 GPU, the difference in the global average between Rao-1 (1.04 s) and both Rao-2 and Rao-3 (1.51 s and 1.50 s) was approximately 45.1% higher. Although this denotes a superior growth rate in computational time when compared with the RTX 3090 GPU, it is noticeable that the A100 GPU achieved an average speedup that was 73.7% higher. This enhanced scalability of the GPU-based algorithm is further reflected in the speedup values attained across the various Rao algorithms. The algorithm with lower computational demands achieved comparatively lower speedup gains. Specifically, for the GPU-based Rao-1 algorithm running on the RTX 3090, the average speedup was 84.8\(\times\), escalating to 155.4\(\times\) for Rao-2 and 169.9\(\times\) for Rao-3. Compared to Rao-1, this represents an increase in speedup of 83.3% and 100.3%, respectively. A similar trend is observed with the A100 GPU, where average speedup gains for the Rao algorithms were 159.8\(\times\), 261.1\(\times\), and 290.0\(\times\). This denotes a comparative increase in speedup achieved with Rao-2 and Rao-3 over Rao-1 of 63.4% and 81.5%, respectively. A similar scenario unfolds with the BWP and MaGI algorithms (Table 3), where the speedup attained by the GPU-based implementation increases when transitioning to a more computationally demanding algorithm. Despite both algorithms being Jaya-based, the MaGI algorithm features a slightly more intricate mathematical model, being based on Rao-2 as opposed to Rao-1 in the case of the BWP algorithm. Consequently, the sequential implementation of the MaGI algorithm resulted in a 34.1% increase in global average computation time compared to BWP. When comparing both algorithms using the GPU-based implementation, the observed increases were smaller. Utilizing the RTX 3090, the increase was approximately 14.7%, and it rose to approximately 26.5% with the A100 GPU. Consistent with previous findings, while the A100 exhibits a greater growth in computational times compared to the RTX 3090 GPU when transitioning to a more demanding algorithm, the speedups achieved by the A100 were superior, resulting in an average increase of 104.5% when considering both the BWP and MaGI algorithms. The behavior of both sequential and parallel implementations of the studied metaphorless algorithms across the different problem dimensions, along with the achieved speedups, is depicted in Figures 3-9. While profiling the different test problems and specifically examining the top three most and least computationally demanding in terms of average execution time, certain patterns become evident. Results from the sequential implementation of the algorithms reveal that problems 5, 9, and 10 consistently rank among the most demanding, with the exception of problem 9, which does not appear in the top three most demanding for the BWP and MaGi algorithms. In parallel testing, the RTX 3090 GPU exhibits a similar pattern, consistently ranking problems 5, 9, and 10 as the most computationally demanding across all algorithms. However, when using the A100 GPU, no similar or consistent pattern emerges. No single problem ranks as the most demanding of all algorithms, but problems 1, 2, and 5 typically rank among the slowest. After analyzing the test problems per individual algorithm, problem 5 appears to be one of the slowest in both sequential and parallel implementations for most tested algorithms.