## 5 Results and Discussion
The exception is in EJAYA, Rao-2, and Rao-3, where problem 5 does not rank among the top three slowest problems when computing with the A100 GPU. Problems 1, 6, 7, and 8 usually emerge as the least computationally demanding in the sequential tests. However, no single problem consistently ranks as the fastest for all algorithms. In the context of the GPU-based implementations, tests utilizing the RTX 3090 GPU consistently position problems 3, 6, and 8 as the fastest across all tested algorithms. Nonetheless, no consistent pattern is observed when using the A100 GPU. Generally, problems 3, 8, 9, and 10 rank among the top three in terms of the lowest average execution time. When individually assessing the test problems for each algorithm, problem 8 generally appears among the least computationally intensive in both sequential and sequential tests. Figure 4: Mean computational times (**top**) and speedup (**bottom**) for the EJAYA algorithm, categorized by problem and dimension. Figure 3: Mean computational times (**top**) and speedup (**bottom**) for the Java algorithm, categorized by problem and dimension. parallel implementations, with the exception of the Rao-2 and Rao-3 algorithms, where no specific pattern has emerged. A consistent trend observed in all sequential implementations reveals an escalating impact with the growing problem dimension, giving rise to a concave upward curve characterized by an increasing slope. This trend indicates that computational time becomes more pronounced as dimensionality increases. Such behavior aligns seamlessly with the nature of the test problems, as scaling up NESs generally leads to a surge in computational  
Figure 5: Mean computational times (**top**) and speedup (**bottom**) for the Rao-1 algorithm, categorized by problem and dimension. Figure 6: Mean computational times (**top**) and speedup (**bottom**) for the Rao-2 algorithm, categorized by problem and dimension. complexity. This underscores the imperative need for efficient algorithmic strategies capable of navigating the computational challenges posed by these intricate mathematical models. Upon analyzing the computational times for GPU-based algorithms, two key observations provide insights into the performance characteristics of the proposed parallel implementation and GPU hardware. The first observation pertains to the grouping of lines representing computation times for each test problem. The general dispersion of lines observed in the data obtained with the RTX 3090 GPU suggests that this hardware may be  
Figure 8: Mean computational times (**top**) and speedup (**bottom**) for the BWP algorithm, categorized by problem and dimension. Figure 7: Mean computational times (**top**) and speedup (**bottom**) for the Rao-3 algorithm, categorized by problem and dimension. more influenced by problem complexity, resulting in higher variability in computational performance. In contrast, the A100 GPU exhibits a more clustered grouping of computation times, indicating more stable and predictable performance across different problem dimensions. Notably, two exceptions to this trend are observed in the GPU-based implementation of BWP (Figure 8) and MaGI (Figure 9) algorithms. The second and more pertinent observation concerns the gradient of computation time. When testing GPU-based algorithms with the RTX 3090 GPU, increases in problem dimension result in a less pronounced rise in computational time compared to the corresponding sequential version of the same algorithm. Conversely, most tests conducted with the A100 GPU suggest an almost linear relationship between computational time and problem dimension. However, it is noteworthy that some results obtained with the BWP and MaGI algorithms deviate more substantially from a linear trend. This implies that the rate at which computational time increases remains more constant with the growing problem dimension when the A100 GPU is used. This observation suggests that GPU-based algorithms can more efficiently handle the scaling of computational demands.