## 3 Methodology
### The Well Sequence
In this study, those benchmark problems are incorporated and have been extensively utilized in the literature for conveying a deep knowledge of the performance related to the abovementioned optimization algorithms. To measure the effectiveness and robustness of optimization algorithms, benchmark functions are applied. In this study, 16 computationally expensive black-box functions are applied to their various abilities and traits. The purpose of utilizing these benchmark functions is to examine the effectiveness of the abovementioned proposed approaches. In this section, for a comparison among low-discrepancies sequence, methods are performed with each other with reference to capabilities and efficiency with the help of high-dimensional 15 benchmark functions. Nevertheless, the whole performance of optimization algorithms varies on the basis of setting parameters and also with other testing criteria. Benchmark problems may be embedded to demonstrate the performance of the low-discrepancies sequence approaches, at various complex levels. Table 6 contains the experimental simulation results on benchmark functions. The exhaustive statistical results are explained in Table 7. From Figures 23-38, the experimental results of constrained benchmark test functions are only exhibited by having a surface with D = 10, 20, and 30. The experimental results of this work may not contemplate the entire competency of new proposed low-discrepancies sequence in accordance with the all possible conditions. The core objective of this section is to review the consequences of tested optimization approaches in high dimensionality, regarding to the accuracy and reliability of achieved solutions at the time of solving complex and computationally expensive optimization problems. From Figures 23-38, the performances of following methods: DE-KN, DE-WE, DE-TO, DE-S, DE-H, and traditional DE, are compared for 16 benchmark functions. In the graphs, the horizontal axis displays the total number of iterations, while on the other hand, the vertical axis displays the mean value of objective functions at the fixed number of function computations. Correspondingly, the value achieved in each iteration is operated as a performance measure. As a result, the exploitation ability of traditional DE is moderately low, particularly for high-dimensional problems. The results are also disclosed that traditional DE, DE-SO, and DE-H are only effective in performance while they are tackling with expensive design problems having low dimensionality. Beside this, H-DE has excellent control on the high-dimensionality problems compared to other methods in spite of complexity and the superficial topology of the examined problems. Figures 23-38 shows the achievements of traditional DE, DE-S, DE-WE, DE-KN, and DE-TO algorithms with regard to their efficiency and capability. The results are demonstrated that DE-H outperforms in higher dimensionality problems. By summarizing it, the dimensionality strongly influences the working of most algorithms. However, it is observed that DE-H is more consistent during the increment of dimensions of the problem. Due to this consistency of DE-H, it is proven that the DE-H algorithm has the greater capability of exploration.