## 3 Methodology
### The Well Sequence
The features of those informational indexes are given in Table 8. These features include the total units participated against each data set, the number of total input instances, the data set nature, and the number of classes against each data set, i.e., binary class problem or multiclass problem. The impact of increasing the number of target classes is independent, as the proposed strategy is purely concerned with weight optimization rather thanfeature selection or reducing high dimensionality. In addition, 10-fold cross-validation method has been carried out for the training and testing process. The experimental results of algorithms such as with backpropagation, standard DE, DE-S, DE-H, DE-WE, DE-TO, and DE-KN are compared with each other on seven well-known real data sets taken from UCI, and their performances are evaluated. In Table 11, the simulation results show that training of neural networks with DE-H algorithm outperforms in accuracy and is capable of providing better classification accuracy than the other traditional approaches. DE-H algorithm may be used effectively for data classification and statistical problems in the future as well. Figure 42 represents the accuracy graph for seven data sets. To prove the experimental results statistically, the testing accuracy of classification data sets were loaded to the software RStudio (1.2.5001 version). The classification results of seven approaches of DE were tested by the one-way ANOVA statistical test and post hoc [PERSON]'s pair-wise comparison statistical test using significance level 0.05 [19; 55]. The findings of classification data set with one-way ANOVA are illustrated in Table 12, where the significance = 0.02043, which is less than the abovementioned threshold of significance level. The findings in Table 12 proved that there are significant dissimilarities in all variants of DE with 95% confidence level. Figure 43 demonstrates the graph of one-way ANOVA that gives \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sr. No**} & \multirow{2}{*}{**Data Sets**} & \multirow{2}{*}{**Type**} & **BPA** & **DE-S** & **DE-WE** & **DE-TO** & **DE-KN** & **DE-H** \\ \cline{3-10}  & & & **Ts. Acc** & **Ts. Acc** & **Ts. Acc** & **Ts. Acc** & **Ts. Acc** & **Ts. Acc** \\ \hline
1 & Diabetes & 2-Class & 65.3\% & 66.1\% & 68.16\% & 69.6\% & 71.30\% & 67.17\% & **75.50\%** \\
2 & Heart & 2-Class & 68.3\% & 70.5\% & 72.5\% & 71.5\% & 74.50\% & 72.56\% & **76.34\%** \\
3 & Wine & 3-Class & 62.17\% & 64.7\% & 65.19\% & 66.20\% & 66.59\% & 68.25\% & **70.51\%** \\
4 & Seed & 3-Class & 70.56\% & 75.16\% & 75.29\% & 75.77\% & 82.13\% & 86.76\% & **91.54\%** \\
5 & Vertebral & 2-Class & 79.95\% & 82.13\% & 84.26\% & 86.15\% & 87.64\% & 90.17\% & **96.25\%** \\
6 & Blood Tissue & 2-Class & 73.47\% & 76.23\% & 74.16\% & 72.21\% & 84.76\% & 81.34\% & **86.45\%** \\
7 & Mammography & 2-Class & 71.26\% & 74.39\% & 68.37\% & 82.45\% & 86.17\% & 96.66\% & **99.21\%** \\ \hline \hline \end{tabular}

* Results of 10-fold classification rates of ANN-training methods in for seven data sets for accuracy.

\end{table} 
Table 11: Results of 10-fold classification rates of ANN-training methods in for seven data sets for accuracy. ## 7 Conclusions

This paper presents three novel pseudorandom initialization strategies called WELL sequence, Knuth sequence, and Torus sequence, which are used to initialize the population in the search space for PSO and DE algorithm. The experimental validation of proposed approaches by using the family of low-discrepancy sequences is tested on the comprehensive set of benchmark test functions and training of the artificial neural network. The simulation results reveal that the use of the family of low-discrepancy sequences maintains the diversity of the swarm, improves the convergence speed, and finds the better region of the swarm. The proposed families of low-discrepancy sequences contain higher diversity and enhance the local searching ability.