## 1 Introduction
The population convergence fails to produce a new population of the swarm due to inappropriate animalization strategies to explore the whole search space [23]. In the field of evolutionary computing, the performance of meta-heuristics algorithms is affected by the generation of random numbers while initializing the population into the multidimensional search space [24]. The meta-heuristics algorithm tends to reach the optimum value while solving the problems in low dimensional search space. However, the performance is supposed to be insignificant when the dimensionality of the problem is high, and this causes the particles to stick in the local optima [25]. Meta-heuristics population-based algorithm initialization can be performed by using chaotic initialization [26; 27; 28], opposition-based initialization, and quasi-random sequences. This paper presents the impact of quasi-random sequences for the initialization of the population of the meta-heuristics algorithm. In accordance with the optimization problem, population initialization plays a significant role in meta-heuristic algorithms. These algorithms can influence diversity, convergence, and also help to find an efficiently optimal solution. Particularly, recognizing the importance of diversity, several researchers have worked on performance for the improvement of meta-heuristic algorithms. In order to improve the convergence, rather applyingthe random distribution for initialization, quasi-random sequences are more useful to initialize the population [29]. Quasi-random sequences suffer from many issues while solving the problems of different dimensionality in real world [30]. Some of the sequences of quasi-random sequences give better results on large dimensions and vice versa [31; 32]. Our objective is to find the most suitable quasi-random sequence for meta-heuristic algorithms, which gives superior results without considering the dimensionality problem. Considering this fact, we have proposed three novel pseudo-random initialization strategies called WELL sequence, Knuth sequence [33], and Torus sequence to initialize the population in the search space. We initialized PSO, BA, and DE algorithm with these proposed pseudo-random strategies (WELL sequence, Knuth sequence, and Torus sequence). In our first contribution, we have compared the novel PSO technique with the simple random distribution [34] and family of low discrepancy sequences [35] on several unimodal and multi modals complex benchmark functions and training of the artificial neural network [36]. The experimental results have shown that PSO with Knuth-based initialization (KN-PSO) outperforms the other traditional PSO, PSO with Sobol-based initialization (SO-PSO), PSO with Halton-based initialization (H-PSO), PSO with Torus-based initialization (TO-PSO), and PSO with WELL-based initialization (WE-PSO) [37]. Similarly, in the second contribution, DE is initialized by these proposed pseudo-random strategies (WELL sequence, Knuth sequence, and Torus sequence) for function optimization and training of the neural network. The simulation results depict that DE with Halton-based initialization (DE-H) is superior to the standard DE, DE with Sobol-based initialization (DE-SO), DE with Knuth-based initialization (DE-KN), DE with Torus-based initialization (DE-TO), and DE with WELL-based initialization (DE-WE). BA is initialized by these proposed pseudo-random strategies (WELL sequence, Knuth sequence, and Torus sequence) for function optimization and training of the neural network. The simulation results depict that BA with WELL-based initialization (BA-WE) is superior to the standard BA, BA with Sobol-based initialization (BA-SO), BA with Halton-based initialization (BA-HA), BA with Torus-based initialization (BA-TO), and BA with Knuth-based initialization (KN-BA) [38; 39; 40]. The rest of the paper is organized as: Section 2 overviews the previous work. In Section 3, the different algorithm methodology is represented with six initialization strategies. Section 4 contains the experimental setup.