Particle Swarm Optimization (PSO) is a well-known extensively utilized algorithm for a distinct type of optimization problem. In meta-heuristic algorithms, population initialization plays a vital role in solving the classical problems of optimization. The population’s initialization in meta-heuristic algorithms urges the convergence rate and diversity, besides this, it is remarkably beneficial for finding the efficient and effective optimal solution. In this study, we proposed an enhanced variation of the PSO algorithm by using a quasi-random sequence (QRS) for population initialization to improve the convergence rate and diversity. Furthermore, this study represents a new approach for population initialization by incorporating the torus sequence with PSO known as TO-PSO. The torus sequence belongs to the family of low discrepancy sequence and it is utilized in the proposed variant of PSO for the initialization of swarm. The proposed strategy of population’s initialization has been observed with the fifteen most famous unimodal and multimodal benchmark test problems. The outcomes of our proposed technique display outstanding performance as compared with the traditional PSO, PSO initialized with Sobol Sequence (SO-PSO) and Halton sequence (HO-PSO). The exhaustive experimental results conclude that the proposed algorithm remarkably superior to the other classical approaches. Additionally, the outcomes produced from our proposed work exhibits anticipation that how immensely the proposed approach highly influences the value of cost function, convergence rate, and diversity.