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Tasks allocation problem in heterogeneous and distributed-multiprocessing computing environments is a nonlinear multi-objective NP-hard problem and from a research perspective, it is considereda major issue. The underlying objective of any allocation mechanism to execute the specified tasks set and enumerating processors is to minimize the overall cost. To solve the tasks allocation problems numerous meta-heuristic techniques have been tried and tested but still, plenty of scopes are there for optimal strategies. In the presented article, a comprehensive task assignment model based on particle swarm optimization (PSO) is developed, which optimizes response time, flowtime, and cost of the distributed computing system. In the present technique, the ‘n’ number of cluster centroids of ‘r’ tasks, is updated by the PSO technique to form the ‘n’ task clusters to minimize the communication costs then their allocation is made by the newly proposed heuristic method. Considering the fact, in the given model objective functions conflict with each other and the good thing about the PSO algorithm are its accuracy and speed. And to come up with the most favorable solution, authors have developed PSO based algorithm.The PSO-based technique that is proposed in this article to solve a given assignment problem in a distributed computing system is able to give better results in a manner of convergence rate as thePSO method integrates local and global search methods in an attempt to strike a balance between research and utilization. To examine the functioning of the developed technique, the well-demonstrated scheduling policies based on different techniques have been compared and obtained finer outcomes. The developed mechanism is acceptable for an erratic number of tasks and processors.