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One of the most complicated and a vital problem in multiprocessor systems is task scheduling, which is an NP complete defined problem. These days, multiprocessor systems are utilized in parallel computing because the size of programs and information increases exponentially. Most of the time we are able to beak an enormous problem into some smaller portions and assign these smaller problems to processors. By doing this, we can gain a remarkable reduction in the execution time of programs. Prior algorithms had various limitations in their assumptions, like tasks regarded independent, task graph produced in a random manner, or the zero considered communication delay. Furthermore, enough attention has not been given the complexity of algorithms. This is of paramount importance because there must be a balance between the quality of solution and execution time of algorithm. Comparative studies with actual assumption on scheduling algorithms prefer quality of solution to execution time of algorithms. This has resulted in their being inapplicable in realistic situations. This study tries to develop a new hybrid approach which genetic algorithm and tabu search for performing task scheduling (HGTS).