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Optimization of the task scheduling represent one of the most important open issues of large scale distributed systems. Generally, the overall performance of a distributed system is highly influenced by the quality of the scheduling solution. This paper addresses the problem of dependent task scheduling, by proposing an innovative solution based on a memetic algorithm that combines the advantages of both imuune and genetic algorithm. The experiments proved that the proposed algorithm converges very fast and provides near-optimal solution by minimizing the make span (or schedule length).