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Task scheduling for a heterogeneous distributed system is one of the most important problems that affects the system performance. We propose an adaptive harmony search algorithm called AHS that has not need to exactly tune the initialization parameters while has high convergence speed. The algorithm adjusts the parameters adaptively and linearly. Moreover, we are presented a method improvise the new solution. This method seeks the best experience of each musician. If experience is repeated several times and it reaches to the good results, it will perform again. Simulation results with random graph and real application graph show that AHS outperforms the mostly used algorithms, IHS and NGHS algorithms.