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In this article, we suggest a new method to improve the harmony search meta-heuristic algorithm. Several approaches are presented for improving the harmony search algorithm. These approaches consider different values for initial parameters in each optimization problem. Differences between the proposed algorithm and the harmony search algorithm are as follows. First, we add a new step to create a new harmony vector, which increases the accuracy and convergence rate and reduces the impact of the initial parameters in achieving an optimal solution. Second, we set introduce a parameter called bandwidth (bw), which is an important factor with great influence on the convergence rate toward optimal solutions. To prove the efficiency and robustness of the proposed algorithm, we examine it through a variety of optimization problems, including constrained and unconstrained functions, mathematical problems with high dimensions and engineering and reliability problems. In all of these problems, the convergence rate and accuracy of the answer are equal to or better than other methods. In addition, in our proposed method, the effect of initial parameters has been reduced with respect to the optimal solution.