To address the issues of low optimization accuracy and the tendency to fall into local optima in the northern goshawk algorithm, an improved version is proposed that integrates the subtraction optimizer and t-distribution wavelet mutation. In the initial phase of the algorithm, the Tent map combined with the dynamic reverse learning strategy is utilized to improve the quality and diversity of the initial population, thereby accelerating the iteration speed of the algorithm.Secondly,in the exploration stage, the subtractive average optimizer and the best value guidance strategy are introduced to update the population position. Finally, an adaptive t-distribution wavelet mutation strategy is employed to perturb the population, preventing it from falling into local optima.Through simulation experiments using test functions and integrating the improved algorithm with the extreme learning machine, the approach was applied to predict photovoltaic power generation. Additionally, it was implemented in two engineering design applications. The experimental results demonstrate that the improved algorithm significantly outperforms other modified algorithms in terms of convergence accuracy and robustness, and effectively enhances the performance in solving complex problems.