<p>The parrot optimization (PO) algorithm is a novel metaheuristic method designed for solving continuous optimization problems. In this paper, a multistrategy enhanced chaotic parrot optimization algorithm (AWTPO) is proposed to address the structural design optimization of a two-stage involute cylindrical gear reducer. The AWTPO integrates a 2D Arnold chaotic map for population initialization and effectively enhances the search space coverage. A reverse learning mechanism is incorporated to improve population diversity and initialization quality. Furthermore, adaptive weight factors (ω₁ and ω₂), designed based on the iterative behavior of the algorithm, are introduced to replace the original random exploitation strategy and thus improve the balance between exploration and exploitation. To improve performance further, an adaptive Cauchy–Gaussian hybrid mutation strategy and a local elite preservation mechanism are employed to accelerate convergence and avoid local optima. To evaluate the effectiveness of AWTPO, 14 benchmark test functions and a real-world gear design problem are investigated. Experimental results demonstrate that AWTPO achieves the best performance across all benchmark cases compared with several state-of-the-art algorithms, including the golden jackal optimization, black winged-kite optimization, sine cosine algorithm, and arithmetic mean optimizer. In the gear design case, AWTPO reduces the minimum center distance by 22.7 % compared with conventional design methods, and thereby significantly improves spatial utilization. These results confirm the superior optimization capability of AWTPO and highlight its strong potential for intelligent design and manufacturing applications.</p>