The Parrot Optimization Algorithm (PO) is a nature-inspired metaheuristic algorithm developed based on the social and adaptive behaviors of Pyrrhura molinae parrots. PO demonstrates robust optimization performance by balancing exploration and exploitation, mimicking foraging and cooperative activities. However, as the algorithm progresses through iterations, it faces critical challenges in maintaining search diversity and movement efficiency diminishes, leading to premature convergence and a reduced ability to find optimal solutions in complex search space. To address these limitations, this work introduces the Dynamic Turbulent-based Parrot Optimization Algorithm (DTPO), which represents a significant advancement over the original PO by incorporating three novel strategies: a novel Differential Mutation (DM), Dynamic Opposite Learning (DOL), and Turbulent Operator (TO). The DM Strategy enhances exploration by introducing controlled variations in the population, allowing DTPO to escape local optima. Also, the DOL Strategy dynamically generates opposite solutions to refresh stagnated populations, expanding the search space and maintaining adaptability. Finally, the TO strategy simulates chaotic movements inspired by turbulence, ensuring a thorough local search while preserving population diversity. Together, these strategies improve the algorithm's ability to explore, exploit, and converge efficiently. Furthermore, the DTPO's performance was rigorously evaluated on benchmark functions from CEC2017 and CEC2022, comparing it against 23 state-of-the-art algorithms. The results demonstrate DTPO's superior convergence speed, search efficiency, and optimization accuracy. Additionally, DTPO was tested on seven engineering design problems, achieving significant improvements over the original PO algorithm, with superior performance gains compared to other algorithms in real-world scenarios. Particularly, DTPO outperformed competing algorithms in 37 out of 41 benchmark functions, achieving an overall success rate of 90.24%. Moreover, DTPO obtained the best Friedman ranks across all comparisons, with values ranging from 3.03 to 1.18, demonstrating its superiority over classical, advanced, and recent algorithms. These results validate the proposed enhancements and highlight DTPO's robustness and effectiveness in solving complex optimization problems.

中文翻译：

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利用 Parrot 优化算法中的动态湍流动力学解决复杂的高维工程问题


鹦鹉优化算法 （PO） 是一种受自然启发的元启发式算法，基于 Pyrrhura molinae 鹦鹉的社交和适应性行为开发。PO 通过平衡勘探和开发、模拟觅食和合作活动来展示强大的优化性能。然而，随着算法的迭代进展，它在保持搜索多样性和移动效率降低方面面临关键挑战，导致过早收敛和在复杂搜索空间中找到最佳解决方案的能力降低。为了解决这些限制，这项工作引入了基于动态湍流的鹦鹉优化算法 （DTPO），该算法通过结合三种新颖的差分突变 （DM）、动态反向学习 （DOL） 和湍流运算符 （TO） 代表了对原始 PO 的重大进步。DM 策略通过在种群中引入受控变异来增强勘探，使 DTPO 能够逃避局部最优值。此外，DOL 策略会动态生成相反的解决方案，以刷新停滞的群体，扩大搜索空间并保持适应性。最后，TO 策略模拟受湍流启发的混乱运动，确保在保持种群多样性的同时进行彻底的本地搜索。这些策略共同提高了算法高效探索、利用和收敛的能力。此外，DTPO 的性能根据 CEC2017 和 CEC2022 的基准函数进行了严格评估，并将其与 23 种最先进的算法进行了比较。结果表明，DTPO 具有出色的收敛速度、搜索效率和优化精度。 此外，DTPO 还在 7 个工程设计问题上进行了测试，与原始 PO 算法相比取得了显著改进，与实际场景中的其他算法相比，性能得到了提升。特别是，DTPO 在 41 个基准测试函数中的 37 个中优于竞争对手算法，总体成功率为 90.24%。此外，DTPO 在所有比较中获得了最好的弗里德曼排名，值范围从 3.03 到 1.18，证明了它优于经典、高级和最新算法。这些结果验证了所提出的增强功能，并突出了 DTPO 在解决复杂优化问题方面的稳健性和有效性。