Abstract: To address the limitations of the Black-winged Kite Algorithm (BKA), which suffers from slow convergence and a tendency to get trapped in local optima, a Hybrid Enhanced Black-winged Kite Algorithm (HEBKA) is proposed to significantly improve global search capability and optimization performance. Firstly, HEBKA replaces the attack phase of BKA with the Red-tailed Hawk Optimization Algorithm and incorporates Bernoulli chaotic mapping as an attack adjustment factor. This modification streamlines the algorithmic process and substantially enhances global search efficiency, thereby accelerating convergence. Secondly, inspired by the pheromone mechanism of the Black Widow Optimization Algorithm, HEBKA divides the population into elite and inferior individuals. Elite individuals undergo migration operations to guide the population toward the global optimum, while inferior individuals are subjected to random perturbations to increase population diversity. This strategy reduces the blind reliance on leader migration, preventing premature convergence. Additionally, when population clustering occurs, HEBKA applies an orthogonal experiment-based quasi-reflection perturbation strategy to the optimal individual. This approach leverages orthogonal experimental design to efficiently explore the solution space and introduces controlled perturbations via quasi-reflection to effectively escape local optima. To validate the effectiveness of these improvements, simulation experiments were conducted on the CEC2017 benchmark functions. Comparative analyses of convergence performance and Wilcoxon nonparametric statistical tests demonstrate that HEBKA significantly outperforms other algorithms in terms of convergence speed, optimization accuracy, and robustness, showcasing its superior global search capabilities and stability. Finally, HEBKA was applied to solve two-dimensional and three-dimensional Traveling Salesman Problems (TSP), verifying its efficiency and practical potential in addressing complex real-world optimization challenges.

Key words: Black-winged kite optimization algorithm, Red-tailed hawk optimization algorithm, Classification strategies for inferior individuals, Orthogonal test - quasi-reflection perturbation, Traveling Salesman Problem

摘要： 针对黑翅鸢优化算法（Black-winged Kite Algorithm, BKA）在收敛速度慢和易陷入局部最优的局限性，提出了一种混合增强黑翅鸢优化算法（Hybrid Enhanced Black-winged Kite Algorithm, HEBKA），旨在提升算法的全局搜索能力和优化性能。首先，HEBKA通过引入红尾鹰优化算法（Red-tailed Hawk Optimization Algorithm）替换BKA的攻击阶段，并结合Bernoulli混沌映射作为攻击调节因子，以简化算法流程并显著增强全局搜索能力，从而有效提高收敛效率。其次，借鉴黑寡妇优化算法（Black Widow Optimization Algorithm）的信息素机制，HEBKA将种群划分为优秀个体和劣质个体两类：对优秀个体实施迁徙操作以引导种群向最优解方向移动，而对劣质个体施加随机扰动以增加种群的多样性，从而减少对领导者迁徙的盲目依赖，避免种群过早收敛。此外，当种群出现聚集现象时，HEBKA针对最优个体引入正交试验-准反射扰动策略，通过正交试验设计高效探索解空间，并利用准反射机制引入适度扰动，进一步增强算法跳出局部最优的能力。为验证HEBKA的改进效果，在CEC2017测试函数集上开展了仿真实验，通过与多种优化算法进行收敛性分析及Wilcoxon非参数统计检验，结果表明HEBKA在收敛速度、优化精度和鲁棒性方面均显著优于对比算法，展现出优秀的全局搜索能力和稳定性。最后，HEBKA被应用于二维和三维旅行商问题（Traveling Salesman Problem, TSP）的求解，通过在实际复杂优化问题中的表现，验证了其高效性和应用潜力。

关键词: 黑翅鸢优化算法, 红尾鹰优化算法, 劣质个体分类策略, 正交试验-准反射扰动, 旅行商问题