Abstract: To address the limitations of the black-winged kite algorithm (BKA), including restricted search intensity due to insufficient information exchange within the population and reduced population diversity caused by the blind following of the optimal individual during the migration phase, a black-winged kite optimization algorithm integrating trust domain and nonlinear simplex method (TDNSBKA) is proposed. Firstly, the elite dynamic reverse learning strategy is used to initialize the initial population of black-winged kite to improve the quality of the initial solution. Secondly, the trust domain mutation strategy is introduced in the attack stage of the algorithm to realize the information exchange within the population, improve the convergence accuracy of the algorithm, and balance the exploration and development capabilities of the algorithm. Finally, in the migration stage of the algorithm, the nonlinear simplex method is used to reflex the individuals with the worst fitness, so as to reduce the blindness of the population following the leader??s migration and improve the diversity of the population. The Markov chain model of TDNSBKA algorithm is established to prove that it has global convergence. Based on the 30-dimensional and 50-dimensional CEC2017 test functions, the simulation experiments verify the effectiveness of the three improved strategies, and the convergence analysis and Wilcoxon rank sum test of the improved algorithm TDNSBKA and the comparison algorithms are carried out, which proves that TDNSBKA has better convergence performance and robustness. The application of TDNSBKA to the solution of gear train design and pressure vessel design verifies the usefulness of TDNSBKA in practical application.

Key words: black-winged kite optimization algorithm, dynamic reverse learning, trust domain variation, nonlinear simplex method, Markov chain

摘要： 针对黑翅鸢优化算法（BKA）因缺乏种群内信息交流而导致搜索力度受限以及迁徙阶段种群跟随最优个体迁徙的盲目性而导致种群多样性下降的问题，提出融合信赖域和非线性单纯形法的黑翅鸢优化算法（TDNSBKA）。对黑翅鸢初始种群利用精英动态反向学习策略进行初始化，提高初始解的质量；在算法的攻击阶段，引入信赖域变异策略，实现种群内的信息交流，提高算法的收敛精度并平衡算法的探索与开发能力；在算法的迁徙阶段，对适应度最差的个体采用非线性单纯形法的反射操作，减小种群跟随领导者迁徙的盲目性，提高种群的多样性。建立TDNSBKA算法的Markov链模型，证明了其具有全局收敛性。仿真实验基于30维与50维的CEC2017测试函数，验证了3种改进策略的有效性，将改进的算法TDNSBKA和对比算法进行收敛性分析、Wilcoxon秩和检验，证明了TDNSBKA具有更优秀的收敛性能以及鲁棒性。将TDNSBKA应用在齿轮系设计和压力容器设计的求解上，验证了其在实际应用中的有用性。

关键词: 黑翅鸢优化算法, 动态反向学习, 信赖域变异, 非线性单纯形法, Markov链