Abstract: Aiming at the shortcomings of sparrow search algorithm (SSA), such as decreased population diversity in the late iteration and easily falling into local optimal solution, a hybrid algorithm of sparrow search algorithm and arithmetic optimization algorithm based on Hamiltonian graph (HSSAAOAH) is proposed. Firstly, the multiplica-tion and division operator of arithmetic optimization algorithm (AOA) is introduced into the discoverer-follower model and reconnaissance mechanism of SSA. The high distribution of multiplication and division operator is used to improve the randomness of later optimization. Secondly, the population composed by all the individuals is transferred into an undirected weight graph. After each iteration, a Hamiltonian cycle and its length composed of individuals will be computed according to a modified cycle algorithm, and the population optimization trend is measured by the ratio of the Hamiltonian cycle length. Then, for the progeny that fails to perform effective convergence, a certain number of individuals are randomly generated to replace the last ones according to the greedy algorithm, which improves the quality of solution and enhances the ability to jump out of local extrema. Finally, HSSAAOAH and different optimization algorithms are simulated on the benchmark function and two engineering design problems. The results show that HSSAAOAH algorithm has faster convergence speed, higher optimization accuracy, and good robustness and optimization performance.

Key words: sparrow search algorithm (SSA), arithmetic optimization algorithm (AOA), Hamiltonian graph, modified cycle algorithm

摘要： 针对麻雀搜索算法（SSA）迭代后期种群多样性减少、易陷入局部最优等问题，提出一种基于哈密顿图的麻雀算术混合优化算法（HSSAAOAH）。首先，在SSA发现者-跟随者模型和侦察机制的基础上，引入算术优化算法（AOA）的乘除算子。利用乘除算子的高分布性，提高算法在迭代后期解的多样性；其次，将种群中所有个体转化成一个无向加权图，在每一轮迭代后，使用改良圈算法计算个体构成的哈密顿环长度，根据相邻两代长度的比值衡量种群收敛趋势；然后，对于没能有效收敛的子代，随机生成一定数量的个体并使用贪婪策略进行选择，替代表现较差的个体，提高解的质量，增强跳出局部极值的能力；最后，将HSSAAOAH与不同优化算法在基准函数和两个工程设计问题上进行仿真实验，结果表明HSSAAOAH算法收敛速度更快，寻优精度更高，具有良好的鲁棒性和寻优性能。

关键词: 麻雀搜索算法（SSA）, 算术优化算法（AOA）, 哈密顿图, 改良圈算法