Abstract:

Aiming at the problems of slow convergence and premature convergence to local solutions of Butterfly Optimization Algorithm （BOA）， a neighborhood centroid opposition-based learning based Hybrid Salp Swarm and Butterfly Optimization Algorithm （HSSBOA） was proposed. Firstly， Salp Swarm Algorithm （SSA） was introduced into BOA to make the algorithm quickly deal with the local search stage， and update the population position. As a result， the optimization process was completed more effectively to avoid the algorithm falling into the local optimum. Then， neighborhood centroid opposition-based learning was introduced to make the algorithm search accurately in a small range of the neighborhood， increasing the accuracy of the algorithm. Finally， dynamic switching probability was introduced to improve the global and local proportion in the search， which accelerated the convergence of the algorithm. With ten benchmark functions selected for testing， HSSBOA was compared with several advanced algorithms from convergence accuracy， high-dimensional data， convergence speed， Wilcoxon rank sum test and Mean Absolute Error （MAE）. Research results show that HSSBOA achieves better results than other algorithms. In addition， the ablation experiment was used to further verify that the proposed improvements are positive. The performance on instance problems show that HSSBOA searches the optimal solution more effectively when solving constrained complex problems compared with other methods. It can be seen that HSSBOA has some advantages in optimization accuracy， stability and convergence efficiency， and it is able to solve complex practical problems.

Key words: Butterfly Optimization Algorithm (BOA), Salp Swarm Algorithm (SSA), neighborhood centroid opposition-based learning, hybrid algorithm, inertia weight, benchmark function

摘要：

针对蝴蝶优化算法（BOA）收敛速度较慢和过早收敛到局部解的问题，提出一种基于邻域重心反向学习的混合樽海鞘群蝴蝶优化算法（HSSBOA）。首先，将樽海鞘群算法（SSA）引入BOA中，使算法快速处理局部搜索阶段，并更新种群位置，从而更有效地完成寻优过程，避免算法陷入局部最优；然后，引入邻域重心反向学习以便更好地帮助算法在邻域内进行小范围精确搜索，从而提高算法的精度；最后，引入动态切换概率以改善搜索中全局与局部的比重，从而加快算法的搜索速度。选取10个标准检测函数进行测试，将HSSBOA与几个先进的优化算法从收敛精度、高维度数据、收敛速度、Wilcoxon秩和检验和平均绝对误差（MAE）五个方面进行对比分析。研究结果表明，相较于其他算法，HSSBOA取得了更优的结果。消融实验进一步验证了各项改进均为正向作用。实例问题上的表现表明相较于其他方法，在求解有约束的复杂问题时，HSSBOA能够更有效地搜索出最优解。可见HSSBOA在寻优精度、稳定性和收敛效率等方面取得了一定的优势，并且能够求解复杂的现实问题。

关键词: 蝴蝶优化算法, 樽海鞘群算法, 邻域重心反向学习, 混合算法, 惯性权重, 标准测试函数