Abstract: Aiming at the problem that the original monarch butterfly optimization algorithm is easy to fall into the local optimal solution and has poor convergence, an adaptive monarch butterfly optimization algorithm based on mutation reverse learning is proposed. Firstly, the mutation idea of genetic algorithm is combined with the reverse learning strategy to replace the original transfer operator to improve the global convergence. Then, an adaptive strategy is integrated into the adjustment operator of the original monarch butterfly optimization algorithm to make the population more diverse. Finally, Cauchy mutation will be carried out among the last five monarch butterflies in the updated population, which will generate greater disturbance near the mutated individuals and make the whole population search for optimization in a larger range. In order to verify the improved monarch butterfly optimization algorithm, benchmark function and Wilcoxon rank sum test are used to test it. The experimental results show that the convergence speed and optimization accuracy of the improved algorithm are greatly improved.

Key words: monarch butterfly optimization algorithm, variation reverse learning, adaptive strategy, Cauchy variation

摘要： 针对于原始帝王蝶优化算法易陷入局部最优解、收敛性不好等问题，提出变异反向学习的自适应帝王蝶优化算法。将遗传算法的变异思想与反向学习策略结合来替代原始的迁移算子，提高全局的收敛性。在原始帝王蝶优化算法的调整算子中融入自适应的策略，使种群更具多样性。在更新的种群中将排序在最后的5只帝王蝶进行柯西变异，让变异个体附近生成更大的扰动，使整个群体在更大的范围内进行寻优。为了验证改进帝王蝶优化算法，通过基准函数和Wilcoxon秩和检验对其进行测试，实验结果表明改进算法的收敛速度及寻优精度得到了很大改进。

关键词: 帝王蝶优化算法, 变异反向学习, 自适应策略, 柯西变异