The butterfly optimization algorithm (BOA) is a new metaheuristic algorithm that is inspired from food foraging behavior of the butterflies. Because of its simplicity and effectiveness, the algorithm has been proved to be effective in solving global optimization problems and applied to practical problems. However, BOA is prone to local optimality and may lose its diversity, thus suffering losses of premature convergence. In this work, a hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism called MBFPA was proposed. Firstly, the flower pollination algorithm has good exploration ability and the hybrid butterfly optimization algorithm and the flower pollination algorithms greatly improve the exploration ability of the algorithm; secondly, the symbiosis organisms search has a strong exploitation capability in the mutualism phase. By introducing the mutualism phase, the algorithm's exploitation capability is effectively increased and the algorithm's convergence speed is accelerated. Finally, the adaptive switching probability is increased to increase the algorithm's balance in exploration and exploitation capabilities. In order to evaluate the effectiveness of the algorithm, in the 49 standard test functions, the proposed algorithm was compared with six basic metaheuristic algorithms and five hybrid metaheuristic algorithms. MBFPA has also been used to solve five classic engineering problems (three-bar truss design problem; multi-plate disc clutch brake design; welded beam design; pressure vessel design problem; and speed reducer design). The results show that the proposed method is feasible and has good application prospect and competitiveness.

中文翻译：

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基于互惠机制的蝶花授粉混合元启发式算法求解全局优化问题

蝴蝶优化算法（BOA）是一种新的元启发式算法，其灵感来自蝴蝶的食物觅食行为。由于其简单性和有效性，该算法已被证明可以有效地解决全局优化问题并应用于实际问题。然而，BOA 容易出现局部最优性，可能会失去多样性，从而遭受过早收敛的损失。在这项工作中，提出了一种基于互惠机制的蝴蝶和花授粉混合元启发式算法，称为MBFPA。首先，花授粉算法具有良好的探索能力，混合蝴蝶优化算法和花授粉算法大大提高了算法的探索能力；第二，共生生物的搜索在共生阶段具有很强的开发能力。通过引入互惠阶段，有效提高了算法的开发能力，加快了算法的收敛速度。最后，增加自适应切换概率，增加算法在探索和开发能力上的平衡。为了评估算法的有效性，在49个标准测试函数中，将所提算法与6种基本元启发式算法和5种混合元启发式算法进行了比较。MBFPA 还被用于解决五个经典工程问题（三杆桁架设计问题；多片盘式离合器制动器设计；焊接梁设计；压力容器设计问题；和减速器设计）。