增强全局搜索和自适应蜉蝣算法

针对蜉蝣算法全局搜索能力较差和自适应能力弱等问题,提出一种增强全局搜索能力和自适应的蜉蝣算法——MIWMA。首先引入非均匀高斯变异策略对雄性蜉蝣和雌性蜉蝣进行位置更新,对全局最优位置变异引导其他个体向优良位置靠近,促使种群具有一定指导,从而提升全局搜索能力和增强种群多样性；其次,引入不完全伽马函数与Beta累加分布的自适应惯性权重对全局搜索和开发能力建立更好的平衡,平衡种群的全局搜索和局部搜索能力,进而提升算法收敛精度,利于种群全局搜索寻找最优解的潜力；引入局部停滞对抗策略,根据迭代停滞情况,调节蜉蝣速度更新的惯性部分和社会部分,使之具有最优搜索状态,增强算法全局搜索能力。利用经典测试函数集和IEEE CEC2021测试竞赛集进行测试优化比较,验证算法的有效性和稳健性,并利用Friedman和Wilcoxon秩和检验,分析表明:提出的算法有更好的稳定性、鲁棒性和可靠性。最后运用两个工程难题进行优化,结果验证了该算法在工程优化问题上的适用性,适合求解需求高精度的优化难题。

Enhance global search and adaptive mayfly algorithm

In view of the problems of poor global search ability and weak adaptive ability of mayfly algorithm, an enhance global search and adaptive mayfly algorithm (MIWMA) was proposed. Firstly, the non-uniform Gaussian mutation strategy was adopted to update the position of male mayfly and female mayfly, guide the global optimal position mutation to leading other individuals to approach the good position, and promote the population to have certain guidance, so as to improve the global search ability and enhance the diversity of the population. Secondly, the adaptive inertia weight of incomplete gamma function and beta cumulative distribution was introduced to establish a better balance between the global search and development ability, regulate the global search and local search ability of the population, and then improve the convergence accuracy of the algorithm, which is conducive to the potential of the global search of the population to find the optimal solution. The local stagnation countermeasure strategy was introduced. On the basis of the iterative stagnation, the inertia part and social part of mayfly speed update were adjusted to make it have the optimal search state and enhance the global search ability of the algorithm. The classic test function set and IEEE CEC2021 test competition set were used for test optimization comparison to verify the effectiveness and robustness of the algorithm. Results show that the proposed algorithm had better stability, robustness, and reliability by using Friedman and Wilcoxon rank sum test. Finally, two engineering problems were used for optimization. The results verified the applicability of the algorithm in engineering optimization problems and are suitable for solving optimization problems requiring high precision.