在人工智能技术发展背景下，数学或统计方法面对高维、多模、非线性等复杂的优化问题时往往表现欠佳，智能算法作为优化算法的一种，其在解决多领域优化问题中优势明显. 蜉蝣算法作为一种新提出的群智能优化算法，因其结构简单，易操作和实现等优势备受学者们的关注. 但在复杂问题求解上，仍存在全局搜索能力不足，收敛速度和稳定性不强、寻优精度较低等问题. 为解决上述问题，本文提出两种改进算法，并通过经典工程优化设计和故障诊断应用加以评估.

针对蜉蝣算法易陷入局部搜索、全局搜索能力弱等问题，引入Sobol序列、不完全伽马函数、柯西-高斯算子和横纵交叉策略，提出了一种混合改进的自适应蜉蝣算法. 10组经典基准测试函数仿真结果表明，本文提出的改进算法提高了原算法的全局寻优能力和收敛速度.

针对蜉蝣算法收敛不稳定、寻优精度不足等问题，利用Logistics混沌映射初始化，丰富种群多样性，引入螺旋函数指导蜉蝣位置更新，通过正余弦自适应权重调节蜉蝣速度更新，采用折射反向学习策略，增强算法寻优能力，提出了一种融合折射反向学习策略改进的自适应蜉蝣算法. 10组经典基准测试函数仿真结果表明，改进算法提高了原算法的寻优精度、收敛速度以及收敛稳定性.

为评估本文所提出的两种改进算法在实际问题的适用性，将两种改进算法应用于三个工程实例设计优化问题，实验结果证明，改进算法在优化问题上具有较高的求解精度. 为进一步验证改进算法在其他领域的适用性，利用第二种改进算法优化SVM的核参数和惩罚参数，建立故障诊断模型，实际DGA数据诊断结果表明，改进算法提高了故障诊断的准确率.

In the context of the development of artificial intelligence technology, mathematical or statistical methods often perform poorly in the face of complex optimization problems such as high-dimensional, multimodal and nonlinear problems. Mayfly algorithm, as a new proposed group intelligence optimization algorithm, has attracted much attention because of its simple structure, easy operation and implementation. However, in solving complex problems, there are still problems such as insufficient global search capability, low convergence speed and stability, and low optimization accuracy. In order to solve these problems, two improved algorithms are proposed and evaluated by classical engineering optimization design and fault diagnosis applications.

Aiming at the problems of local search and weak global search ability of mayfly algorithm, a hybrid and improved adaptive mayfly algorithm is proposed by introducing Sobol sequence, incomplete gamma function, Cauchy-Gaussian operator and horizontal and vertical cross strategy. The simulation results of 10 sets of classical benchmark functions show that the improved algorithm proposed in this paper improves the global optimization ability and convergence speed of the original algorithm.

Aiming at the problems of unstable convergence and insufficient optimization accuracy of ephemera algorithm, Logistics chaotic mapping initialization is used to improve the population diversification of the algorithm, a spiral function is introduced to guide the position update of mayflies, the speed update of mayflies is adjusted by sine and cosine adaptive weights, and the refracted opposition-based learning strategy is adopted to enhance the optimization ability of the algorithm, and an adaptive ephemera algorithm with improved refracted opposition-based learning is proposed. The simulation results of 10 sets of classical benchmark functions show that the improved algorithm improves the optimization accuracy, convergence speed and convergence stability of the original algorithm.

To evaluate the applicability of the two improved algorithms proposed in this paper to practical problems, the two improved algorithms were applied to three engineering examples to design optimization problems, and the experimental results proved that the improved algorithms have higher solution accuracy in optimization problems. In order to further verify the applicability of the improved algorithms in other fields, the second improved algorithm was used to optimize the kernel parameters and penalty parameters of the SVM and establish the fault diagnosis model.