基于T分布扰动和透镜成像反向学习的算术优化算法及应用

Arithmetic Optimization Algorithm Based on T-Distribution Perturbation and Lens Imaging Opposition-Based Learning with Its Applications

摘要: 针对算术优化算法(Arithmetic optimization algorithm, AOA)易陷入局部最优、收敛速度慢等问题，提出一种基于T分布透镜成像反向学习策略的算术优化算法(TOBLAOA)，设计动态平衡机制调节全局探索强度与局部开采深度的配比，从而突破早熟收敛瓶颈并提高解精度稳定性。对2005、2017、2015测试集中的部分基准函数(共15个)进行仿真实验，首先引入4种不同改进策略的改进透镜成像反向学习策略的算术优化算法(OBLAOA)算法进行比较，再与哈里斯鹰优化算法、雷电附着优化算法等6个优化算法进行了实验结果对比和差异显著性Wilcoxon秩和检验，结果表明改进后的算术优化算法在求解精度、收敛速度上均有显著提升。最后将算法应用于工程优化中的常见的压力容器设计、三杆桁架设计、齿轮系设计中，进一步验证此算法的有效性。

Abstract: To address issues such as the Arithmetic Optimization Algorithm (AOA) being prone to local optima and having slow convergence speed, this paper proposes a T-distribution lens imaging opposition-based learning arithmetic optimization algorithm (TOBLAOA). The algorithm designs a dynamic balance mechanism to regulate the ratio between global exploration intensity and local exploitation depth, thereby breaking through the bottleneck of premature convergence and improving the stability of solution accuracy. Simulation experiments were conducted on selected benchmark functions (totaling 15) from the 2005, 2017, and 2015 test sets. The study first compares four improved OBLAOA algorithms with different enhancement strategies, and then performs experimental result comparisons and Wilcoxon rank-sum significance tests with six optimization algorithms including Harris Hawk Optimization and Lightning Attachment Procedure Optimization. The results demonstrate that the enhanced arithmetic optimization algorithm achieves significant improvements in both solution accuracy and convergence speed. Finally, the algorithm was applied to common engineering optimization problems such as pressure vessel design, three-bar truss design, and gear train design, further verifying its effectiveness.