一种基于引导学习策略改进的Adam梯度下降优化算法

An Adam Gradient Descent Optimization Algorithm Improved Based on the Guided Learning Strategy

摘要: 针对原始Adam梯度下降优化算法在复杂多峰及高维优化问题中易陷入局部最优、全局探索与局部开发难以有效平衡的局限，文章提出了一种基于引导学习策略(GLS)改进的Adam梯度下降优化算法(GAGDO)。该算法在AGDO的渐进梯度动量积分与动态梯度交互框架基础上，引入GLS的反馈–引导机制，通过周期性评估种群分布的标准差，动态自适应地调节探索与开发行为，有效克服早熟收敛，增强跳出局部最优的能力。为验证算法性能，在CEC2022基准测试集与压力容器设计问题上开展仿真实验。结果表明，GAGDO在收敛速度、寻优精度及鲁棒性方面均优于原始AGDO及GWO、DBO、PSO、SSA等主流算法；在压力容器设计问题中，GAGDO获得最低制造成本且多次运行稳定性优异，充分证明了其在复杂非线性约束问题中的可靠性。

Abstract: In response to the limitations of the original Adam gradient descent optimization algorithm, which is prone to getting stuck in local optima in complex multi-modal and high-dimensional optimization problems, and where it is difficult to effectively balance global exploration and local exploitation, this paper proposes an improved Adam gradient descent optimization algorithm based on the guided learning strategy (GLS) (GAGDO). This algorithm is built upon the progressive gradient momentum integration and dynamic gradient interaction framework of AGDO, and introduces the feedback-guidance mechanism of GLS. By periodically evaluating the standard deviation of the population distribution, it dynamically and adaptively adjusts the exploration and exploitation behaviors, effectively overcoming premature convergence and enhancing the ability to escape local optima. To verify the performance of the algorithm, simulation experiments were conducted on the CEC2022 benchmark test set and the pressure vessel design problem. The results show that GAGDO outperforms the original AGDO and mainstream algorithms such as GWO, DBO, PSO, and SSA in terms of convergence speed, optimization accuracy, and robustness; in the pressure vessel design problem, GAGDO achieves the lowest manufacturing cost and has excellent stability in multiple runs, fully demonstrating its reliability in complex nonlinear constrained problems.