基于动态学习因子与凸函数速度衰减策略的改进粒子群算法

Improved Particle Swarm Algorithm Based on Dynamic Learning Factors and Convex Function Velocity Decay Strategy

摘要: 针对标准粒子群算法在连续优化中容易出现前期搜索不足或后期收敛过快的问题，本文在原有PSO框架上引入了动态学习因子和速度上限衰减策略。具体而言，个体学习因子随迭代逐步减小，社会学习因子逐步增大，使粒子搜索由偏重自身经验逐渐转向群体信息；同时，采用三次凸函数对速度上限进行非线性压缩，以控制后期粒子的搜索步长。为检验该策略的作用，本文选取Sphere、Rastrigin、Rosenbrock和Ackley四个标准测试函数，将改进算法与标准PSO以及两个消融版本进行10次独立实验对比。实验结果显示，完整改进算法在Sphere、Rosenbrock和Ackley函数上整体表现较好，收敛结果更稳定；在Rastrigin函数上，改进算法未表现出明显优势，但仍能保持接近基线算法的结果。说明该方法对单峰或相对平滑问题更有效，对多峰复杂问题的提升仍有一定局限。

Abstract: Aiming at the problems of insufficient early-stage search and premature convergence in the late stage of the standard Particle Swarm Optimization (PSO) algorithm in continuous optimization, this paper introduces dynamic learning factors and a velocity upper bound decay strategy into the original PSO framework. Specifically, the cognitive learning factor decreases gradually with iterations, while the social learning factor increases, shifting the particle search from relying heavily on individual experience to utilizing swarm information. Meanwhile, a cubic convex function is adopted to nonlinearly compress the velocity upper bound, thereby controlling the search step size of particles in the later stages. To verify the effectiveness of the proposed strategy, four standard benchmark functions—Sphere, Rastrigin, Rosenbrock, and Ackley—are selected. The improved algorithm is compared with the standard PSO and two ablation versions through 10 independent experiments. The experimental results show that the complete improved algorithm performs better overall and achieves more stable convergence on the Sphere, Rosenbrock, and Ackley functions. On the Rastrigin function, although the improved algorithm does not demonstrate a significant advantage, it still maintains results close to the baseline algorithms. This indicates that the proposed method is more effective for unimodal or relatively smooth problems, while its improvement for complex multimodal problems remains somewhat limited.