自适应惯性权重的改进粒子群算法

针对标准PSO算法求解高维非线性问题时存在的大量无效迭代(经过一轮迭代后全局最优位置保持不变),提出了一种自适应惯性权重的改进粒子群算法。基于单次迭代中单粒子运动状态的分析,提出并证明了论点:上一轮迭代适应度值变差的粒子,当前迭代中其惯性分量将引导粒子往适应度值变差的方向运动,导致粒子群体无效迭代次数增加。设计了标准PSO算法改进方案,将上一轮迭代中适应度值变差的全体粒子的惯性权重置为零,消除当前迭代中不利惯性分量对算法收敛的不良影响。采用6个标准测试函数,将该算法与标准PSO算法、固定惯性权重PSO算法和具有领袖的PSO算法进行性能对比分析。试验表明,该改进算法无效迭代次数更少,在收敛率、收敛速度和收敛稳定性上均具有明显的优势。

Improved Particle Swarm Optimization with Adaptive Inertia Weight

To reduce the invalid iterations (the iteration in which the global optimum position is unchanged) of the particle swarm while solving the high-dimensional nonlinear problems by the standard particle swarm optimization (PSO) algorithm, an improved PSO algorithm with adaptive inertia weight is proposed in this paper. Based on the analysis of the instantaneous movement of single particle at each iteration, a significant argument is given and proved. In the improved algorithm, the inertia weights of the particles whose fitness become worse at the last iterations are set to zero. Six benchmark functions were used to test the proposed improved PSO algorithm, the standard PSO algorithm, the fixed inertia weight PSO algorithm, and the PSO algorithm with the leader. Experiments show that the invalid iterations of the proposed algorithm are less and it has obvious superiority on the convergence ratio, the convergence speed, and the convergence stability.