基于小生境和交叉选择算子的改进粒子群优化算法

Improved Particle Swarm Optimization Algorithm Based on Niche, Crossover and Selection Operators

在求解高维多峰函数时,如果个体历史最好位置缺少多样性分布,粒子群优化算法就容易陷入局部最优,出现早熟现象。为此,结合小生境和交叉选择算子提出了一种改进粒子群优化算法(简称NCSPSO)。该算法在进行速度和位置更新之后,根据小生境数确定个体历史最好位置中的孤立点;然后对所有个体历史最好值劣于孤立点值的粒子使用交叉和选择算子进行更新。函数测试表明,NCSPSO有效地克服了标准PSO的缺点,性能上也有了明显提高。最后,将NCSPSO应用于高次非线性复数方程的求解,较好地解决了POGO振动研究中的固有频率计算问题。

An improved particle swarm optimization algorithm based on the niche, crossover and selection operators （NCSPSO） was developed to overcome the problem of the standard PSO in optimizing multimodal function, i.e. being trapped into local minima as well as premature due to the lack of the coordinates variation associated with the best solution for each particle, known as pbest. After the update of the particle velocity and position, the outlier particle was identified in the NCSPSO by comparing the niche number of every particle, with which the crossover and selection operators were employed sequently for those particles, whose personal best values were less than that of the outlier particle. Numerical test results on benchmark functions show the better performance of the NCSPSO compared to the original one. Finally, the NCSPSO was applied to solve higher degree nonlinear equations, which can provide effective and practical solutions to the calculation of intrinsic frequency in the POGO vibration study.