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粒子群算法(particle swarm optimization,PSO)是仿真于生物群体的社会行为的一种智能优化算法,其原始形式难以体现数学的直观性和本质性。然而,在简化算法原始模型的基础上,PSO算法的理论分析得到其数学模型,并且说明了其是一个迭代进化系统。利用PSO算法的数学模型代替标准PSO算法速度及位置的迭代公式,并选择适当的参数,从而构造了一种新的进化算法。新的进化算法形式更能直接体现PSO算法的数学思想。经仿真试验表明,新的进化算法效果不差于标准PSO算法,并且参数少且容易分析。
Particle swarm optimization (PSO) is an intelligent optimization algorithm that simulates the social behavior of biological communities. Its original form is difficult to reflect the intuition and essence of mathematics. However, on the basis of simplifying the original model of the algorithm, the mathematical model of the PSO algorithm is obtained through theoretical analysis and it is proved that it is an iterative evolutionary system. A new evolutionary algorithm is constructed by using the mathematical model of PSO instead of the iterative formula of velocity and position of standard PSO algorithm and selecting the appropriate parameters. The new evolutionary algorithm can directly reflect the mathematical thinking of PSO algorithm. The simulation results show that the new evolutionary algorithm is not inferior to the standard PSO algorithm, and the parameters are few and easy to analyze.