一种基于叠加Logistic映射分布的FWA-PSO新算法

A FWA-PSO New Algorithm Based on Superposition Logistic Map Distribution

为了解决传统粒子群算法早熟收敛陷入局部最优、粒子中期震荡及收敛结果不精确的问题,提出一种基于叠加Logistic映射分布的FWA-PSO算法对其进行改进。具体方法是:叠加Logistic映射用于对粒子位置的混沌初始化,在粒子数量一定的情况下,平衡最大遍历路径与最快收敛速度;引入FWA算法,同时根据迭代次数与粒子位置标准差,基于惩罚机制非线性调整爆炸半径r、惯性权重w、个体学习因子c1和社会学习因子c2,融合高斯变异算子与循环单维度寻优策略,在维系粒子群多样性的同时,也能避免粒子越过最优解。实验结果表明:FWA-PSO算法针对单峰函数50次平均值均能达到最优解0,证明了算法的稳定性与可靠性;对于多峰函数,FWA-PSO算法也能求得最优解,证明该算法可跳出局部最优,得到全局最优解。

In order to solve the problem that the traditional particle swarm algorithm premature convergence is trapped in local optimum,the medium-term oscillator is inaccurate,and the convergence result is inaccurate,an improved algorithm is proposed,i.e.,FWA-PSO(Fireworks Algorithm-Particle Swarm Optimization)algorithm based on superimposed logistic map distribution.The specific method is as follows:superimposed Logistic map is used to initialize chaotic of particle position,balance the maximum traversal path and the fastest convergence speed when the number of particles is constant;FWA algorithm is introduced,and based on the number of iterations and the standard deviation of particle position.Based on punishment the mechanism nonlinearly adjusts the blast radius r,the inertia weight w,the individual learning factor c1 and the social learning factor c2,and combines the Gaussian mutation operator with the cyclic one-dimensional optimization strategy to maintain the particle group diversity while avoiding the particles crossing the optimal solution.The experimental results show that the FWA-PSO algorithm can achieve the optimal solution for the 30-time average of the unimodal function,which proves the stability and reliability of the algorithm.For the multi-peak function,the FWA-PSO algorithm can also find the optimal.The solution proves that the algorithm can jump out of the local optimum and get the global optimal solution.