结合质心思想和柯西变异策略的粒子群优化算法

摘要

针对基本粒子群优化(PSO)算法收敛精度低、容易陷入局部最优的问题,提出了一个结合质心思想和柯西变异策略的粒子群优化算法.首先,在粒子的初始化阶段采用混沌初始化策略,以提高初始粒子的均匀分布能力;其次,为了提高粒子群的收敛速度和寻优能力,引入了质心的概念,通过计算获得种群中所有粒子所构成的全局质心和所有个体极值构成的个体质心,使得粒子群内部可以实现充分的信息共享;为避免粒子陷入局部最优解,在粒子群算法中引入了柯西变异运算对当前最优粒子进行扰动,并依据柯西变异运算的规律,适应性地调整扰动步长,该算法以群体多样性为依据,动态调整惯性权重;最后,使用7个经典的测试函数对算法进行验证,通过函数运行结果的均值、方差和最小值能够表明,新算法在收敛精度上有较好的优越性.%Concerning the problem of low convergence accuracy and being easily to fall into local optimum of the Particle Swarm Optimization (PSO),an improved PSO algorithm combined Centroid and Cauchy Mutation,namely CCMPSO,was proposed.Firstly,at the initialization stage,chaos initialization was adopted to improve the ability of initial particle uniform distribution.Secondly,the concept of centroid was introduced to improve the convergence rate and optimization capability.By calculating the global centroid of all the particles in the population and the individaual centroid formed by all of the individuals' extreme values,sufficient information sharing could be realized in the interior of the particle swarm.To avoid falling into local optimal solution,Cauchy mutation operation was used to perturb the current optimal particle,in addition,the step length of disturbance was adaptively adjusted according to the operation rule of Cauchy mutation;the inertia weights were also dynamically adjusted according to population diversity.Finally,seven classical test functions were used to verify the algorithm.Experimental results indicate that the new algorithm has good performance in convergence precision of the function execution results,including the mean,the variance and the minimum value.