依概率收敛的改进粒子群优化算法

粒子群优化算法是一种随机优化算法，但它不依概率1收敛到全局最优解。因此提出一种新的依概率收敛的粒子群优化算法。在该算法中，首先引入了具有探索和开发能力的两个变异算子，并依一定概率对粒子当前最好位置应用这两个算子，然后证明了该算法是依概率1收敛到ε-最优解。最后，把该算法应用到13个典型的测试函数中，并与其他粒子群优化算法比较，数值结果表明所给出的算法能够提高求解精度和收敛速度。

Improved particle swarm optimization algorithmwith probability convergence

The particle swarm optimization (PSO) algorithm is a stochastic optimization algorithm that does not converge to a global optimal solution on the basis of probability 1. In this paper, we present a new probability-based convergent PSO algorithm that introduces two mutation operators with exploration and exploitation abilities, which are applied to the previous best position of a particle with a certain probability. This algorithm converges to the-optimum solution on the basis of probability 1.We applied the proposed algorithm in 13 typical test functions and compared its performance with that of other PSO algorithms. Our numerical results show that the proposed algorithm can improve solution precision and convergence speed.