基于惯性权重矩阵的自适应粒子群算法

An Adaptive Particle Swarm Optimization Algorithm Based on Inertia Weight Matrix

为得到一种简单易实现、寻优能力强的粒子群算法,以便满足实际工程优化问题的需求,提出一种基于惯性权重矩阵的自适应粒子群算法（RDR-PSO）。首先,定义了算法稳定运行概念并从离散状态空间方程角度分析了粒子群算法,在该概念下得到算法稳定运行时参数限制条件和粒子的运动规律;然后,定义了粒子活跃度,引入使算法每一步较大概率收敛较小概率发散的参数组合选择策略、惯性权重矩阵策略、根据粒子活跃度速度重置和历史最优值扰动策略,得到一种改进的粒子群算法（RDR-PSO）;最后,对RDR-PSO算法性能进行仿真测试,结果表明,该算法具有收敛精度高、全局寻优能力强和简单易实现的优点,具有广泛的应用前景。

In order to obtain a kind of PSO algorithm which is easy to implement and has strong ability of searching optimization, and meet the needs of engineering optimization problems, an adaptive PSO algorithm based on inertia weight matrix（RDR-PSO） is proposed. Firstly, the concept of stability is defined and the PSO algorithm is analyzed from the discrete state space equation. Under this concept, the parameters restriction condition and the particle motion law are obtained in the stable operation of the algorithm. Secondly, an improved PSO algorithm（RDR-PSO） is proposed by defining the particle activity, and introducing the parameter combination strategy that makes the algorithm in each step has a larger probability of convergence and a smaller probability of divergence, the inertia weight matrix method, the particle activity velocity reset and the historical optimal value perturbation strategy. Finally, the performance of RDR-PSO algorithm is simulated and tested. The results show that the algorithm has the advantages of high convergence precision, strong global searching ability and easy implementation, so it has a wide range of application prospects.