Convergence Analysis of a Dynamic Discrete PSO Algorithm

The particle swarm optimization (PSO) algorithm has exhibited good performance on continuous optimization problems in static environment. However, there are lots of real-world optimization problems that are dynamic and discrete, which is a new research field of PSO. So a dynamic discrete PSO (DDPSO) algorithm is proposed in this paper. In this algorithm, we design a new strategy of environmental monitoring and response. When environment is changed, it can be apperceived by the change of fitness and position of particles and be responded by environment sensitivity and environmental change gene in time. Finally, to analyze the convergence of DDPSO based on the solving of zero state response in discrete-time systems, we get its convergence condition and motion track of particles. As a result, we find that DDPSO has good convergence and diversity of swarm owing to environmental change gene which has randomicity and variability.