Algebraic and Dynamic Analysis on the Modified Swarm Optimizers

The modified particle swarm optimizers were proposed that use special velocity-updating modes and velocity-changing tracks to control velocity of evolved particles, and to tune the search process for the globally-optimal solution. Based on a reduced one-dimensional PSO system with only one particle, contrastive researches were made to interpret essential reasonability of the modified swarm optimizers, from both algebraic and dynamic viewpoint. Optimization example showed that the modified swarm optimizers are superior to the BPSO, on not only convergence precision but also computation expense.