Effect on Convergence from Different Particle Swarms with a Unified and Simplified Formula for Position Updating

A unified and simplified formula for position updating in the existing particle swarm optimization (PSO) has been presented in one reference. The weighted average of specified previous best positions in this formula implies the characteristics of different PSOs, whose effects on convergence were observed in this paper. Four representative PSOs were selected, and according to the experimental methodology presented in another reference, their convergence was quantitatively compared. Experimental results presented the convergence difference caused by the difference among these algorithms' strategies, and illustrated the effect on convergence from the weighted average of specified previous best positions. This is helpful for researchers to adopt appropriate strategies when designing PSOs with the unified and simplified formula for position updating, and this also provides a useful example for convergence comparison of swarm intelligence.