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In evolutionary algorithm, population diversity is an important factor for solving performance. In this paper, combined with some population diversity analysis methods in other evolutionary algorithms, three indicators are introduced to be measures of population diversity in PSO algorithms, which are standard deviation of population fitness values, population entropy, and Manhattan norm of standard deviation in population positions. The three measures are used to analyze the population diversity in a relatively new PSO variant—Dynamic Probabilistic Particle Swarm Optimization (DPPSO). The results show that the three measure methods can fully reflect the evolution of population diversity in DPPSO algorithms from different angles, and we also discuss the impact of population diversity on the DPPSO variants. The relevant conclusions of the population diversity on DPPSO can be used to analyze, design, and improve the DPPSO algorithms, thus improving optimization performance, which could also be beneficial to understand the working mechanism of DPPSO theoretically

Analysis of Population Diversity of Dynamic Probabilistic Particle Swarm Optimization Algorithms