A quarter century of particle swarm optimization

Particle swarm optimization (PSO) is a population-based stochastic algorithm modeled on the social behaviors observed in flocking birds. Over the past quarter century, the particle swarm optimization algorithm has attracted many researchers’ attention. Through the convergent operation and divergent operation, individuals in PSO group and diverge in the search space/objective space. In this paper, the historical development, the state-of-the-art, and the applications of the PSO algorithms are reviewed. In addition, the characteristics and issues of the PSO algorithm are also discussed from the evolution and learning perspectives. Every individual in the PSO algorithm learns from itself and another particle with good fitness value. The search performance and convergence speed were affected by different learning strategies. The scheduling and data-mining problems are illustrated as two typical cases of PSO algorithm solving real-world application problems. With the analysis of different evolution and learning strategies, particle swarm optimization algorithm could be utilized on solving more real-world application problems effectively, and the strength and limitation of various PSO algorithms could be revealed.