Population size in Particle Swarm Optimization

Particle Swarm Optimization (PSO) is among the most universally applied population-based metaheuristic optimization algorithms. PSO has been successfully used in various scientific fields, ranging from humanities, engineering, chemistry, medicine, to advanced physics. Since its introduction in 1995, the method has been widely investigated, which led to the development of hundreds of PSO versions and numerous theoretical and empirical findings on their convergence and parameterization. However, so far there is no detailed study on the proper choice of PSO swarm size, although it is widely known that population size crucially affects the performance of metaheuristics. In most applications, authors follow the initial suggestion from 1995 and restrict the population size to 20-50 particles. In this study, we relate the performance of eight PSO variants to swarm sizes that range from 3 up to 1000 particles. Tests are performed on sixty 10- to 100-dimensional scalable benchmarks and twentytwo 1- to 216-dimensional real-world problems. Although results do differ for the specific PSO variants, for the majority of considered PSO algorithms the best performance is obtained with swarms composed of 70-500 particles, indicating that the classical choice is often too small. Larger swarms frequently improve efficiency of the method for more difficult problems and practical applications. For unimodal problems slightly lower swarm sizes are recommended for the majority of PSO variants, but some would still perform best with hundreds of particles.