Runtime Analysis of Binary PSO

We investigate the runtime of the Binary Particle Swarm Optimization (PSO) algorithm introduced by Kennedy and Eberhart (1997). The Binary PSO maintains a global best solution and a swarm of particles. Each particle consists of a current position, an own best position and a velocity vector used in a probabilistic process to update the particle's position. We present lower bounds for a broad class of implementations with swarms of polynomial size. To prove upper bounds, we transfer a fitness-level argument well-established for evolutionary algorithms (EAs) to PSO. This method is then applied to estimate the expected runtime on the class of unimodal functions. A simple variant of the Binary PSO is considered in more detail. The1-PSO only maintains one particle, hence own best and global best solutions coincide. Despite its simplicity, the 1-PSO is surprisingly efficient. A detailed analysis for the function Onemax shows that the 1-PSO is competitive to EAs.