Runtime analysis of binary PSO

Abstract

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 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 applied to estimate the expected runtime on the class of unimodal functions. A simple variant of the Binary PSO is considered in more detail. The 1-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.

Lower Bounds for Comparison Based Evolution Strategies Using VC-dimension and Sign Patterns

“…This gives n 0, = Ω(d log(p)/λ), which is better than the previous bound when λ/ log λ < d. This generalizes e.g. [25,Theorem 2] by considering a wider family of algorithms and possibly p > 2.…”

“…We also generalize existing results in the discrete case by considering arbitrary values of parameters λ and µ, and improve previous results from [10] in the special cases of (1 + λ)-ES or (µ + 1)-ES -a detailed comparison with state of the art is provided within the paper regarding these cases. We also remark that [25,Theorem 2], which is a complexity lower bound for a variant of particle swarm optimization, is included in the main theorem of [26].…”

Cancer microarray data feature selection using Multi-Objective Binary Particle Swarm Optimization algorithm

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Runtime analysis of search heuristics on software engineering problems

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