Runtime analysis of a binary particle swarm optimizer

We investigate the runtime of a Binary Particle Swarm Optimizer (PSO) for optimizing pseudo-Boolean functions f : {0, 1}n → R. The Binary PSO maintains a swarm of particles searching for good solutions. Each particle consists of a current position from {0, 1}n , an own best position and a velocity vector used in a probabilistic process to update its current position. The velocities for a particle are then updated in the direction of its own best position and the position of the best particle in the swarm. We present a lower bound for the time needed to optimize any function with unique optimum. 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 on the test function OneMax, showing that there the Binary PSO is competitive to EAs. An additional experimental compar...

• Type: Journal
• Year: 2010
• Where: TCS
• Authors: Dirk Sudholt, Carsten Witt
• Keywords: Binary PSO, Current Position, Particle Swarm Optimizer, TCS 2010, Theoretical Computer Science