Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology

Abstract

Niching is an important technique for multimodal optimization. Most existing niching methods require specification of certain niching parameters in order to perform well. These niching parameters, often used to inform a niching algorithm how far apart between two closest optima or the number of optima in the search space, are typically difficult to set as they are problem dependent. This paper describes a simple yet effective niching algorithm, a particle swarm optimization (PSO) algorithm using a ring neighborhood topology, which does not require any niching parameters. A PSO algorithm using the ring topology can operate as a niching algorithm by using individual particles' <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local memories</i> to form a stable network retaining the best positions found so far, while these particles explore the search space more broadly. Given a reasonably large population uniformly distributed in the search space, PSO algorithms using the ring topology are able to form stable niches across different local neighborhoods, eventually locating multiple global/local optima. The complexity of these niching algorithms is only <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the population size. Experimental results suggest that PSO algorithms using the ring topology are able to provide superior and more consistent performance over some existing PSO niching algorithms that require niching parameters.