Neighborhood Re-structuring in Particle Swarm Optimization

Abstract

Abstract. This paper considers the use of randomly generated directed graphs as neighborhoods for particle swarm optimizers (PSO) using fully informed particles (FIPS), together with dynamic changes to the graph during an algorithm run as a diversity-preserving measure. Different graph sizes, constructed with a uniform out-degree were studied with regard to their effect on the performance of the PSO on optimization problems. Comparisons were made with a static random method, as well as with several canonical PSO and FIPS methods. The results indicate that under appropriate parameter settings, the use of random directed graphs with a probabilistic disruptive re-structuring of the graph produces the best results on the test functions considered.

Particle swarm optimization with spatially meaningful neighbours

“…FDR (112) is used in our experiments, as this was the best performer amongst the FDR variations as reported by Veermachaneni et al [4]. Tests were run on five of the most commonly used benchmark test functions for testing neighbourhood structures [6][13] [4], The commonly used sphere function was omitted from our test bed, since it is too simple in low dimensions, approaches always find the global best. Tests were run in 2D, 3D and 4D.…”

“…Static random topologies with undirected connections such as the star and ring neighbourhoods are the most commonly used in PSO implementations [6]. The Von Neumann topology has shown exceptional performance in the fully informed particle swarm (FIPS) PSO [15].…”

“…3) Dynamic neighbour connections are beneficial for introducing diversity [6]. 4) Dynamic topologies are useful for tackling multiobjective optimization problems [7].…”

Particle swarm optimisation with gradually increasing directed neighbourhoods

“…Mohais et al [11,21] have proposed to use random neighbourhoods in the PSOs, together with dynamism operators. Their random neighbourhoods can be represented using directed graphs as the relationships between particles are single directional.…”

“…Both the size and member of the in-neighbourhood set H + t (p i ) are generated uniformly. Two methods of dynamism called random edge migration and total re-structuring are given in [11,21].…”