Alternative Topologies for GREEN-PSO

Abstract

The expense of evaluating the function to be optimized can make it difficult to apply the Particle Swarm Optimization (PSO) algorithm in the real world. Approximating the function is one way to address this issue, but an alternative is conservation of function evaluations. GREEN-PSO (GR-PSO) adopts the latter approach: given a fixed number of function evaluations, GR-PSO conserves them by probabilistically choosing a subset of particles smaller than the entire swarm on each iteration and allowing only those particles to perform function evaluations. Since fewer function evaluations are used on each iteration, the algorithm can use more particles and/or more iterations for a given number of function evaluations. GR-PSO has been shown to be effective using the global topology, performing as well as, or better than, the standard PSO algorithm (S-PSO) [7]. We extend these results by showing that GR-PSO can achieve significantly better performance than S-PSO, in terms of both best function value achieved and rate of error reduction, using three other topologies—ring, von Neumann, and Moore—on a set of six standard benchmark functions, and that the von Neumann and Moore topologies can be more effective topologies for GR-PSO than the global topology.