Impact of Communication Topology in Particle Swarm Optimization

Particle swarm optimization (PSO) has two salient components: (1) a dynamical rule governing particle motion and (2) an interparticle communication topology. Recent practice has focused on the fully connected topology (Gbest) despite earlier indications on the superiority of local particle neighborhoods. This paper seeks to address the controversy with empirical trials with canonical PSO on a large benchmark of functions, categorized into 14 properties. This paper confirms the early lore that Gbest is the overall better algorithm for unimodal and separable problems and that a ring neighborhood of connectivity two (Lbest) is the preferred choice for multimodal, nonseparable and composition functions. Topologies of intermediate particle connectivity were also tested and the difference in global/local performance was found to be even more marked. A measure of significant improvement is introduced in order to distinguish major improvements from refinements. Lbest, according to the experiments on the 84 test functions and a bi-modal problem of adjustable severity, is found to have significant improvements later in the run, and to be more diverse at termination. A mobility study shows that Lbest is better able to jump between optimum basins. Indeed Gbest was unable to switch basins in the bi-modal trial. The implication is that Lbest's larger terminal diversity, its better ability to basin hop and its later significant improvement account for the performance enhancement. In several cases where Lbest was not the better algorithm, the trials show that Lbest was not stuck but would have continued to improve with an extended evaluation budget. Canonical PSO is a baseline algorithm and the ancestor of all contemporary PSO variants. These variants build on the basic structure of baseline PSO and the broad conclusions of this paper are expected to follow through. In particular, research that fails to consider local topologies risks underplaying the success of the promoted algorithm.