Numerical Comparison of Neighbourhood Topologies in Particle Swarm Optimization

TL;DR

This paper compares five different neighbourhood topologies in Particle Swarm Optimization, analyzing their effects on convergence and performance across various benchmark problems to identify effective configurations.

Contribution

It provides a numerical comparison of multiple neighbourhood topologies combined with different coefficients' settings in PSO, highlighting the importance of dynamic topologies for general optimization.

Findings

Dynamic neighbourhoods with increasing interconnections perform well.

Performance is problem-dependent but dynamic topologies are generally advantageous.

The choice of topology significantly influences convergence speed and solution quality.

Abstract

Particle Swarm Optimization is a global optimizer in the sense that it has the ability to escape poor local optima. However, if the spread of information within the population is not adequately performed, premature convergence may occur. The convergence speed and hence the reluctance of the algorithm to getting trapped in suboptimal solutions are controlled by the settings of the coefficients in the velocity update equation as well as by the neighbourhood topology. The coefficients settings govern the trajectories of the particles towards the good locations identified, whereas the neighbourhood topology controls the form and speed of spread of information within the population (i.e. the update of the social attractor). Numerous neighbourhood topologies have been proposed and implemented in the literature. This paper offers a numerical comparison of the performances exhibited by five different neighbourhood topologies combined with four different coefficients' settings when optimizing a set of benchmark unconstrained problems. Despite the optimum topology being problem-dependent, it appears that dynamic neighbourhoods with the number of interconnections increasing as the search progresses should be preferred for a non-problem-specific optimizer.