Towards a network-based approach to analyze particle swarm optimizers

Abstract

In Particle Swarm Optimizers (PSO), the way particles communicate plays an important role on their search behavior influencing the trade-off between exploration and exploitation. The interactions boundaries defined by the swarm topology is an example of this influence. For instance, a swarm with the ring topology tends to explore the environment more than with the fully connected global topology. On the other hand, more connected topologies tend to present a higher exploitation capability. We propose that the analysis of the particles interactions can be used to assess the swarm search mode, without the need for any particles properties (e.g. the particle's position, the particle's velocity, etc.). We define the weighted swarm influence graph I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tw</sup> that keeps track of the interactions from the last t <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</inf> iterations before a given iteration t. We show that the search mode of the swarm does have a signature on this graph based on the analysis of its components and the distribution of the node strengths.