Particle Swarms Reformulated towards a Unified and Flexible Framework

TL;DR

This paper proposes a unified, flexible framework for Particle Swarm Optimization that encompasses various existing variants, allowing for more adaptable and generalized particle behaviors and features.

Contribution

It introduces a comprehensive formulation that captures many PSO variants, decouples stochasticity, and redefines global features as particle attributes for enhanced flexibility.

Findings

Closed-form trajectory difference equations derived

Different particle behaviors identified

Global features redefined as particle attributes

Abstract

The Particle Swarm Optimisation (PSO) algorithm has undergone countless modifications and adaptations since its original formulation in 1995. Some of these have become mainstream whereas many others have not been adopted and faded away. Thus, a myriad of alternative formulations have been proposed to the extent that the question arises as to what the basic features of an algorithm must be to belong in the PSO family. The aim of this paper is to establish what defines a PSO algorithm and to attempt to formulate it in such a way that it encompasses many existing variants. Therefore, different versions of the method may be posed as settings within the proposed unified framework. In addition, the proposed formulation generalises, decouples and incorporates features to the method providing more flexibility to the behaviour of each particle. The closed forms of the trajectory difference equation are obtained, different types of behaviour are identified, stochasticity is decoupled, and traditionally global features such as sociometries and constraint-handling are re-defined as particle's attributes.