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Four-Points Particle Swarm Optimization Algorithms
E. Garcia-Gonzalo, J.L. Fernandez-Martinez and Ana Cernea

PSO can be physically interpreted as a stochastic damped mass-spring system (the PSO continuous model). Furthermore, PSO corresponds to a particular discretization of the PSO continuous model (regressive in velocity and centered in acceleration). Based on this mechanical analogy we derived a whole family of three-points PSO versions. All these algorithms are related to different second order stochastic difference equations that are used to perform their stability and convergence analysis. In this paper we present the stochastic stability, convergence, and numerical analysis of the four remaining PSO members that can be useful in different practical applications, such as in the solution and appraisal of nonlinear inverse and machine learning problems, where exploratory versions are needed to provide an approximately sampling of the posterior distribution of the model parameters (sampling while optimizing).

Keywords: Global optimization, PSO family, stochastic stability, convergence, parameter tuning, numerical simulation

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