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Particle Swarm Optimization (PSO) is a meta-heuristic for continuousblack-box optimization problems. In this paper we focus on the convergence ofthe particle swarm, i.e., the exploitation phase of the algorithm. We introducea new convergence indicator that can be used to calculate whether the particleswill finally converge to a single point or diverge. Using this convergenceindicator we provide the actual bounds completely characterizing parameterregions that lead to a converging swarm. Our bounds extend the parameterregions where convergence is guaranteed compared to bounds induced byconverging variance which are usually used in the literature. To evaluate ourcriterion we describe a numerical approximation using cubic splineinterpolation. Finally we provide experiments showing that our concept,formulas and the resulting convergence bounds represent the actual behavior ofPSO.

The Convergence Indicator: Improved and completely characterized parameter bounds for actual convergence of Particle Swarm Optimization