Equivalence of the Constriction Factor and Inertia Weight Models in Particle Swarm Optimization: A Geometric Series Analysis

In this work we show the equivalence of the models of constriction factor and weighted inertia for particle swarm optimization. This equivalence is shown through expressing the formula for updating a particle´s velocity as a geometric series in both models. We also present the mathematical basis for the convergence conditions on an unified model based on geometric series. These mathematical results tell us directly what are adequate numeric values for the model´s parameters, which is a very useful pragmatic result.