Theoretical and empirical study of particle swarms with additive stochasticity and different recombination operators
Jorge Peña · 2008
Standard particle swarms exhibit both multiplicative and additive stochasticity in their update equations. Recently, a simpler particle swarm with just additive stochasticity has been proposed and studied using a new theoretical approach. In this paper we extend the main results of that study to a large number of existing particle swarm optimisers by defining a general update rule from which actual algorithms can be instantiated via the choice of specific recombination operators. In particular, we derive the stability conditions and the dynamic equations for the first two moments of the sampling distribution during stagnation, and show how they depend on the used recombination operator. Finally, the optimisation efficiency of several particle swarms with additive stochasticity is compared in a suite of 16 benchmark functions.