We present a hierarchy of accelerate Monte Carlo (MC) algorithms which can be used to investigate the kinetic evolution of systems consisting of interacting defects or impurities in a solid matrix. Local models are used to approximate the interactions among particles and a specific application of the algorithms to the study of vacancy agglomeration is presented. It is shown that an extension of the Ising model, including an effective second neighbour interaction, gives a vacancy clusters energetics in good agreement with some recent quantum mechanical calculations. The accelerate algorithms implemented allow to speed up the calculations avoiding the bottlenecks which occur when the standard Metropolis algorithm is applied. These bottlenecks are due to the huge amount of rejected transition attempts and to the rapid fluctuations between quasi-degenerate configurations. We demonstrate the equivalence …