Dynamic Multi-swarm Particle Swarm Optimization with Fractional Global Best Formation

Particle swarm optimization (PSO) has been initially proposed as an optimization technique for static environments; however, many real problems are dynamic, meaning that the environment and the characteristics of the global optimum can change over time. Thanks to its stochastic and population based nature, PSO can avoid being trapped in local optima and find the global optimum. However, this is never guaranteed and as the complexity of the problem rises, it becomes more probable that the PSO algorithm gets trapped into a local optimum due to premature convergence. In dynamic environments the optimization task is even more difficult, since after an environment change the earlier global optimum might become just a local optimum, and if the swarm is converged to that optimum, it is likely that new real optimum will not be found. For the same reason, local optima cannot be just discarded, because they can be later transformed into global optima. In this paper, we propose novel techniques, which successfully address these problems and exhibit a significant performance over multi-modal and non-stationary environments. In order to address the premature convergence problem and improve the rate of PSO’s convergence to global optimum, Fractional Global Best Formation (FGBF) technique is developed. FGBF basically collects all the best dimensional components and fractionally creates an artificial Global Best particle (aGB) that has the potential to be a better “guide” than the PSO’s native gbest particle. In this way the potential diversity that is present among the dimensions of swarm particles can be efficiently used within the aGB particle. To establish follow-up of (current) local optima, we then introduce a novel multi-swarm algorithm, which enables each swarm to converge to a different optimum and use FGBF technique distinctively. We investigated the proposed techniques over the Moving Peaks Benchmark (MPB), which is a publicly available test bench for testing optimization algorithms in a multi-modal dynamic environment. An extensive set of experiments show that FGBF technique with multi-swarms exhibits an impressive speed gain and tracks the global maximum peak with the minimum error so far achieved with respect to the other competitive PSO-based methods.