A comparison of three Differential Evolution strategies in terms of early convergence with different population sizes

Abstract

Differential Evolution (DE) is a popular population-based continuous optimization algorithm that generates new candidate solutions by perturbing the existing ones, using scaled differences of randomly selected solutions in the population. While the number of generation increases, the differences between the solutions in the population decrease and the population tends to converge to a small hyper-volume within the search space. When these differences become too small, the evolutionary process becomes inefficient as no further improvements on the fitness value can be made - unless specific mechanisms for diversity preservation or restart are implemented. In this work, we present a set of preliminary results on measuring the population diversity during the DE process, to investigate how different DE strategies and population sizes can lead to early convergence. In particular, we compare two standard DE strategies, namely “DE/rand/1/bin” and “DE/rand/1/exp”, and a rotation-invariant strategy, “DE/current-to-random/1”, with populations of 10, 30, 50, 100, 200 solutions. Our results show, quite intuitively, that the lower is the population size, the higher is the chance of observing early convergence. Furthermore, the comparison of the different strategies shows that “DE/rand/1/exp” preserves the population diversity the most, whereas “DE/current-to-random/1” preserves diversity the least.