Some convergence properties of differential evolution

Differential Evolution uses fitness-based selection – a new solution will replace a reference target solution only if it is at least as fit. In a multi-modal search space, we are more interested in the (fitness of the) nearby local optimum that a search solution could lead to than its current fitness. Fitnessbased selection can in fact lead to "Failed Exploration" – the rejection of a search solution from a region of the search space that could lead to fitter (local) optimum because it is less fit than the reference solution (which leads to a less fit local optimum). We conduct several experiments to observe the occurrence of Failed Exploration in Differential Evolution, and we provide some insights into its operation and convergence properties.