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. Fitness- based 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. Index Terms—Exploration, Exploitation, Multi-Modal Search Spaces, Differential Evolution