Erratum: Differential evolution: difference vectors and movement in solution space

This technical report corrects errors in Table III in Section III-C of Differential Evolution: Difference Vectors and Movement in Solution Space [5]1 which appears in the proceedings of the 2009 Congress on Evolutionary Computation. The contents of that paper are reproduced here for ease of reference, but with corrections to Table III (now Table 3) and Section III-C (now Section 3.3), inclusion in an appendix of graphs relevant to Section III-E (now Section 3.5) and an altered conclusion given the corrected data presented in Section 3.3. In the commonly used DE/rand/1 variant of differential evolution the primary mechanism of generating new solutions is the perturbation of a randomly selected point by a difference vector. The newly selected point may, if good enough, then replace a solution from the current generation. As the magnitude of difference vectors diminishes as the population converges, the size of moves made also diminishes, an oft-touted and obvious benefit of the approach. Additionally, when the population splits into separate clusters difference vectors exist for both small and large moves. Given that a replaced solution is not the one perturbed to create the new, candidate solution, are the large difference vectors responsible for movement of population members between clusters? This report examines the mechanisms of small and large moves, finding that small moves within one cluster result in solutions from another being replaced and so appearing to move a large distance. As clusters tighten this is the only mechanism for movement between them. Additionally, with some problem instances the relative quality of such moves is considerably higher than those occurring via the expected mechanism.