Review and Study of Genotypic Diversity Measures for Real-Coded Representations

The exploration/exploitation balance is a major concern in the control of evolutionary algorithms (EAs) performance. Exploration is associated with the distribution of individuals on a landscape, and can be estimated by a genotypic diversity measure (GDM). In contrast, exploitation is related to individual responses, which can be described with a phenotypic diversity measure. Many diversity measures have been proposed in the literature without a comprehensive study of their differences. This paper looks at surveys of GDMs published over the years for real-coded representations, and compares them based on a new benchmark, one that allows a better description of their behavior. The results demonstrate that none of the available GDMs is able to reflect the true diversity of all search processes. Nonetheless, the normalized pairwise diversity measurement (D-PW(N)) proves to be the best genotypic diversity measurement for standard EAs, as it shows nondominated behavior with respect to the desired GDM requirements.