In the Semantic Web context, OWL ontologies represent the conceptualization of domains of interest while the corresponding assertional knowledge is given by RDF data referring to them. Because of its open, distributed, and collaborative nature, such knowledge can be incomplete, noisy, and sometimes inconsistent. By exploiting the evidence coming from the assertional data, we aim at discovering hidden knowledge patterns in the form of multi-relational association rules while taking advantage of the intensional knowledge available in ontological knowledge bases. An evolutionary search method applied to populated ontological knowledge bases is proposed for finding rules with a high inductive power. The proposed method, EDMAR, uses problem-aware genetic operators, echoing the refinement operators of ILP, and takes the intensional knowledge into account, which allows it to restrict and guide the search. Discovered rules are coded in SWRL, and as such they can be straightforwardly integrated within the ontology, thus enriching its expressive power and augmenting the assertional knowledge that can be derived. Additionally , discovered rules may also suggest new axioms to be added to the ontology. We performed experiments on publicly available ontologies, validating the performances of our approach and comparing them with the main state-of-the-art systems.