Numerous applications, like in case-based reasoning or information retrieval systems, require to measure the similarity of objects. When graphs are used to model objects, measuring objects similarity turns into determining graphs similarity, i.e., finding the best matching between the vertices of the two graphs. In our work, we address the problem of computing this graph similarity. More precisely, we investigate the ability of the ant colony optimization metaheuristic. Two cases are considered in our study: the static case, where the problem definition remains invariant through time, and the dynamic case, when some criterions defining matchings quality change over the time so that solutions must be dynamically adapted to these changes.