Many applications involve matching two graphs in order to identify their common features and compute their similarity. Different kinds of graph matchings, giving rise to different graph similarity measures, have been proposed. In particular [CS03] proposed a multi-labeled graph similarity measure based on a multivalent matching of the graph vertices and [SS05] showed that it is generic in the sense that other well known graph similarity measures can be viewed as special cases of it. In this paper, we address the problem of computing this graph similarity measure. We propose and compare two different kinds of algorithms: an Ant Colony Optimization based algorithm and a Reactive Search. We compare the efficiency of these two algorithms on two different kinds of difficult graph matching problems and we show that they obtain complementary results.