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Reduced graph representations of chemical structures have been shown to be effective in similarity searching applications where they offer comparable performance to other 2D descriptors in terms of recall experiments. They have also been shown to complement existing descriptors and to offer potential to scaffold hop from one chemical series to another. Various methods have been developed for quantifying the similarity between reduced graphs including fingerprint approaches, graph matching, and an edit distance method. The edit distance approach quantifies the degree of similarity of two reduced graphs based on the number and type of operations required to convert one graph to the other. An attractive feature of the edit distance method is the ability to assign different weights to different operations. For example, the mutation of an aromatic ring node to an acyclic node may be assigned a higher weight than the mutation of an aromatic ring to an aliphatic ring node. In this paper, we describe a genetic algorithm (GA) for training the weights of the different edit distance operations. The method is applied to specific activity classes extracted from the MDDR database to derive activity-class specific weights. The GA-derived weights give substantially improved results in recall experiments as compared to using weights assigned on intuition. Furthermore, such activity specific weights may provide useful structure--activity information for subsequent design efforts. In a virtual screening setting when few active compounds are known, it may be more useful to have weights that perform well across a variety of different activity classes. Thus, the GA is also trained on multiple activity classes simultaneously to derive a generalized set of weights. These more generally applicable weights also represent a substantial improvement on previous work.