Embedding task graphs into hypercubes is a difficult problem. When the embeddingis one-to-one, schedule length is strongly influenced by dilation. Therefore, it is desirable to find low dilation embeddings. This paper describes a heuristic embedding technique based upon evolutionary strategies. The technique has been extensively investigated using task graphs which are trees, forests, and butterflies. In all cases the technique has found low dilation embeddings. An efficient parallel implementation of the evolutionary strategy is also given.