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Our main focus is on barycenters, i.e., minimizers of a<jats:italic>q<\/jats:italic>-th-order Fr\u00e9chet functional with respect to these metrics. We present a heuristic algorithm that terminates in a local minimum and is shown to be fast and reliable in a simulation study. The algorithm serves as a general plug-in method that can be applied to point patterns on any state space where an appropriate algorithm for solving the location problem for individual points is available. We present applications to geocoded data of crimes in Euclidean space and on a street network, illustrating that barycenters serve as informative summary statistics. 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