AbstractAn algorithm is described for the optimization of character data (e.g. qualitative, nucleic acid sequence) on softwired phylogenetic networks. The algorithm presented here is an extension of those developed for trees under the parsimony criterion and can form the basis for phylogenetic network search procedures. Although the problem is (in general) an NP‐Hard optimization, the resolution‐based algorithm we describe here capitalizes on the significant amount of shared structure in sub‐graphs containing network edges, reducing the execution time and allowing for the analysis of empirical datasets.