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In this paper, we consider the permutation representation of genetic algorithms, and more generally, local search algorithms. We use a variety of permutation distance measures to profile the behavior of the most commonly used mutation operators for permutation-based genetic algorithms. Our operator profiles are also applicable to other local search algorithms, such as simulated annealing, as the most common permutation mutation operators are also commonly found as neighborhood operators for other metaheuristics in a search of the space of permutations. In addition to using several existing distance measures, we introduce two specific instances of the edit distance measure. Our aim is to offer the GA, and local search practitioner, guidance in the selection of mutation and neighborhood operators.