In this contribution instances of a problem introduced by the differential cryptanalysis of Feistel cryptosystems are formulated as optimization tasks. The performance of Evolutionary Computation methods on these tasks is studied for a representative Feistel cryptosystem, the Data Encryption Standard. The results indicate that the proposed methodology is efficient in handling this type of problems and furthermore, that its effectiveness depends mainly on the construction of the objective function. This approach is applicable to all Feistel cryptosystems that are amenable to differential cryptanalysis.