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This work is dedicated to a study of the NP-hard Cyclic Bandwidth Problem with the paradigm of memetic algorithms. To find out how to choose or design a suitable recombination operator for the problem, we study five classical permutation crossovers within a basic memetic algorithm integrating a simple descent local search procedure. We investigate the correlation between algorithmic performances and population diversity measured by the average population distance and entropy. This work invites more research to improve the two key components of the memetic algorithm: reinforcement of the local search and design of a meaningful recombination operator suitable for the problem.