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The paper presents and discusses the shape optimization of a destroyer-type vessel by means of several multi-fidelity approaches. The hull-form design (bare hull) of the DTMB 5415 model (an open-to-public concept used in the development of the DDG-51, the lead vessel of the Arleigh Burke-class guided-missile destroyers) is addressed for optimal resistance performance in calm water and formulated as a global optimization problem. The design performance is assessed using a variety of physical models and solvers (from potential flow models to Reynolds-Averaged Navier Stokes equations), and spatial discretizations, which are combined together in dedicated multi-fidelity frameworks developed within the activities of the NATO-AVT-331 Research Task Group on “Goal-driven, multi-fidelity approaches for military vehicle system-level design.” Problems description, design parameterization methods, physical models and solvers are presented and discussed, as well as multi-fidelity approaches and results. The present effort highlights how the dimensionality of the optimization problem may be a critical issue for the surrogate model training. Nevertheless, it is shown how the proposed multi-fidelity approaches are able to achieve significant design performance improvements, even if only a few high-fidelity computations are used, with a ratio between the number of high- and low-fidelity evaluations required to solve the global optimization problem as low as nearly 1/50. Finally, the challenges arisen during the process are discussed and future research directions outlined.