This paper considers large-scale structural optimization problems featuring discrete variables, as well as nonlinear implicit constraints which can only be evaluated through time-expensive computations. A prominent application consists in the preliminary structural design of large ships, where many of the variables take their values in discrete sets which model standard element dimensions to be selected from catalogs, and where the evaluation of the constraints involves a complex structural analysis performed by black-box software. The resulting large-scale nonlinear combinatorial problems are particularly hard, and even nding a discrete feasible solution may prove challenging for some instances. In this paper, we propose two heuristics that combine local search methods and a sequential optimization method based on approximations of the implicit constraints. The heuristics are applied to the structural optimization of several large ships. For these instances, the heuristics provide discrete feasible solutions whose value is close to the optimal value of the continuous relaxation obtained by disregarding the discrete nature of the variables
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