Local search heuristics for large-scale discrete structural optimization with expensive black-box evaluations

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.