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In a traditional design optimization process, the variables and the parameters are usually considered as deterministic inputs. The resulting deterministic optimum has a high probability of violating the design constraints, due to the inherent geometrical, operational and modeling/numerical uncertainties involved in the simulation-based design process.

This paper highlights a few recent contributions in the field of optimization under uncertainty with application to ship hydrodynamic design, assuming that objective functions and constraints are evaluated via high fidelity (i.e. computationally expensive) solvers.

The development of advanced, efficient tools for uncertainty quantification and design optimization of ships operating in a real scenario are described. This requires a significant reformulation of both optimization problem and solution methods compared to deterministic approaches.

To afford the cost of the stochastic optimization process, a number of new techniques have had to be developed and/or implemented: (i) metamodels for the high-fidelity solvers and associated uncertainty quantification of stochastic simulation outputs, (ii) variable-fidelity approaches coupled with trust region methods, (iii) new global optimization derivative-free algorithms, (iv) principal component analysis algorithms — such as Proper Orthogonal Decompositions (POD) or Karhunen-Loève expansion (KLE) — to identify reduced dimensionality representations of large-scale design spaces, truncating basis functions with small significance to the solution.

Examples of real ship hydrodynamic design optimization cases are given, reporting results mostly collected through a series of projects funded by the Office of Naval Research (US Navy)