The paper is concerned with black-box nonlinear constrained multi-objective optimization problems. Our interest is the definition of a multi-objective deterministic partition-based algorithm. The main target of the proposed algorithm is the solution of a real ship hull optimization problem. To this purpose and in pursuit of an efficient method, we develop an hybrid algorithm by coupling a multi-objective DIRECT-type algorithm with an efficient derivative-free local algorithm. The results obtained on a set of "hard" nonlinear constrained multi-objective test problems show viability of the proposed approach. Results on a hull-form optimization of a high-speed catamaran (sailing in head waves in the North Pacific Ocean) are also presented. In order to consider a real ocean environment, stochastic sea state and speed are taken into account. The problem is formulated as a multi-objective optimization aimed at (i) the reduction of the expected value of the mean total resistance in irregular head waves, at variable speed and (ii) the increase of the ship operability, with respect to a set of motion-related constraints. We show that the hybrid method performs well also on this industrial problem.

The paper presents a study on four adaptive sampling methods of a multi-fidelity (MF) metamodel, based on stochastic radial basis functions (RBF), for global design optimisation based on expen-sive CFD computer simulations and adaptive grid refinement. The MF metamodel is built as the sum of a low-fidelity-trained metamodel and an error metamodel, based on the difference between high-and low-fidelity simulations. The MF metamodel is adaptively refined using dynamic sam-pling criteria, based on the prediction uncertainty in combination with the objective optimum and the computational cost of highand low-fidelity evaluations. The adaptive sampling methods are demonstrated by four analytical benchmark and two design optimisation problems, pertaining to the resistance reduction of a NACA hydrofoil and a destroyer-type vessel. The performance of the adaptive sampling methods is assessed via objective function convergence.

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