Global optimization algorithms for robust optimization in naval design

One of the main concerns of ship designer with respect to numerical optimization is about the stability of the optimal solution to small changes in the operative conditions. In fact, typically the optimal solution shows an high level of dependence from the environmental conditions, and a large deterioration of the performances may occur if the real-life situation becomes too different with respect to the hypothetical one. Some of the different off-design conditions are partly predictable, while a number of other operative situations are not completely predictable. Robust Design Optimization (RDO) associates a probability to the different sources of uncertainty related to the real usage conditions of the system and solves an optimization problem for which the final solution represents an optimal trade-off, able to keep good performances in a large probabilistic scenario. The main difficulty stems from the necessity to include information about the variance of the objective function with respect to several environmental stochastic (or probabilistic) conditions. In the present paper, some recent work to test the effectiveness of a Particle Swarm Optimization (PSO) algorithm within the context of RDO are presented. The focus is put on the mean value and the variance of an objective function (which represent a sort of a cost in the deterministic approach) with respect to the variation of a number of probabilistic parameters. After the solution of some analytical test cases, the optimization of a naval design is performed using both single objective and multi-objective approach, accounting for the mean value and the variance of the "deterministic" objective function.