Nonlinear Programming Approaches in the Multidisciplinary Design Optimization of a Sailing Yacht Keel Fin

This paper discusses certain shape optimization problems in which the solution depends on more disciplines, presenting results for the optimal shape of the keel fin of a sailing yacht, simultaneously accounting for hydrodynamics and elasticity. A pure fluid dynamic approach would simply consider the hull, the keel fin and the bulb as rigid, connected bodies. In the Multidisciplinary Design Optimization (MDO) framework these are considered instead as elastic and the shape of the keel fin is hence modified by the hydrodynamic loads. As a result, the final performances of the yacht are also influenced by the structural behavior of the fin. For this problem we study and compare a suite of different MDO formulations. The optimal design problem is finally tackled considering a Global Optimization (GO) problem within a MDO framework. MDO both includes difficult theoretical and computational aspects, determined by the simultaneous solution of different disciplines affecting each other, and by the related solvers involved all at once in the convergence of the overall optimization framework. We first introduce and describe some MDO approaches from the literature. Then, we consider our MDO scheme where we deal with the GO box constrained problem min_{aR. In general, the objective function f(x) is non-linear and non-convex and, in simulation based design approaches, also costly. We also assume that the solution of the problem requires the use of a derivative-free method since the derivatives of f(x) are unavailable and/or the function must be treated as a ‘black-box’ (see [30] and [23], [40]). Within this framework we study some globally convergent modifications of the evolutionary Particle Swarm Optimization (PSO) algorithm [24], suitably adapted for box-constrained optimization. To this purpose we adopt both the theory described in [27] for exact methods, and the generalized PSO scheme [10], which includes the standard PSO scheme. Finally, we report our numerical experience for the design of the sailing yacht elastic keel fin