Penalty function approaches for ship multidisciplinary design optimisation (MDO)

This paper focuses on the solution of difficult multidisciplinary optimisation formulations arising in ship design. The latter schemes are by nature the result of the interaction among several optimisation problems. Each optimisation problem summarises the issues related to a specific aspect (discipline) of the formulation, and it may be hardly solved by stand-alone methods which ignore the other disciplines. This usually yields very challenging numerical optimisation problems, due to the simultaneous solution of different schemes. In particular, in our ship design applications we stress the strong interaction between fluid-dynamics and optimisation, in order to get remarkable achievements. The ordinary stand-alone methods from mathematical programming prove to be often unsatisfactory on the latter multidisciplinary problems. This scenario requires a specific integration of both fluid-dynamics and optimisation, where constrained optimisation schemes frequently arise. We give evidence that the proper use of penalty methods, combined with global optimisation techniques, may both be a theoretically correct approach, and may yield a fruitful class of techniques for the solution of multidisciplinary problems. We provide numerical results with different penalty functions, over difficult multidisciplinary formulations from ship design. Here, the introduction of penalty methods proved to be a valuable tool since feasibility issues strongly affect the formulation.