Multidisciplinary Robust Optimization for Ship Design

Design optimization formulations and techniques are intended for supporting the designer in the decision making process, relying on a rigorous mathematical framework, able to give the "best" solution to the design problem at hand. Over the years, optimization has been playing an increasingly important role in engineering. Advanced modeling and algorithms in optimization constitute now an essential part in the design and in the operations of complex aerospace (Hicks and Henne, 1978; Sobieszczanski-Sobieski and Haftka, 1997; Alexandrov and Lewis, 2002;Willcox andWakayama, 2003; Morino et. al., 2006; Iemma and Diez, 2006) and automotive (Baumal et. al., 1998; Kodiyalam and Sobieszczanski- Sobieski, 2001) applications, when, for example, it is by all means important to reduce costs and shorten time of development. In the design of large and complex systems, the use of efficient optimization tools leads to better product quality and improved functionality (Mohammadi et. al., 2001). The success of design optimization has attracted the naval community, so that the recent years have seen progress in optimization for ships too (Ray et. al., 1995; Peri and Campana, 2003; Parsons and Scott, 2004; Pinto et al., 2004; Peri and Campana, 2005; Campana et al., 2007, 2009; Papanikolaou, 2009). Generally speaking, the task of designing a ship (as well as an aerial or ground vehicle) possibly requires that the engineering team considers a host of multidisciplinary design goals and requirements. Multidisciplinary Design Optimization (MDO) classically refers to the quest for the best solution with respect to optimality criteria and constraints, whose definition involves a number of disciplines mutually coupled. Therefore, MDO encompasses the interaction of different discipline-systems, formally joined together and inter-connected in a multidisciplinary framework, which leads to a multidisciplinary equilibrium. In this context, design engineers increasingly rely on computer simulations to develop new designs and to assess their models. However, even if most simulation codes are deterministic, in practice systems' design should be permeated with uncertainty. On this guideline, the most straightforward example in the naval hydrodynamics context is offered by any existing ship, that must perform under a variety of operating conditions (e.g. different, stochastic environmental conditions). The general question is now: "how can the results of computer simulations be properly exploited in the framework of design optimization, when the overall context is affected by uncertainty ?" Moreover "how can deterministic analysis be integrated in an ad hoc formulation that includes uncertainty ? How can it be used to get designs that are relatively insensible to stochastic variations of the external inputs and of the variables?". The latter questions stress one of the major issues arising in the optimization of a (ship) design: the perspective from which the optimization task has to be formulated and per- formed. Indeed, one may argue that a "tight" deterministic optimization leads to specialized solutions that are often inadequate to face the "real-life" world, which is instead characterized by a high level of uncertainty. In other words, specialized optimization procedures which include only deterministic parameters are often unable to model the overall problem and, consequently, are unable to provide adequate solutions to it. In this respect Marczyk (2000) states that, in a deterministic engineering context, optimization is the synonymous of specializa- tion and, consequently, the opposite of robustness. The perspective we try to give in the present work has the aim of broadening the standard-optimization-problem framing, leading to a formulation in which optimalit