Numerical Optimization Methods for Ship Hydrodynamic Design

The use of computational methods in design engineering is growing rapidly at all stages of the design process, with the final goal of a substantial reduction of the cost and time for the development of a design. Simulations and optimization algorithms can be combined together into what is known as Simulation-Based Design (SBD) techniques. Using these tools the designers may find the minimum of some user defined objective functions with constraints, under the general mathematical framework of a Non-Linear Programming problem. There are problems of course: computational complexity, noise, robustness and accuracy of the numerical simulations, flexibility in the use of these tools; all these issues will have to be solved before the SBD methodology can become more widespread. In the paper, some derivative-based algorithms and methods are initially described, including efficient ways to compute the gradient of the objective function. Derivative-free methods -- such as genetic algorithms and swarm methods--are then described and compared on both algebraic tests and on hydrodynamic design problems. Both local and global hydrodynamic ship design optimization problems are addressed, defined in either a single- or a multi-objective formulation framework. Methods for reducing the computational expense are presented. Metamodels (or surrogated mod- els) are a rigorous framework for optimizing expensive computer simulations through the use of inexpensive approximations of expensive analysis codes. The Variable Fi- delity idea tries instead to alleviate the computational expense of relying exclusively on high-fidelity models by taking advantage of well-established engineering approximation concepts. Examples of real ship hydrodynamic design optimization cases are given, re- porting results mostly collected through a series of projects funded by the Office of Naval Research . Whenever possible, an experimental check of the success of the optimization process is always advisable. Several examples of this testing activity are reported in the paper--one is illustrated by the two pictures at the top of this page, which show the wave pattern close to the sonar dome of an Italian Navy Anti-Submarine Warfare corvette: left, the original design; right, the optimized one.