Multilevel modelling for engineering design optimization

Physical systems can be modeled at many levels of approximation. The right model depends on the problem to be solved. In many cases, a combination of models will be more eeective than a single model alone. Our research investigates this idea in the context of engineering design optimization. We present a family of strategies that use multiple models for unconstrained optimization of engineering designs. The strategies are useful when multiple approximations of an objective function can be implemented by compositional modeling techniques. We show how a compositional modeling library can be used to construct a variety of locally calibratable approximation schemes that can be incorporated into the optimization strategies. We analyze the optimization strategies and approximation schemes to formulate and prove suucient conditions for correctness and convergence. We also report experimental tests of our methods in the domain of sailing yacht design. Our results demonstrate dramatic reductions in the CPU time required for optimization, on the problems we tested, with no signiicant loss in design quality.