Robust Optimization Exploration Using NURBs-Based Metamodeling Techniques

Non-uniform rational B-splines (NURBs) demonstrate properties that are highly conductive to performing metamodeling for engineering design purposes. Previous research has resulted in the development of algorithms capable of fitting NURBs metamodels to design spaces of many input variables and performance indicies, and performing various discreet optimizations upon these metamodels. In the present research we expand upon this basis by illustrating the development of robust optimization algorithms that leverages the unique properties of NURBs metamodels. This optimization is conducted in a general fashion by considering both optimality and various robustness metrics as global or local model properties, and illustrates the tradeoffs between them using a novel graphical approach. The appeal of this approach is demonstrated by a series of test functions of one performance index and one or two performance indicies. A case study in designing composite structures of specific stiffness, of four and five design variables, follows. We proceed to discuss the future of NURBs metamodeling techniques and the potential for considering model properties besides optimality and robustness during optimization.