Robust Optimization and Analysis of NURBs-Based Metamodels Using Graph Theory

NURBs-based metamodels have been shown to accurately reproduce the behavior of computationally expensive models. These models in turn represent engineering problems of great complexity and importance. While the structure of NURBs-based metamodels has facilitated the development of discrete optimization algorithms, other analysis areas such as robust and multiobjective optimization have proven to be more difficult. We present here a new method for the analysis and optimization of these metamodels which is based on graph theory principles. The adoption of these principles allows the use of powerful existing algorithms for graph analysis. We have focused on the problem of robust optimization in this work, as the robust optimization of NURBs-based metamodels has been previously examined using more conventional techniques. We demonstrate that the graph-based analysis technique provides the design engineer a more comprehensive understanding of design problems and their behavior. We also demonstrate the new technique on a range of test functions in order to establish its validity and usefulness in the context of product and process optimization. We conclude with a discussion of the use of this new approach in addressing other analysis challenges such as multiobjective or mixed-integer optimization.