  Global Sensitivity Analysis (GSA) is the study of the influence of any given
inputs on the outputs of a model. In the context of engineering design, GSA has
been widely used to understand both individual and collective contributions of
design variables on the design objectives. So far, global sensitivity studies
have often been limited to design spaces with only quantitative (numerical)
design variables. However, many engineering systems also contain, if not only,
qualitative (categorical) design variables in addition to quantitative design
variables. In this paper, we integrate Latent Variable Gaussian Process (LVGP)
with Sobol' analysis to develop the first metamodel-based mixed-variable GSA
method. Through numerical case studies, we validate and demonstrate the
effectiveness of our proposed method for mixed-variable problems. Furthermore,
while the proposed GSA method is general enough to benefit various engineering
design applications, we integrate it with multi-objective Bayesian optimization
(BO) to create a sensitivity-aware design framework in accelerating the Pareto
front design exploration for metal-organic framework (MOF) materials with
many-level combinatorial design spaces. Although MOFs are constructed only from
qualitative variables that are notoriously difficult to design, our method can
utilize sensitivity analysis to navigate the optimization in the many-level
large combinatorial design space, greatly expediting the exploration of novel
MOF candidates.
