  Although Bayesian Optimization (BO) has been employed for accelerating
materials design in computational materials engineering, existing works are
restricted to problems with quantitative variables. However, real designs of
materials systems involve both qualitative and quantitative design variables
representing material compositions, microstructure morphology, and processing
conditions. For mixed-variable problems, existing Bayesian Optimization (BO)
approaches represent qualitative factors by dummy variables first and then fit
a standard Gaussian process (GP) model with numerical variables as the
surrogate model. This approach is restrictive theoretically and fails to
capture complex correlations between qualitative levels. We present in this
paper the integration of a novel latent-variable (LV) approach for
mixed-variable GP modeling with the BO framework for materials design. LVGP is
a fundamentally different approach that maps qualitative design variables to
underlying numerical LV in GP, which has strong physical justification. It
provides flexible parameterization and representation of qualitative factors
and shows superior modeling accuracy compared to the existing methods. We
demonstrate our approach through testing with numerical examples and materials
design examples. It is found that in all test examples the mapped LVs provide
intuitive visualization and substantial insight into the nature and effects of
the qualitative factors. Though materials designs are used as examples, the
method presented is generic and can be utilized for other mixed variable design
optimization problems that involve expensive physics-based simulations.
