  Recently, there has been a growing interest in mixed-categorical metamodels
based on Gaussian Process (GP) for Bayesian optimization. In this context,
different approaches can be used to build the mixed-categorical GP. Many of
these approaches involve a high number of hyperparameters; in fact, the more
general and precise the strategy used to build the GP, the greater the number
of hyperparameters to estimate. This paper introduces an innovative dimension
reduction algorithm that relies on partial least squares regression to reduce
the number of hyperparameters used to build a mixed-variable GP. Our goal is to
generalize classical dimension reduction techniques commonly used within GP
(for continuous inputs) to handle mixed-categorical inputs. The good potential
of the proposed method is demonstrated in both structural and multidisciplinary
application contexts. The targeted applications include the analysis of a
cantilever beam as well as the optimization of a green aircraft, resulting in a
significant 439-kilogram reduction in fuel consumption during a single mission.
