Multidisciplinary design optimization (MDO) methods aim at adapting numerical
optimization techniques to the design of engineering systems involving multiple
disciplines. In this context, a large number of mixed continuous, integer, and
categorical variables might arise during the optimization process, and
practical applications involve a significant number of design variables.
Recently, there has been a growing interest in mixed-categorical metamodels
based on Gaussian Process (GP) for Bayesian optimization. In particular, to
handle mixed-categorical variables, several existing approaches employ
different strategies to build the GP. These strategies either use continuous
kernels, such as the continuous relaxation or the Gower distance-based kernels,
or direct estimation of the correlation matrix, such as the exponential
homoscedastic hypersphere (EHH) or the Homoscedastic Hypersphere (HH) kernel.
Although the EHH and HH kernels are shown to be very efficient and lead to
accurate GPs, they are based on a large number of hyperparameters. In this
paper, we address this issue by constructing mixed-categorical GPs with fewer
hyperparameters using Partial Least Squares (PLS) regression. Our goal is to
generalize Kriging with PLS, commonly used for continuous inputs, to handle
mixed-categorical inputs. The proposed method is implemented in the open-source
software SMT and has been efficiently applied to structural and
multidisciplinary applications. Our method is used to effectively demonstrate
the structural behavior of a cantilever beam and facilitates MDO of a green
aircraft, resulting in a 439-kilogram reduction in the amount of fuel consumed
during a single aircraft mission.

通过使用偏最小二乘回归构建少量超参数的混合分类高斯过程（Gaussian Process），我们提出了一种处理混合分类输入的广义克里金方法，并将其有效地应用于结构和多学科应用中，以展示悬臂梁的结构行为并促进绿色飞机的多学科优化，从而在单次飞行任务中减少 439 公斤燃油消耗。