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.

翻译：近期，基于高斯过程的混合类别元模型在贝叶斯优化中日益受到关注。在此背景下，构建混合类别高斯过程可采用多种不同方法，其中许多方法涉及大量超参数——实际上，用于构建高斯过程的策略越通用、越精确，需要估计的超参数数量就越多。本文提出了一种创新的降维算法，该算法基于偏最小二乘回归以减少构建混合变量高斯过程所用的超参数数量。我们的目标是推广高斯过程中（针对连续输入）常用的经典降维技术，使其能够处理混合类别输入。所提方法在结构领域和多学科应用情境中均展现出良好潜力。目标应用包括悬臂梁分析以及绿色飞机优化，结果在一次飞行任务中实现了439公斤的显著油耗降低。