# High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft

arXiv: https://arxiv.org/abs/2311.06130 · HTML: https://mlsanity.com/paper/2311.06130/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 73 references that are in the map.
- First posted on arXiv 10 Nov 2023.

## Builds on (most cited first, 19 of 19)

- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1706.03673/) (2017)
- [Batched High-dimensional Bayesian Optimization via Structural Kernel Learning](https://mlsanity.com/paper/1703.01973/) (2017)
- [Active Learning of Linear Embeddings for Gaussian Processes](https://mlsanity.com/paper/1310.6740/) (2013)
- [TREGO: a Trust-Region Framework for Efficient Global Optimization](https://mlsanity.com/paper/2101.06808/) (2021)
- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [Group kernels for Gaussian process metamodels with categorical inputs](https://mlsanity.com/paper/1802.02368/) (2018)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [A mixed-categorical correlation kernel for Gaussian process](https://mlsanity.com/paper/2211.08262/) (2022)
- [Gradient-enhanced kriging for high-dimensional problems](https://mlsanity.com/paper/1708.02663/) (2017)
- [Efficient global optimization of constrained mixed variable problems](https://mlsanity.com/paper/1806.03975/) (2018)
- [Upper Trust Bound Feasibility Criterion for Mixed Constrained Bayesian Optimization with Application to Aircraft Design](https://mlsanity.com/paper/2005.05067/) (2020)
- [Deep Gaussian Process Emulation using Stochastic Imputation](https://mlsanity.com/paper/2107.01590/) (2021)
- [Revisiting Bayesian Optimization in the light of the COCO benchmark](https://mlsanity.com/paper/2103.16649/) (2021)
- [Global sensitivity analysis for optimization with variable selection](https://mlsanity.com/paper/1811.04646/) (2018)
- [A general mathematical framework for constrained mixed-variable blackbox optimization problems with meta and categorical variables](https://mlsanity.com/paper/2204.00886/) (2022)
- [A comparison of mixed-variables Bayesian optimization approaches](https://mlsanity.com/paper/2111.01533/) (2021)
- [Multioutput Gaussian Processes with Functional Data: A Study on Coastal Flood Hazard Assessment](https://mlsanity.com/paper/2007.14052/) (2020)

## Built on by (most cited first, 8 of 8)

- [Surrogate Modeling and Explainable Artificial Intelligence for Complex Systems: A Workflow for Automated Simulation Exploration](https://mlsanity.com/paper/2510.16742/) (2025)
- [SMT-EX: An Explainable Surrogate Modeling Toolbox for Mixed-Variables Design Exploration](https://mlsanity.com/paper/2503.19496/) (2025)
- [Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design](https://mlsanity.com/paper/2506.22621/) (2025)
- [Bayesian Optimization of a Lightweight and Accurate Neural Network for Aerodynamic Performance Prediction](https://mlsanity.com/paper/2503.19479/) (2025)
- [High-Dimensional Bayesian Optimization Using Both Random and Supervised Embeddings](https://mlsanity.com/paper/2502.00854/) (2025)
- [System-of-systems Modeling and Optimization: An Integrated Framework for Intermodal Mobility](https://mlsanity.com/paper/2507.08715/) (2025)
- [Efficient multidisciplinary design via Bayesian optimization](https://mlsanity.com/paper/2607.22560/) (2026)
- [Hierarchical Bayesian optimization of an aircraft-based multi-agent system-of-systems](https://mlsanity.com/paper/2609.22130/) (2026)

## Abstract (arXiv)

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.