# Bayesian optimization for mixed variables using an adaptive dimension reduction process: applications to aircraft design

arXiv: https://arxiv.org/abs/2504.08682 · HTML: https://mlsanity.com/paper/2504.08682/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 62 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Builds on (most cited first, 17 of 17)

- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Combinatorial Bayesian Optimization using the Graph Cartesian Product](https://mlsanity.com/paper/1902.00448/) (2019)
- [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)
- [Bayesian Optimization for Categorical and Category-Specific Continuous Inputs](https://mlsanity.com/paper/1911.12473/) (2019)
- [Mercer Features for Efficient Combinatorial Bayesian Optimization](https://mlsanity.com/paper/2012.07762/) (2020)
- [On the choice of the low-dimensional domain for global optimization via random embeddings](https://mlsanity.com/paper/1704.05318/) (2017)
- [Group kernels for Gaussian process metamodels with categorical inputs](https://mlsanity.com/paper/1802.02368/) (2018)
- [High-Dimensional Bayesian Optimization via Nested Riemannian Manifolds](https://mlsanity.com/paper/2010.10904/) (2020)
- [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)
- [An efficient application of Bayesian optimization to an industrial MDO framework for aircraft design](https://mlsanity.com/paper/2006.08434/) (2020)
- [Revisiting Bayesian Optimization in the light of the COCO benchmark](https://mlsanity.com/paper/2103.16649/) (2021)
- [Continuous surrogate-based optimization algorithms are well-suited for expensive discrete problems](https://mlsanity.com/paper/2011.03431/) (2020)

## Built on by (most cited first, 7 of 7)

- [Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design](https://mlsanity.com/paper/2506.22621/) (2025)
- [System-of-systems Modeling and Optimization: An Integrated Framework for Intermodal Mobility](https://mlsanity.com/paper/2507.08715/) (2025)
- [A reproducible comparative study of categorical kernels for Gaussian process regression, with new clustering-based nested kernels](https://mlsanity.com/paper/2510.01840/) (2025)
- [Transfer Learning in Bayesian Optimization for Aircraft Design](https://mlsanity.com/paper/2603.28999/) (2026)
- [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)
- [Energy-aware frugal Bayesian optimization](https://mlsanity.com/paper/2609.31638/) (2026)

## Abstract (arXiv)

Multidisciplinary design optimization 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 large number of design variables. Recently, there has been a growing interest in mixed variables constrained Bayesian optimization but most existing approaches severely increase the number of the hyperparameters related to the surrogate model. In this paper, we address this issue by constructing surrogate models using less hyperparameters. The reduction process is based on the partial least squares method. An adaptive procedure for choosing the number of hyperparameters is proposed. The performance of the proposed approach is confirmed on analytical tests as well as two real applications related to aircraft design. A significant improvement is obtained compared to genetic algorithms.