# Bayesian optimization of variable-size design space problems

arXiv: https://arxiv.org/abs/2003.03300 · HTML: https://mlsanity.com/paper/2003.03300/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2020.

## Built on by (most cited first, 10 of 10)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterization](https://mlsanity.com/paper/2210.10199/) (2022)
- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [A distance for mixed-variable and hierarchical domains with meta variables](https://mlsanity.com/paper/2405.13073/) (2024)
- [Fully Bayesian inference for latent variable Gaussian process models](https://mlsanity.com/paper/2211.02218/) (2022)
- [Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design](https://mlsanity.com/paper/2506.22621/) (2025)
- [Surrogate-based optimization of system architectures subject to hidden constraints](https://mlsanity.com/paper/2504.08721/) (2025)
- [Learning non-stationary and discontinuous functions using clustering, classification and Gaussian process modelling](https://mlsanity.com/paper/2211.16909/) (2022)
- [Multi-objective robust optimization using adaptive surrogate models for problems with mixed continuous-categorical parameters](https://mlsanity.com/paper/2203.01996/) (2022)
- [Flow Battery Manifold Design with Heterogeneous Inputs Through Generative Adversarial Neural Networks](https://mlsanity.com/paper/2508.08863/) (2025)

## Abstract (arXiv)

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables. Additionally, complex system design problems occasionally present a variable-size design space. This results in an optimization problem for which the search space varies dynamically (with respect to both number and type of variables) along the optimization process as a function of the values of specific discrete decision variables. Similarly, the number and type of constraints can vary as well. In this paper, two alternative Bayesian Optimization-based approaches are proposed in order to solve this type of optimization problems. The first one consists in a budget allocation strategy allowing to focus the computational budget on the most promising design sub-spaces. The second approach, instead, is based on the definition of a kernel function allowing to compute the covariance between samples characterized by partially different sets of variables. The results obtained on analytical and engineering related test-cases show a faster and more consistent convergence of both proposed methods with respect to the standard approaches.