# Efficient global optimization of constrained mixed variable problems

arXiv: https://arxiv.org/abs/1806.03975 · HTML: https://mlsanity.com/paper/1806.03975/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2018.

## Built on by (most cited first, 11 of 11)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (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 mixed-categorical correlation kernel for Gaussian process](https://mlsanity.com/paper/2211.08262/) (2022)
- [High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft](https://mlsanity.com/paper/2311.06130/) (2023)
- [Bayesian optimization for mixed variables using an adaptive dimension reduction process: applications to aircraft design](https://mlsanity.com/paper/2504.08682/) (2025)
- [A comparison of mixed-variables Bayesian optimization approaches](https://mlsanity.com/paper/2111.01533/) (2021)
- [Bayesian Optimization For Multi-Objective Mixed-Variable Problems](https://mlsanity.com/paper/2201.12767/) (2022)
- [A distance for mixed-variable and hierarchical domains with meta variables](https://mlsanity.com/paper/2405.13073/) (2024)
- [SMT-EX: An Explainable Surrogate Modeling Toolbox for Mixed-Variables Design Exploration](https://mlsanity.com/paper/2503.19496/) (2025)
- [A sampling criterion for constrained Bayesian optimization with uncertainties](https://mlsanity.com/paper/2103.05706/) (2021)
- [Bayesian Quality-Diversity approaches for constrained optimization problems with mixed continuous, discrete and categorical variables](https://mlsanity.com/paper/2310.05955/) (2023)

## Abstract (arXiv)

Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In this paper, several variants of the Efficient Global Optimization algorithm for costly constrained problems depending simultaneously on continuous decision variables as well as on quantitative and/or qualitative discrete design parameters are proposed. The adaptation that is considered is based on a redefinition of the Gaussian Process kernel as a product between the standard continuous kernel and a second kernel representing the covariance between the discrete variable values. Several parameterizations of this discrete kernel, with their respective strengths and weaknesses, are discussed in this paper. The novel algorithms are tested on a number of analytical test-cases and an aerospace related design problem, and it is shown that they require fewer function evaluations in order to converge towards the neighborhoods of the problem optima when compared to more commonly used optimization algorithms.