# Bayesian Optimization For Multi-Objective Mixed-Variable Problems

arXiv: https://arxiv.org/abs/2201.12767 · HTML: https://mlsanity.com/paper/2201.12767/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 72 references that are in the map.
- First posted on arXiv 30 Jan 2022.

## Builds on (most cited first, 21 of 21)

- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [Combinatorial Bayesian Optimization using the Graph Cartesian Product](https://mlsanity.com/paper/1902.00448/) (2019)
- [ChemBO: Bayesian Optimization of Small Organic Molecules with Synthesizable Recommendations](https://mlsanity.com/paper/1908.01425/) (2019)
- [Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1706.03673/) (2017)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (2019)
- [BOCK : Bayesian Optimization with Cylindrical Kernels](https://mlsanity.com/paper/1806.01619/) (2018)
- [Bayesian Optimization of Combinatorial Structures](https://mlsanity.com/paper/1806.08838/) (2018)
- [Multi-objective Bayesian Optimization using Pareto-frontier Entropy](https://mlsanity.com/paper/1906.00127/) (2019)
- [Bayesian Optimisation over Multiple Continuous and Categorical Inputs](https://mlsanity.com/paper/1906.08878/) (2019)
- [Bayesian Optimization in AlphaGo](https://mlsanity.com/paper/1812.06855/) (2018)
- [Combining Latent Space and Structured Kernels for Bayesian Optimization over Combinatorial Spaces](https://mlsanity.com/paper/2111.01186/) (2021)
- [Mixed-Variable Bayesian Optimization](https://mlsanity.com/paper/1907.01329/) (2019)
- [Bayesian Optimization for Categorical and Category-Specific Continuous Inputs](https://mlsanity.com/paper/1911.12473/) (2019)
- [BORE: Bayesian Optimization by Density-Ratio Estimation](https://mlsanity.com/paper/2102.09009/) (2021)
- [Bayesian Optimization over Hybrid Spaces](https://mlsanity.com/paper/2106.04682/) (2021)
- [Bayesian Optimization over Permutation Spaces](https://mlsanity.com/paper/2112.01049/) (2021)
- [Efficient global optimization of constrained mixed variable problems](https://mlsanity.com/paper/1806.03975/) (2018)
- [Mixed Variable Bayesian Optimization with Frequency Modulated Kernels](https://mlsanity.com/paper/2102.12792/) (2021)

## Built on by (most cited first, 5 of 5)

- [Forecasting steam mass flow in power plants using the parallel hybrid network](https://mlsanity.com/paper/2307.09483/) (2023)
- [Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design](https://mlsanity.com/paper/2506.22621/) (2025)
- [Optimization of the Shape of a Hydrokinetic Turbine's Draft Tube and Hub Assembly Using Design-by-Morphing with Bayesian Optimization](https://mlsanity.com/paper/2207.11451/) (2022)
- [Portfolio-Based Constrained Multi-Objective Bayesian Optimization for Materials Design](https://mlsanity.com/paper/2609.19550/) (2026)
- [Simple Extensions of Single-Objective Acquisition Functions and Hedge Strategies for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2609.31940/) (2026)

## Abstract (arXiv)

Optimizing multiple, non-preferential objectives for mixed-variable, expensive black-box problems is important in many areas of engineering and science. The expensive, noisy, black-box nature of these problems makes them ideal candidates for Bayesian optimization (BO). Mixed-variable and multi-objective problems, however, are a challenge due to BO's underlying smooth Gaussian process surrogate model. Current multi-objective BO algorithms cannot deal with mixed-variable problems. We present MixMOBO, the first mixed-variable, multi-objective Bayesian optimization framework for such problems. Using MixMOBO, optimal Pareto-fronts for multi-objective, mixed-variable design spaces can be found efficiently while ensuring diverse solutions. The method is sufficiently flexible to incorporate different kernels and acquisition functions, including those that were developed for mixed-variable or multi-objective problems by other authors. We also present HedgeMO, a modified Hedge strategy that uses a portfolio of acquisition functions for multi-objective problems. We present a new acquisition function, SMC. Our results show that MixMOBO performs well against other mixed-variable algorithms on synthetic problems. We apply MixMOBO to the real-world design of an architected material and show that our optimal design, which was experimentally fabricated and validated, has a normalized strain energy density 104 times greater than existing structures.