# Scalarizing Functions in Bayesian Multiobjective Optimization

arXiv: https://arxiv.org/abs/1904.05760 · HTML: https://mlsanity.com/paper/1904.05760/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2019.

## Built on by (most cited first, 15 of 15)

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- [What Makes an Effective Scalarising Function for Multi-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2104.04790/) (2021)
- [Surrogate-Assisted Reference Vector Adaptation to Various Pareto Front Shapes for Many-Objective Bayesian Optimization](https://mlsanity.com/paper/2110.04689/) (2021)
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- [Combinatorial Bandit Bayesian Optimization for Tensor Outputs](https://mlsanity.com/paper/2602.00640/) (2026)
- [Mutual Information Collapse Explains Disentanglement Failure in β-VAEs](https://mlsanity.com/paper/2602.09277/) (2026)
- [Accelerating Multi-Objective Bayesian Optimisation via Predictive-Gradient Catalysts](https://mlsanity.com/paper/2606.06984/) (2026)
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## Abstract (arXiv)

Scalarizing functions have been widely used to convert a multiobjective optimization problem into a single objective optimization problem. However, their use in solving (computationally) expensive multi- and many-objective optimization problems in Bayesian multiobjective optimization is scarce. Scalarizing functions can play a crucial role on the quality and number of evaluations required when doing the optimization. In this article, we study and review 15 different scalarizing functions in the framework of Bayesian multiobjective optimization and build Gaussian process models (as surrogates, metamodels or emulators) on them. We use expected improvement as infill criterion (or acquisition function) to update the models. In particular, we compare different scalarizing functions and analyze their performance on several benchmark problems with different number of objectives to be optimized. The review and experiments on different functions provide useful insights when using and selecting a scalarizing function when using a Bayesian multiobjective optimization method.