# What Makes an Effective Scalarising Function for Multi-Objective Bayesian Optimisation?

arXiv: https://arxiv.org/abs/2104.04790 · HTML: https://mlsanity.com/paper/2104.04790/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 41 references that are in the map.
- First posted on arXiv 10 Apr 2021.

## Builds on (most cited first, 5 of 5)

- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms](https://mlsanity.com/paper/1904.12672/) (2019)
- [Scalarizing Functions in Bayesian Multiobjective Optimization](https://mlsanity.com/paper/1904.05760/) (2019)
- [Dynamic Control of Explore/Exploit Trade-Off In Bayesian Optimization](https://mlsanity.com/paper/1807.01279/) (2018)
- [Uncrowded Hypervolume-based Multi-objective Optimization with Gene-pool Optimal Mixing](https://mlsanity.com/paper/2004.05068/) (2020)

## Abstract (arXiv)

Performing multi-objective Bayesian optimisation by scalarising the objectives avoids the computation of expensive multi-dimensional integral-based acquisition functions, instead of allowing one-dimensional standard acquisition functionstextemdash such as Expected Improvementtextemdash to be applied. Here, two infill criteria based on hypervolume improvementtextemdash one recently introduced and one noveltextemdash are compared with the multi-surrogate Expected Hypervolume Improvement. The reasons for the disparities in these methods' effectiveness in maximising the hypervolume of the acquired Pareto Front are investigated. In addition, the effect of the surrogate model mean function on exploration and exploitation is examined: careful choice of data normalisation is shown to be preferable to the exploration parameter commonly used with the Expected Improvement acquisition function. Finally, the effectiveness of all the methodological improvements defined here is demonstrated on a real-world problem: the optimisation of a wind turbine blade aerofoil for both aerodynamic performance and structural stiffness. With effective scalarisation, Bayesian optimisation finds a large number of new aerofoil shapes that strongly dominate standard designs.