Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties
Abstract
The problem of multiobjective optimization under uncertainties is often approached by taking the expectation of each objective. In this work, we propose instead to formulate this as a Bayesian decision problem and to rely on the expected value of the hypervolume, which is to be maximized with respect to a finite set of input points. We show that this can be performed using methods based on gradients in a stochastic optimization framework, provided that care is taken with respect to dominated points. Moreover, in the absence of readily available differentiable code, we propose to use Gaussian Processes as differentiable surrogate models, in order to perform the optimization. An additional contribution in this work are some active learning strategies, through acquisition functions which helps construct a surrogate model well-designed for the multiobjective optimization problem at stake. These strategies are compared on simple analytical problems to assess their performances.
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BibTeX
@misc{trappler2026expected,
title = {{Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties}},
author = {Victor Trappler},
howpublished = {HAL},
year = {2026},
month = sep,
eprint = {2609.19858},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05720605v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties
AU - Victor Trappler
PY - 2026
DA - 2026/09/16
PB - HAL
UR - https://hal.science/hal-05720605v2
AB - The problem of multiobjective optimization under uncertainties is often approached by taking the expectation of each objective. In this work, we propose instead to formulate this as a Bayesian decision problem and to rely on the expected value of the hypervolume, which is to be maximized with respect to a finite set of input points. We show that this can be performed using methods based on gradients in a stochastic optimization framework, provided that care is taken with respect to dominated points. Moreover, in the absence of readily available differentiable code, we propose to use Gaussian Processes as differentiable surrogate models, in order to perform the optimization. An additional contribution in this work are some active learning strategies, through acquisition functions which helps construct a surrogate model well-designed for the multiobjective optimization problem at stake. These strategies are compared on simple analytical problems to assess their performances.
ER -