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Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature

Alma Rahat Orcid Logo, Tinkle Chugh Orcid Logo, Jonathan Fieldsend Orcid Logo, Richard Allmendinger Orcid Logo, Kaisa Miettinen Orcid Logo

Lecture Notes in Computer Science, Volume: 13398, Pages: 90 - 103

Swansea University Author: Alma Rahat Orcid Logo

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DOI (Published version): 10.1007/978-3-031-14714-2_7

Abstract

Many methods for performing multi-objective optimisation of computationally expensive problems have been proposed recently. Typically, a probabilistic surrogate for each objective is constructed from an initial dataset. The surrogates can then be used to produce predictive densities in the objective...

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Published in: Lecture Notes in Computer Science
ISBN: 9783031147135 9783031147142
ISSN: 0302-9743 1611-3349
Published: Cham Springer International Publishing 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa60513
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Abstract: Many methods for performing multi-objective optimisation of computationally expensive problems have been proposed recently. Typically, a probabilistic surrogate for each objective is constructed from an initial dataset. The surrogates can then be used to produce predictive densities in the objective space for any solution. Using the predictive densities, we can compute the expected hypervolume improvement (EHVI) due to a solution. Maximising the EHVI, we can locate the most promising solution that may be expensively evaluated next. There are closed-form expressions for computing the EHVI, integrating over the multivariate predictive densities. However, they require partitioning of the objective space, which can be prohibitively expensive for more than three objectives. Furthermore, there are no closed-form expressions for a problem where the predictive densities are dependent, capturing the correlations between objectives. Monte Carlo approximation is used instead in such cases, which is not cheap. Hence, the need to develop new accurate but cheaper approximation methods remains. Here we investigate an alternative approach toward approximating the EHVI using Gauss-Hermite quadrature. We show that it can be an accurate alternative to Monte Carlo for both independent and correlated predictive densities with statistically significant rank correlations for a range of popular test problems.
Item Description: PPSN 2022; Parallel Problem Solving From Nature, 17th International Conference, September 10-14th 2022, Dortmund, Germany.
Keywords: Gauss-Hermite, Expected hypervolume improvement, Bayesian optimisation, Multi-objective optimisation, Correlated objectives
College: Faculty of Science and Engineering
Funders: This work is a part of the thematic research area Decision Analytics Utilizing Causal Models and Multiobjective Optimization (DEMO, jyu.fi/demo) at the University of Jyvaskyla. Dr. Rahat was supported by the Engineering and Physical Research Council [grant number EP/W01226X/1].
Start Page: 90
End Page: 103

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