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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

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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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spelling 2022-11-16T17:41:54.7390658 v2 60513 2022-07-15 Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature 6206f027aca1e3a5ff6b8cd224248bc2 0000-0002-5023-1371 Alma Rahat Alma Rahat true false 2022-07-15 SCS 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. Conference Paper/Proceeding/Abstract Lecture Notes in Computer Science 13398 90 103 Springer International Publishing Cham 9783031147135 9783031147142 0302-9743 1611-3349 Gauss-Hermite, Expected hypervolume improvement, Bayesian optimisation, Multi-objective optimisation, Correlated objectives 14 8 2022 2022-08-14 10.1007/978-3-031-14714-2_7 PPSN 2022; Parallel Problem Solving From Nature, 17th International Conference, September 10-14th 2022, Dortmund, Germany. COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University Other 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]. 2022-11-16T17:41:54.7390658 2022-07-15T21:04:03.2421727 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Alma Rahat 0000-0002-5023-1371 1 Tinkle Chugh 0000-0001-5123-8148 2 Jonathan Fieldsend 0000-0002-0683-2583 3 Richard Allmendinger 0000-0003-1236-3143 4 Kaisa Miettinen 0000-0003-1013-4689 5 Under embargo Under embargo 2022-08-04T14:24:28.0686873 Output 684020 application/pdf Accepted Manuscript true 2023-08-14T00:00:00.0000000 true eng
title Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature
spellingShingle Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature
Alma Rahat
title_short Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature
title_full Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature
title_fullStr Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature
title_full_unstemmed Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature
title_sort Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature
author_id_str_mv 6206f027aca1e3a5ff6b8cd224248bc2
author_id_fullname_str_mv 6206f027aca1e3a5ff6b8cd224248bc2_***_Alma Rahat
author Alma Rahat
author2 Alma Rahat
Tinkle Chugh
Jonathan Fieldsend
Richard Allmendinger
Kaisa Miettinen
format Conference Paper/Proceeding/Abstract
container_title Lecture Notes in Computer Science
container_volume 13398
container_start_page 90
publishDate 2022
institution Swansea University
isbn 9783031147135
9783031147142
issn 0302-9743
1611-3349
doi_str_mv 10.1007/978-3-031-14714-2_7
publisher Springer International Publishing
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
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description 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.
published_date 2022-08-14T04:18:41Z
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