Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms

authored by: Fangqi Hong, Pengfei Wei, Michael Beer
Abstract: Purpose: Bayesian cubature (BC) has emerged to be one of most competitive approach for estimating the multi-dimensional integral especially when the integrand is expensive to evaluate, and alternative acquisition functions, such as the Posterior Variance Contribution (PVC) function, have been developed for adaptive experiment design of the integration points. However, those sequential design strategies also prevent BC from being implemented in a parallel scheme. Therefore, this paper aims at developing a parallelized adaptive BC method to further improve the computational efficiency. Design/methodology/approach: By theoretically examining the multimodal behavior of the PVC function, it is concluded that the multiple local maxima all have important contribution to the integration accuracy as can be selected as design points, providing a practical way for parallelization of the adaptive BC. Inspired by the above finding, four multimodal optimization algorithms, including one newly developed in this work, are then introduced for finding multiple local maxima of the PVC function in one run, and further for parallel implementation of the adaptive BC. Findings: The superiority of the parallel schemes and the performance of the four multimodal optimization algorithms are then demonstrated and compared with the k-means clustering method by using two numerical benchmarks and two engineering examples. Originality/value: Multimodal behavior of acquisition function for BC is comprehensively investigated. All the local maxima of the acquisition function contribute to adaptive BC accuracy. Parallelization of adaptive BC is realized with four multimodal optimization methods.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): Northwestern Polytechnical University
University of Liverpool
Tongji University
Type: Article
Journal: Engineering Computations (Swansea, Wales)
Volume: 41
Pages: 413-437
No. of pages: 25
ISSN: 0264-4401
Publication date: 16.04.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Software, General Engineering, Computer Science Applications, Computational Theory and Mathematics
Electronic version(s): https://doi.org/10.1108/EC-12-2023-0957 (Access: Closed)

BibTeX

@article{89ba355b8dcd4fe980401c49c0f2bcae,
title = "Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms",
abstract = "Purpose: Bayesian cubature (BC) has emerged to be one of most competitive approach for estimating the multi-dimensional integral especially when the integrand is expensive to evaluate, and alternative acquisition functions, such as the Posterior Variance Contribution (PVC) function, have been developed for adaptive experiment design of the integration points. However, those sequential design strategies also prevent BC from being implemented in a parallel scheme. Therefore, this paper aims at developing a parallelized adaptive BC method to further improve the computational efficiency. Design/methodology/approach: By theoretically examining the multimodal behavior of the PVC function, it is concluded that the multiple local maxima all have important contribution to the integration accuracy as can be selected as design points, providing a practical way for parallelization of the adaptive BC. Inspired by the above finding, four multimodal optimization algorithms, including one newly developed in this work, are then introduced for finding multiple local maxima of the PVC function in one run, and further for parallel implementation of the adaptive BC. Findings: The superiority of the parallel schemes and the performance of the four multimodal optimization algorithms are then demonstrated and compared with the k-means clustering method by using two numerical benchmarks and two engineering examples. Originality/value: Multimodal behavior of acquisition function for BC is comprehensively investigated. All the local maxima of the acquisition function contribute to adaptive BC accuracy. Parallelization of adaptive BC is realized with four multimodal optimization methods.",
keywords = "Acquisition function, Adaptive experiment design, Bayesian cubature, Multimodal optimization, Parallel computation",
author = "Fangqi Hong and Pengfei Wei and Michael Beer",
note = "This work is supported by the National Natural Science Foundation of China under grant number 72171194, and the Sino-German Mobility Programme under grant number M-0175 (2021–2024) and the National Science and Technology Major Project (Project No.: J2019-V-0016-0111).",
year = "2024",
month = apr,
day = "16",
doi = "10.1108/EC-12-2023-0957",
language = "English",
volume = "41",
pages = "413--437",
journal = "Engineering Computations (Swansea, Wales)",
issn = "0264-4401",
publisher = "Emerald Group Publishing Ltd.",
number = "2",
}