Details
| Original language | English |
|---|---|
| Pages (from-to) | 413-437 |
| Number of pages | 25 |
| Journal | Engineering Computations (Swansea, Wales) |
| Volume | 41 |
| Issue number | 2 |
| Early online date | 5 Apr 2024 |
| Publication status | Published - 16 Apr 2024 |
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
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Engineering(all)
- Computer Science(all)
- Computer Science Applications
- Computer Science(all)
- Computational Theory and Mathematics
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In: Engineering Computations (Swansea, Wales), Vol. 41, No. 2, 16.04.2024, p. 413-437.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms
AU - Hong, Fangqi
AU - Wei, Pengfei
AU - Beer, Michael
N1 - 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).
PY - 2024/4/16
Y1 - 2024/4/16
N2 - 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.
AB - 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.
KW - Acquisition function
KW - Adaptive experiment design
KW - Bayesian cubature
KW - Multimodal optimization
KW - Parallel computation
UR - http://www.scopus.com/inward/record.url?scp=85189924722&partnerID=8YFLogxK
U2 - 10.1108/EC-12-2023-0957
DO - 10.1108/EC-12-2023-0957
M3 - Article
AN - SCOPUS:85189924722
VL - 41
SP - 413
EP - 437
JO - Engineering Computations (Swansea, Wales)
JF - Engineering Computations (Swansea, Wales)
SN - 0264-4401
IS - 2
ER -