Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms

Hong, Fangqi, Wei, Pengfei and Beer, Michael ORCID: 0000-0002-0611-0345 (2024) Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms. Engineering Computations, 41 (2). pp. 413-437.

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Official URL: http://dx.doi.org/10.1108/ec-12-2023-0957

Abstract

<jats:sec><jats:title content-type="abstract-subheading">Purpose</jats:title><jats:p>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.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Design/methodology/approach</jats:title><jats:p>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.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Findings</jats:title><jats:p>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.</jats:p></jats:sec><jats:sec><jats:title content-type="abstract-subheading">Originality/value</jats:title><jats:p>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.</jats:p></jats:sec>

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	22 Apr 2024 07:39
Last Modified:	23 Apr 2024 08:56
DOI:	10.1108/ec-12-2023-0957
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3180469