Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms

verfasst von

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.

Organisationseinheit(en)

Institut für Risiko und Zuverlässigkeit

Externe Organisation(en)

Northwestern Polytechnical University
The University of Liverpool
Tongji University

Typ

Artikel

Journal

Engineering Computations (Swansea, Wales)

Band

41

Seiten

413-437

Anzahl der Seiten

25

ISSN

0264-4401

Publikationsdatum

16.04.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Software, Ingenieurwesen (insg.), Angewandte Informatik, Theoretische Informatik und Mathematik

Elektronische Version(en)

https://doi.org/10.1108/EC-12-2023-0957 (Zugang: Geschlossen)