Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms

PurposeBayesian 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 develope...

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Veröffentlicht in:Engineering computations Jg. 41; H. 2; S. 413 - 437
Hauptverfasser: Hong, Fangqi, Wei, Pengfei, Beer, Michael
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Bradford Emerald Publishing Limited 16.04.2024
Emerald Group Publishing Limited
Schlagworte:
Algorithms
Approximation
Bayesian analysis
Cluster analysis
Clustering
Design of experiments
Engineering
Experiments
Integrals
Maxima
Numerical analysis
Optimization
Optimization algorithms
Partial differential equations
Probability distribution
Stochastic models
Vector quantization
Adaptive experiment design
Parallel computation
Acquisition function
Multimodal optimization
Bayesian cubature
ISSN:0264-4401, 1758-7077
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Zusammenfassung:PurposeBayesian 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/approachBy 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.FindingsThe 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/valueMultimodal 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.
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ISSN:0264-4401
1758-7077
DOI:10.1108/EC-12-2023-0957