The Effect of Multi-Additional Sampling for Multi-Fidelity Efficient Global Optimization

Atthaphon Ariyarit,Sujin Bureerat,Tharathep Phiboon,Masahiro Kanazaki

doi:10.3390/sym12091499

Atthaphon Ariyarit, Sujin Bureerat + Show 2 more

Open Access

https://doi.org/10.3390/sym12091499

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Abstract

Powerful computer-aided design tools are presently vital for engineering product development. Efficient global optimization (EGO) is one of the most popular methods for design of a high computational cost problem. The original EGO is proposed for only one additional sample point. In this work, parallel computing is applied to the original EGO process via a multi-additional sampling technique. The weak point of the multi-additional sampling is it has slower convergence rate when compared with the original EGO. This paper applies the multi-fidelity technique to the multi-additional EGO process to see the effect of the number of multi-additional sampling points and the converge rate. A co-kriging method and a hybrid RBF/Kriging surrogate model are selected for the surrogate model in the EGO process to show the advantage of the multi-additional EGO process compared with the single-fidelity Kriging surrogate model. In the experiment, single-additional sampling points and two to four number of multi-additional sampling per iteration are tested with symmetry and asymmetry mathematical test functions. The results show the hybrid RBF/Kriging surrogate model can obtain the similar optimal points when using the multi-additional sampling EGO.

Highlights

Computer-aided optimization is one of the most important computer-aided design tools for product development and improvement
The Kriging surrogate model results show that the accuracy of this surrogate model is slightly increased when using higher multi-additional sampling, but the accuracy of the Kriging model is still less than the accuracy of the Co-Kriging and radial basis function (RBF)/Kriging multi-fidelity surrogate models
This study investigated the effect of multi-fidelity technique to the multi-additional Efficient global optimization (EGO) process

Summary

Introduction

Computer-aided optimization is one of the most important computer-aided design tools for product development and improvement. The optimization design for expensive function was carried out using a combination of global optimization techniques. Due to high-cost computation function, a surrogate model and an optimization technique are combined to increase the efficiency of the optimization algorithm. One of the popular methods that combined the surrogate model and the optimization technique to solved an expensive function is an efficient global optimization (EGO) [7] because it can reduce the computational cost for an optimization process. The EGO process starts with generating an initial set of sampling points. The objective of this process is to increase the diversity of the sampling points. The most popular method for generating the initial sampling is the Latin Hypercube Sampling (LHS) [8].

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