Bifidelity Surrogate Modelling: Showcasing the Need for New Test Instances

Abstract

In recent years, multifidelity expensive black-box (Mf-EBB) methods have received increasing attention due to their strong applicability to industrial design problems. The challenge, however, is that knowledge of the relationship between decisions and objective values is limited to a small set of sample observations of variable quality. In the field of Mf-EBB, a problem instance consists of an expensive yet accurate source of information, and one or more cheap yet less accurate sources of information. The field aims to provide techniques either to accurately explain how decisions affect design outcome, or to find the best decisions to optimise design outcomes. Many techniques that use surrogate models have been developed to provide solutions to both aims. Only in recent years, however, have researchers begun to explore the conditions under which these new techniques are reliable, often focusing on problems with a single low-fidelity function, known as bifidelity expensive black-box (Bf-EBB) problems. This study extends the existing Bf-EBB test instances found in the literature, as well as the features used to determine when the low-fidelity information source should be used. A literature test suite is constructed and augmented with new instances to demonstrate the potentially misleading results that could be reached using only the instances currently found in the literature, and to expose the criticality of a more heterogeneous test suite for algorithm assessment. Addressing the shortcomings of the existing literature, a new set of features is presented, as well as a new instance creation procedure, and a study of their impact on algorithm assessment is conducted. The low-fidelity information source is shown to be valuable if it is often locally accurate, even when its overall accuracy is relatively low. This contradicts the existing literature guidelines, which indicate the low-fidelity information is only useful if it has a high overall accuracy. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms – Continuous. Funding: This work was supported by Australian Research Council [Grant IC200100009] for the ARC Training Centre in Optimisation Technologies, Integrated Methodologies and Applications (OPTIMA), and the University of Melbourne Research Computing Services and Petascale Campus Initiative. N. Andrés-Thió is also supported by a Research Training Program scholarship from the University of Melbourne. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1217 ] or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at [ http://dx.doi.org/10.5281/zenodo.6578060 ].